diff --git "a/parse/train/BkglSTNFDB/BkglSTNFDB_model.json" "b/parse/train/BkglSTNFDB/BkglSTNFDB_model.json" new file mode 100644--- /dev/null +++ "b/parse/train/BkglSTNFDB/BkglSTNFDB_model.json" @@ -0,0 +1,32281 @@ +[ + { + "layout_dets": [ + { + "category_id": 1, + "poly": [ + 398, + 993, + 1304, + 993, + 1304, + 1321, + 398, + 1321 + ], + "score": 0.981 + }, + { + "category_id": 1, + "poly": [ + 297, + 1466, + 1404, + 1466, + 1404, + 1712, + 297, + 1712 + ], + "score": 0.979 + }, + { + "category_id": 1, + "poly": [ + 298, + 1727, + 1405, + 1727, + 1405, + 1972, + 298, + 1972 + ], + "score": 0.975 + }, + { + "category_id": 1, + "poly": [ + 314, + 545, + 1029, + 545, + 1029, + 668, + 314, + 668 + ], + "score": 0.964 + }, + { + "category_id": 0, + "poly": [ + 300, + 219, + 1400, + 219, + 1400, + 323, + 300, + 323 + ], + "score": 0.963 + }, + { + "category_id": 1, + "poly": [ + 313, + 715, + 1024, + 715, + 1024, + 838, + 313, + 838 + ], + "score": 0.942 + }, + { + "category_id": 2, + "poly": [ + 332, + 2006, + 730, + 2006, + 730, + 2034, + 332, + 2034 + ], + "score": 0.914 + }, + { + "category_id": 0, + "poly": [ + 302, + 1392, + 574, + 1392, + 574, + 1427, + 302, + 1427 + ], + "score": 0.905 + }, + { + "category_id": 1, + "poly": [ + 313, + 374, + 946, + 374, + 946, + 499, + 313, + 499 + ], + "score": 0.871 + }, + { + "category_id": 2, + "poly": [ + 299, + 75, + 817, + 75, + 817, + 105, + 299, + 105 + ], + "score": 0.87 + }, + { + "category_id": 0, + "poly": [ + 773, + 919, + 927, + 919, + 927, + 952, + 773, + 952 + ], + "score": 0.836 + }, + { + "category_id": 2, + "poly": [ + 840, + 2088, + 856, + 2088, + 856, + 2112, + 840, + 2112 + ], + "score": 0.737 + }, + { + "category_id": 0, + "poly": [ + 315, + 717, + 461, + 717, + 461, + 746, + 315, + 746 + ], + "score": 0.162 + }, + { + "category_id": 13, + "poly": [ + 759, + 1177, + 899, + 1177, + 899, + 1222, + 759, + 1222 + ], + "score": 0.94, + "latex": "\\begin{array} { r } { \\tilde { O } \\big ( \\frac { S A } { \\epsilon ^ { 2 } ( 1 - \\gamma ) ^ { 7 } } \\big ) } \\end{array}" + }, + { + "category_id": 13, + "poly": [ + 575, + 1218, + 715, + 1218, + 715, + 1263, + 575, + 1263 + ], + "score": 0.93, + "latex": "\\begin{array} { r } { \\tilde { O } \\big ( \\frac { S A } { \\epsilon ^ { 4 } ( 1 - \\gamma ) ^ { 8 } } \\big ) } \\end{array}" + }, + { + "category_id": 13, + "poly": [ + 738, + 1820, + 764, + 1820, + 764, + 1850, + 738, + 1850 + ], + "score": 0.82, + "latex": "Q" + }, + { + "category_id": 13, + "poly": [ + 1141, + 1260, + 1163, + 1260, + 1163, + 1288, + 1141, + 1288 + ], + "score": 0.8, + "latex": "S" + }, + { + "category_id": 13, + "poly": [ + 822, + 1564, + 838, + 1564, + 838, + 1587, + 822, + 1587 + ], + "score": 0.75, + "latex": "r" + }, + { + "category_id": 13, + "poly": [ + 1007, + 1266, + 1022, + 1266, + 1022, + 1287, + 1007, + 1287 + ], + "score": 0.73, + "latex": "\\epsilon" + }, + { + "category_id": 13, + "poly": [ + 1213, + 1260, + 1238, + 1260, + 1238, + 1287, + 1213, + 1287 + ], + "score": 0.7, + "latex": "A" + }, + { + "category_id": 13, + "poly": [ + 615, + 1565, + 632, + 1565, + 632, + 1586, + 615, + 1586 + ], + "score": 0.7, + "latex": "a" + }, + { + "category_id": 13, + "poly": [ + 298, + 1565, + 314, + 1565, + 314, + 1586, + 298, + 1586 + ], + "score": 0.52, + "latex": "s" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 219.0, + 1405.0, + 219.0, + 1405.0, + 272.0, + 294.0, + 272.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 275.0, + 1142.0, + 275.0, + 1142.0, + 327.0, + 294.0, + 327.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 329.0, + 1998.0, + 733.0, + 1998.0, + 733.0, + 2040.0, + 329.0, + 2040.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 1388.0, + 579.0, + 1388.0, + 579.0, + 1435.0, + 294.0, + 1435.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 73.0, + 817.0, + 73.0, + 817.0, + 108.0, + 295.0, + 108.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 768.0, + 915.0, + 934.0, + 915.0, + 934.0, + 958.0, + 768.0, + 958.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 839.0, + 2087.0, + 859.0, + 2087.0, + 859.0, + 2117.0, + 839.0, + 2117.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 310.0, + 709.0, + 465.0, + 709.0, + 465.0, + 754.0, + 310.0, + 754.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 393.0, + 993.0, + 1308.0, + 993.0, + 1308.0, + 1029.0, + 393.0, + 1029.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 393.0, + 1022.0, + 1305.0, + 1022.0, + 1305.0, + 1061.0, + 393.0, + 1061.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 394.0, + 1055.0, + 1305.0, + 1055.0, + 1305.0, + 1090.0, + 394.0, + 1090.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 394.0, + 1085.0, + 1305.0, + 1085.0, + 1305.0, + 1120.0, + 394.0, + 1120.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 395.0, + 1116.0, + 1304.0, + 1116.0, + 1304.0, + 1148.0, + 395.0, + 1148.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 393.0, + 1146.0, + 1305.0, + 1146.0, + 1305.0, + 1184.0, + 393.0, + 1184.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 388.0, + 1173.0, + 758.0, + 1173.0, + 758.0, + 1231.0, + 388.0, + 1231.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 900.0, + 1173.0, + 1311.0, + 1173.0, + 1311.0, + 1231.0, + 900.0, + 1231.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 380.0, + 1202.0, + 574.0, + 1202.0, + 574.0, + 1279.0, + 380.0, + 1279.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 716.0, + 1202.0, + 1318.0, + 1202.0, + 1318.0, + 1279.0, + 716.0, + 1279.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 393.0, + 1258.0, + 1006.0, + 1258.0, + 1006.0, + 1295.0, + 393.0, + 1295.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1023.0, + 1258.0, + 1140.0, + 1258.0, + 1140.0, + 1295.0, + 1023.0, + 1295.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1164.0, + 1258.0, + 1212.0, + 1258.0, + 1212.0, + 1295.0, + 1164.0, + 1295.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1239.0, + 1258.0, + 1305.0, + 1258.0, + 1305.0, + 1295.0, + 1239.0, + 1295.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 394.0, + 1290.0, + 619.0, + 1290.0, + 619.0, + 1323.0, + 394.0, + 1323.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 1468.0, + 1404.0, + 1468.0, + 1404.0, + 1501.0, + 295.0, + 1501.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 1498.0, + 1404.0, + 1498.0, + 1404.0, + 1531.0, + 295.0, + 1531.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 1528.0, + 1406.0, + 1528.0, + 1406.0, + 1563.0, + 292.0, + 1563.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 1559.0, + 297.0, + 1559.0, + 297.0, + 1593.0, + 294.0, + 1593.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 315.0, + 1559.0, + 614.0, + 1559.0, + 614.0, + 1593.0, + 315.0, + 1593.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 633.0, + 1559.0, + 821.0, + 1559.0, + 821.0, + 1593.0, + 633.0, + 1593.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 839.0, + 1559.0, + 1407.0, + 1559.0, + 1407.0, + 1593.0, + 839.0, + 1593.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 1590.0, + 1406.0, + 1590.0, + 1406.0, + 1624.0, + 294.0, + 1624.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 1620.0, + 1406.0, + 1620.0, + 1406.0, + 1654.0, + 295.0, + 1654.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 1650.0, + 1407.0, + 1650.0, + 1407.0, + 1686.0, + 292.0, + 1686.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 1682.0, + 1044.0, + 1682.0, + 1044.0, + 1715.0, + 295.0, + 1715.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 1724.0, + 1406.0, + 1724.0, + 1406.0, + 1764.0, + 292.0, + 1764.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 1758.0, + 1405.0, + 1758.0, + 1405.0, + 1792.0, + 295.0, + 1792.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 1790.0, + 1405.0, + 1790.0, + 1405.0, + 1823.0, + 293.0, + 1823.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 1817.0, + 737.0, + 1817.0, + 737.0, + 1853.0, + 293.0, + 1853.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 765.0, + 1817.0, + 1405.0, + 1817.0, + 1405.0, + 1853.0, + 765.0, + 1853.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 1849.0, + 1405.0, + 1849.0, + 1405.0, + 1884.0, + 293.0, + 1884.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 1876.0, + 1410.0, + 1876.0, + 1410.0, + 1915.0, + 292.0, + 1915.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 1908.0, + 1409.0, + 1908.0, + 1409.0, + 1945.0, + 293.0, + 1945.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 1937.0, + 411.0, + 1937.0, + 411.0, + 1976.0, + 293.0, + 1976.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 312.0, + 545.0, + 477.0, + 545.0, + 477.0, + 580.0, + 312.0, + 580.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 311.0, + 574.0, + 1031.0, + 574.0, + 1031.0, + 610.0, + 311.0, + 610.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 310.0, + 604.0, + 521.0, + 604.0, + 521.0, + 642.0, + 310.0, + 642.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 313.0, + 637.0, + 586.0, + 637.0, + 586.0, + 672.0, + 313.0, + 672.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 310.0, + 710.0, + 465.0, + 710.0, + 465.0, + 751.0, + 310.0, + 751.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 312.0, + 745.0, + 1023.0, + 745.0, + 1023.0, + 778.0, + 312.0, + 778.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 311.0, + 772.0, + 798.0, + 772.0, + 798.0, + 811.0, + 311.0, + 811.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 311.0, + 807.0, + 670.0, + 807.0, + 670.0, + 841.0, + 311.0, + 841.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 312.0, + 373.0, + 675.0, + 373.0, + 675.0, + 411.0, + 312.0, + 411.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 310.0, + 404.0, + 890.0, + 404.0, + 890.0, + 443.0, + 310.0, + 443.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 311.0, + 436.0, + 545.0, + 436.0, + 545.0, + 471.0, + 311.0, + 471.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 314.0, + 467.0, + 948.0, + 467.0, + 948.0, + 503.0, + 314.0, + 503.0 + ], + "score": 1.0, + "text": "" + } + ], + "page_info": { + "page_no": 0, + "width": 1700, + "height": 2200 + } + }, + { + "layout_dets": [ + { + "category_id": 1, + "poly": [ + 298, + 1490, + 1404, + 1490, + 1404, + 1645, + 298, + 1645 + ], + "score": 0.979 + }, + { + "category_id": 1, + "poly": [ + 298, + 1113, + 1404, + 1113, + 1404, + 1328, + 298, + 1328 + ], + "score": 0.978 + }, + { + "category_id": 1, + "poly": [ + 298, + 935, + 1404, + 935, + 1404, + 1098, + 298, + 1098 + ], + "score": 0.978 + }, + { + "category_id": 1, + "poly": [ + 298, + 428, + 1405, + 428, + 1405, + 614, + 298, + 614 + ], + "score": 0.977 + }, + { + "category_id": 1, + "poly": [ + 298, + 229, + 1404, + 229, + 1404, + 415, + 298, + 415 + ], + "score": 0.976 + }, + { + "category_id": 1, + "poly": [ + 299, + 1343, + 1403, + 1343, + 1403, + 1476, + 299, + 1476 + ], + "score": 0.976 + }, + { + "category_id": 1, + "poly": [ + 299, + 766, + 1404, + 766, + 1404, + 920, + 299, + 920 + ], + "score": 0.976 + }, + { + "category_id": 1, + "poly": [ + 299, + 629, + 1404, + 629, + 1404, + 752, + 299, + 752 + ], + "score": 0.976 + }, + { + "category_id": 1, + "poly": [ + 299, + 1659, + 1403, + 1659, + 1403, + 1813, + 299, + 1813 + ], + "score": 0.974 + }, + { + "category_id": 1, + "poly": [ + 297, + 1971, + 1402, + 1971, + 1402, + 2035, + 297, + 2035 + ], + "score": 0.942 + }, + { + "category_id": 2, + "poly": [ + 300, + 76, + 816, + 76, + 816, + 104, + 300, + 104 + ], + "score": 0.892 + }, + { + "category_id": 0, + "poly": [ + 300, + 1886, + 551, + 1886, + 551, + 1921, + 300, + 1921 + ], + "score": 0.884 + }, + { + "category_id": 2, + "poly": [ + 841, + 2088, + 858, + 2088, + 858, + 2112, + 841, + 2112 + ], + "score": 0.7 + }, + { + "category_id": 2, + "poly": [ + 841, + 2088, + 859, + 2088, + 859, + 2112, + 841, + 2112 + ], + "score": 0.176 + }, + { + "category_id": 13, + "poly": [ + 606, + 2002, + 711, + 2002, + 711, + 2036, + 606, + 2036 + ], + "score": 0.94, + "latex": "p ( s ^ { \\prime } | s , a )" + }, + { + "category_id": 13, + "poly": [ + 599, + 969, + 739, + 969, + 739, + 1012, + 599, + 1012 + ], + "score": 0.94, + "latex": "\\begin{array} { r } { \\tilde { \\mathcal { O } } \\big ( \\frac { S A } { \\epsilon ^ { 4 } ( 1 - \\gamma ) ^ { 8 } } \\big ) } \\end{array}" + }, + { + "category_id": 13, + "poly": [ + 868, + 1376, + 1009, + 1376, + 1009, + 1419, + 868, + 1419 + ], + "score": 0.93, + "latex": "\\begin{array} { r } { \\tilde { \\mathcal { O } } \\big ( \\frac { S A } { \\epsilon ^ { 2 } ( 1 - \\gamma ) ^ { 7 } } \\big ) } \\end{array}" + }, + { + "category_id": 13, + "poly": [ + 644, + 1234, + 739, + 1234, + 739, + 1270, + 644, + 1270 + ], + "score": 0.92, + "latex": "\\Omega ( 1 / \\epsilon ^ { 3 } )" + }, + { + "category_id": 13, + "poly": [ + 1191, + 720, + 1306, + 720, + 1306, + 754, + 1191, + 754 + ], + "score": 0.92, + "latex": "1 / ( 1 - \\gamma )" + }, + { + "category_id": 13, + "poly": [ + 1013, + 1973, + 1166, + 1973, + 1166, + 2005, + 1013, + 2005 + ], + "score": 0.91, + "latex": "\\langle S , \\mathcal { A } , p , r , \\gamma \\rangle" + }, + { + "category_id": 13, + "poly": [ + 989, + 2005, + 1190, + 2005, + 1190, + 2036, + 989, + 2036 + ], + "score": 0.9, + "latex": "r : S \\times \\mathcal { A } [ 0 , 1 ]" + }, + { + "category_id": 13, + "poly": [ + 1117, + 1114, + 1160, + 1114, + 1160, + 1148, + 1117, + 1148 + ], + "score": 0.86, + "latex": "1 / \\epsilon" + }, + { + "category_id": 13, + "poly": [ + 1253, + 1974, + 1275, + 1974, + 1275, + 2000, + 1253, + 2000 + ], + "score": 0.81, + "latex": "s" + }, + { + "category_id": 13, + "poly": [ + 371, + 2004, + 395, + 2004, + 395, + 2030, + 371, + 2030 + ], + "score": 0.8, + "latex": "\\mathcal { A }" + }, + { + "category_id": 13, + "poly": [ + 1258, + 664, + 1278, + 664, + 1278, + 692, + 1258, + 692 + ], + "score": 0.8, + "latex": "\\gamma" + }, + { + "category_id": 13, + "poly": [ + 323, + 1445, + 344, + 1445, + 344, + 1473, + 323, + 1473 + ], + "score": 0.72, + "latex": "S" + }, + { + "category_id": 13, + "poly": [ + 395, + 1446, + 419, + 1446, + 419, + 1472, + 395, + 1472 + ], + "score": 0.68, + "latex": "A" + }, + { + "category_id": 13, + "poly": [ + 298, + 1451, + 312, + 1451, + 312, + 1472, + 298, + 1472 + ], + "score": 0.41, + "latex": "\\epsilon" + }, + { + "category_id": 15, + "poly": [ + 296.0, + 73.0, + 817.0, + 73.0, + 817.0, + 108.0, + 296.0, + 108.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 1883.0, + 556.0, + 1883.0, + 556.0, + 1927.0, + 292.0, + 1927.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 839.0, + 2085.0, + 862.0, + 2085.0, + 862.0, + 2120.0, + 839.0, + 2120.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 838.0, + 2085.0, + 862.0, + 2085.0, + 862.0, + 2120.0, + 838.0, + 2120.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 296.0, + 1490.0, + 1405.0, + 1490.0, + 1405.0, + 1528.0, + 296.0, + 1528.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 1520.0, + 1402.0, + 1520.0, + 1402.0, + 1557.0, + 294.0, + 1557.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 1550.0, + 1406.0, + 1550.0, + 1406.0, + 1590.0, + 293.0, + 1590.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 296.0, + 1583.0, + 1404.0, + 1583.0, + 1404.0, + 1617.0, + 296.0, + 1617.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 1611.0, + 1195.0, + 1611.0, + 1195.0, + 1650.0, + 292.0, + 1650.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 1113.0, + 1116.0, + 1113.0, + 1116.0, + 1152.0, + 293.0, + 1152.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1161.0, + 1113.0, + 1405.0, + 1113.0, + 1405.0, + 1152.0, + 1161.0, + 1152.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 1143.0, + 1404.0, + 1143.0, + 1404.0, + 1180.0, + 293.0, + 1180.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 296.0, + 1177.0, + 1404.0, + 1177.0, + 1404.0, + 1208.0, + 296.0, + 1208.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 1203.0, + 1404.0, + 1203.0, + 1404.0, + 1241.0, + 293.0, + 1241.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 1236.0, + 643.0, + 1236.0, + 643.0, + 1271.0, + 294.0, + 1271.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 740.0, + 1236.0, + 1405.0, + 1236.0, + 1405.0, + 1271.0, + 740.0, + 1271.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 1266.0, + 1404.0, + 1266.0, + 1404.0, + 1300.0, + 294.0, + 1300.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 1297.0, + 1240.0, + 1297.0, + 1240.0, + 1331.0, + 293.0, + 1331.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 935.0, + 1404.0, + 935.0, + 1404.0, + 972.0, + 294.0, + 972.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 287.0, + 964.0, + 598.0, + 964.0, + 598.0, + 1019.0, + 287.0, + 1019.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 740.0, + 964.0, + 1411.0, + 964.0, + 1411.0, + 1019.0, + 740.0, + 1019.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 1006.0, + 1405.0, + 1006.0, + 1405.0, + 1042.0, + 293.0, + 1042.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 1038.0, + 1406.0, + 1038.0, + 1406.0, + 1071.0, + 294.0, + 1071.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 296.0, + 1067.0, + 698.0, + 1067.0, + 698.0, + 1100.0, + 296.0, + 1100.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 428.0, + 1405.0, + 428.0, + 1405.0, + 464.0, + 295.0, + 464.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 291.0, + 460.0, + 1406.0, + 460.0, + 1406.0, + 494.0, + 291.0, + 494.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 488.0, + 1405.0, + 488.0, + 1405.0, + 525.0, + 293.0, + 525.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 521.0, + 1405.0, + 521.0, + 1405.0, + 557.0, + 295.0, + 557.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 291.0, + 546.0, + 1410.0, + 546.0, + 1410.0, + 591.0, + 291.0, + 591.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 580.0, + 1162.0, + 580.0, + 1162.0, + 619.0, + 293.0, + 619.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 229.0, + 1403.0, + 229.0, + 1403.0, + 263.0, + 295.0, + 263.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 258.0, + 1408.0, + 258.0, + 1408.0, + 298.0, + 293.0, + 298.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 296.0, + 293.0, + 1405.0, + 293.0, + 1405.0, + 325.0, + 296.0, + 325.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 322.0, + 1406.0, + 322.0, + 1406.0, + 354.0, + 294.0, + 354.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 351.0, + 1405.0, + 351.0, + 1405.0, + 387.0, + 294.0, + 387.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 383.0, + 566.0, + 383.0, + 566.0, + 419.0, + 294.0, + 419.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 1343.0, + 1404.0, + 1343.0, + 1404.0, + 1380.0, + 293.0, + 1380.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 1375.0, + 867.0, + 1375.0, + 867.0, + 1418.0, + 294.0, + 1418.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1010.0, + 1375.0, + 1410.0, + 1375.0, + 1410.0, + 1418.0, + 1010.0, + 1418.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 1413.0, + 1403.0, + 1413.0, + 1403.0, + 1448.0, + 294.0, + 1448.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 1443.0, + 297.0, + 1443.0, + 297.0, + 1481.0, + 294.0, + 1481.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 313.0, + 1443.0, + 322.0, + 1443.0, + 322.0, + 1481.0, + 313.0, + 1481.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 345.0, + 1443.0, + 394.0, + 1443.0, + 394.0, + 1481.0, + 345.0, + 1481.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 420.0, + 1443.0, + 711.0, + 1443.0, + 711.0, + 1481.0, + 420.0, + 1481.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 764.0, + 1409.0, + 764.0, + 1409.0, + 805.0, + 294.0, + 805.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 798.0, + 1406.0, + 798.0, + 1406.0, + 831.0, + 295.0, + 831.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 826.0, + 1406.0, + 826.0, + 1406.0, + 864.0, + 294.0, + 864.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 858.0, + 1406.0, + 858.0, + 1406.0, + 895.0, + 294.0, + 895.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 291.0, + 888.0, + 417.0, + 888.0, + 417.0, + 923.0, + 291.0, + 923.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 629.0, + 1409.0, + 629.0, + 1409.0, + 665.0, + 294.0, + 665.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 660.0, + 1257.0, + 660.0, + 1257.0, + 693.0, + 295.0, + 693.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1279.0, + 660.0, + 1404.0, + 660.0, + 1404.0, + 693.0, + 1279.0, + 693.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 691.0, + 1403.0, + 691.0, + 1403.0, + 723.0, + 294.0, + 723.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 718.0, + 1190.0, + 718.0, + 1190.0, + 757.0, + 293.0, + 757.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1307.0, + 718.0, + 1387.0, + 718.0, + 1387.0, + 757.0, + 1307.0, + 757.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 1658.0, + 1405.0, + 1658.0, + 1405.0, + 1696.0, + 294.0, + 1696.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 297.0, + 1691.0, + 1405.0, + 1691.0, + 1405.0, + 1724.0, + 297.0, + 1724.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 1720.0, + 1403.0, + 1720.0, + 1403.0, + 1753.0, + 295.0, + 1753.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 1752.0, + 1405.0, + 1752.0, + 1405.0, + 1789.0, + 294.0, + 1789.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 1784.0, + 443.0, + 1784.0, + 443.0, + 1814.0, + 295.0, + 1814.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 296.0, + 1971.0, + 1012.0, + 1971.0, + 1012.0, + 2007.0, + 296.0, + 2007.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1167.0, + 1971.0, + 1252.0, + 1971.0, + 1252.0, + 2007.0, + 1167.0, + 2007.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1276.0, + 1971.0, + 1406.0, + 1971.0, + 1406.0, + 2007.0, + 1276.0, + 2007.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 2000.0, + 370.0, + 2000.0, + 370.0, + 2038.0, + 292.0, + 2038.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 396.0, + 2000.0, + 605.0, + 2000.0, + 605.0, + 2038.0, + 396.0, + 2038.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 712.0, + 2000.0, + 988.0, + 2000.0, + 988.0, + 2038.0, + 712.0, + 2038.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1191.0, + 2000.0, + 1405.0, + 2000.0, + 1405.0, + 2038.0, + 1191.0, + 2038.0 + ], + "score": 1.0, + "text": "" + } + ], + "page_info": { + "page_no": 1, + "width": 1700, + "height": 2200 + } + }, + { + "layout_dets": [ + { + "category_id": 1, + "poly": [ + 297, + 413, + 1405, + 413, + 1405, + 601, + 297, + 601 + ], + "score": 0.979 + }, + { + "category_id": 1, + "poly": [ + 297, + 712, + 1406, + 712, + 1406, + 806, + 297, + 806 + ], + "score": 0.968 + }, + { + "category_id": 1, + "poly": [ + 298, + 1922, + 1404, + 1922, + 1404, + 2043, + 298, + 2043 + ], + "score": 0.966 + }, + { + "category_id": 1, + "poly": [ + 297, + 894, + 1403, + 894, + 1403, + 989, + 297, + 989 + ], + "score": 0.964 + }, + { + "category_id": 1, + "poly": [ + 299, + 307, + 1401, + 307, + 1401, + 402, + 299, + 402 + ], + "score": 0.961 + }, + { + "category_id": 1, + "poly": [ + 300, + 614, + 1399, + 614, + 1399, + 708, + 300, + 708 + ], + "score": 0.952 + }, + { + "category_id": 1, + "poly": [ + 293, + 228, + 1402, + 228, + 1402, + 294, + 293, + 294 + ], + "score": 0.951 + }, + { + "category_id": 1, + "poly": [ + 298, + 827, + 1401, + 827, + 1401, + 889, + 298, + 889 + ], + "score": 0.944 + }, + { + "category_id": 0, + "poly": [ + 299, + 1195, + 574, + 1195, + 574, + 1232, + 299, + 1232 + ], + "score": 0.921 + }, + { + "category_id": 1, + "poly": [ + 299, + 1007, + 1011, + 1007, + 1011, + 1040, + 299, + 1040 + ], + "score": 0.915 + }, + { + "category_id": 2, + "poly": [ + 299, + 74, + 816, + 74, + 816, + 105, + 299, + 105 + ], + "score": 0.914 + }, + { + "category_id": 1, + "poly": [ + 286, + 1263, + 1322, + 1263, + 1322, + 1298, + 286, + 1298 + ], + "score": 0.913 + }, + { + "category_id": 8, + "poly": [ + 387, + 1045, + 1286, + 1045, + 1286, + 1117, + 387, + 1117 + ], + "score": 0.91 + }, + { + "category_id": 1, + "poly": [ + 288, + 1121, + 1370, + 1121, + 1370, + 1157, + 288, + 1157 + ], + "score": 0.897 + }, + { + "category_id": 0, + "poly": [ + 300, + 1396, + 777, + 1396, + 777, + 1429, + 300, + 1429 + ], + "score": 0.885 + }, + { + "category_id": 0, + "poly": [ + 298, + 1330, + 518, + 1330, + 518, + 1363, + 298, + 1363 + ], + "score": 0.869 + }, + { + "category_id": 2, + "poly": [ + 841, + 2087, + 859, + 2087, + 859, + 2113, + 841, + 2113 + ], + "score": 0.652 + }, + { + "category_id": 2, + "poly": [ + 841, + 2087, + 860, + 2087, + 860, + 2113, + 841, + 2113 + ], + "score": 0.581 + }, + { + "category_id": 1, + "poly": [ + 307, + 1435, + 1402, + 1435, + 1402, + 1893, + 307, + 1893 + ], + "score": 0.47 + }, + { + "category_id": 5, + "poly": [ + 307, + 1435, + 1402, + 1435, + 1402, + 1893, + 307, + 1893 + ], + "score": 0.446, + "html": "
Parameters: ∈, γ, δ E ,H← ln1/(1-2)∈1). In 1/q Define (k)= ln(SA(k + 1)(k + 2)/δ),αk = H· H+1 for t=1,2,.. do
5: Take action at ← arg maxa' Q(st, a') Receive reward rt and transit to St+1 N(st,at)← N(st,at)+1
k←N(st,at),bk←1√ H(k) k c2 is a constant and can be set to 4√2
V(St+1) ← maXa∈A Q(st+1,a)
Q(st,at) ←(1-ak)Q(st,at)+αk [r(st,at)+bk +γV(st+1)] 10:
Q(st,at) ← min(Q(st,at),Q(st,at))
" + }, + { + "category_id": 13, + "poly": [ + 470, + 1996, + 618, + 1996, + 618, + 2043, + 470, + 2043 + ], + "score": 0.94, + "latex": "\\frac { \\ln { 1 } / ( ( 1 - \\gamma ) \\epsilon _ { 1 } ) } { \\ln { 1 } / \\gamma }" + }, + { + "category_id": 13, + "poly": [ + 648, + 1924, + 941, + 1924, + 941, + 1968, + 648, + 1968 + ], + "score": 0.94, + "latex": "\\begin{array} { r } { R = \\lceil \\ln \\frac { 3 } { \\epsilon ( 1 - \\gamma ) } / ( 1 - \\gamma ) \\rceil } \\end{array}" + }, + { + "category_id": 13, + "poly": [ + 799, + 1995, + 1010, + 1995, + 1010, + 2042, + 799, + 2042 + ], + "score": 0.93, + "latex": "H \\leq \\frac { \\ln 1 / ( ( 1 - \\gamma ) \\epsilon _ { 1 } ) } { 1 - \\gamma }" + }, + { + "category_id": 13, + "poly": [ + 360, + 1923, + 481, + 1923, + 481, + 1958, + 360, + 1958 + ], + "score": 0.93, + "latex": "c _ { 2 } = 4 \\sqrt { 2 }" + }, + { + "category_id": 13, + "poly": [ + 774, + 340, + 853, + 340, + 853, + 369, + 774, + 369 + ], + "score": 0.93, + "latex": "s _ { t } \\in S" + }, + { + "category_id": 13, + "poly": [ + 1079, + 230, + 1171, + 230, + 1171, + 264, + 1079, + 264 + ], + "score": 0.93, + "latex": "S = | S |" + }, + { + "category_id": 13, + "poly": [ + 533, + 231, + 653, + 231, + 653, + 262, + 533, + 262 + ], + "score": 0.93, + "latex": "0 \\leq \\gamma < 1" + }, + { + "category_id": 13, + "poly": [ + 1222, + 230, + 1320, + 230, + 1320, + 264, + 1222, + 264 + ], + "score": 0.92, + "latex": "A = | { \\mathcal { A } } |" + }, + { + "category_id": 13, + "poly": [ + 1005, + 340, + 1088, + 340, + 1088, + 369, + 1005, + 369 + ], + "score": 0.91, + "latex": "a _ { t } \\in \\mathcal A" + }, + { + "category_id": 13, + "poly": [ + 1158, + 477, + 1402, + 477, + 1402, + 509, + 1158, + 509 + ], + "score": 0.91, + "latex": "V ^ { * } ( s ) = \\operatorname* { s u p } _ { \\pi } V ^ { \\pi } ( s )" + }, + { + "category_id": 13, + "poly": [ + 725, + 447, + 808, + 447, + 808, + 479, + 725, + 479 + ], + "score": 0.91, + "latex": "V ^ { \\pi _ { t } } ( s )" + }, + { + "category_id": 13, + "poly": [ + 295, + 536, + 824, + 536, + 824, + 573, + 295, + 573 + ], + "score": 0.91, + "latex": "\\begin{array} { r } { \\mathbb { E } [ \\sum _ { i = 2 } ^ { \\infty } \\gamma ^ { i - 1 } r ( s _ { i } , \\pi _ { t + i - 1 } ( s _ { i } ) ) | s _ { 1 } = \\stackrel { \\cdot } { s } , a _ { 1 } = \\stackrel { \\cdot } { a } ] } \\end{array}" + }, + { + "category_id": 13, + "poly": [ + 1117, + 1963, + 1393, + 1963, + 1393, + 1999, + 1117, + 1999 + ], + "score": 0.91, + "latex": "\\alpha _ { k } = ( H + 1 ) / ( H + k )" + }, + { + "category_id": 13, + "poly": [ + 663, + 374, + 716, + 374, + 716, + 402, + 663, + 402 + ], + "score": 0.9, + "latex": "s _ { t + 1 }" + }, + { + "category_id": 13, + "poly": [ + 298, + 773, + 564, + 773, + 564, + 807, + 298, + 807 + ], + "score": 0.89, + "latex": "\\dot { V } ^ { \\pi _ { t } } \\left( s _ { t } \\right) \\dot { < } V ^ { * } \\left( s _ { t } \\right) - \\epsilon ." + }, + { + "category_id": 13, + "poly": [ + 1209, + 540, + 1307, + 540, + 1307, + 570, + 1209, + 570 + ], + "score": 0.89, + "latex": "Q ^ { * } ( s , a )" + }, + { + "category_id": 14, + "poly": [ + 397, + 1043, + 1286, + 1043, + 1286, + 1120, + 397, + 1120 + ], + "score": 0.89, + "latex": "\\left\\{ \\begin{array} { l l } { V ^ { \\pi _ { t } } ( s ) = Q ^ { \\pi _ { t } } \\left( s , \\pi _ { t } ( s ) \\right) } \\\\ { Q ^ { \\pi _ { t } } ( s , a ) : = \\left( r _ { t } + \\gamma \\mathbb { P } V ^ { \\pi _ { t + 1 } } \\right) ( s , a ) , } \\end{array} \\right. \\quad \\left\\{ \\begin{array} { l l } { V ^ { * } ( s ) = Q ^ { * } \\left( s , \\pi ^ { * } ( s ) \\right) } \\\\ { Q ^ { * } ( s , a ) : = \\left( r _ { t } + \\gamma \\mathbb { P } V ^ { * } \\right) ( s , a ) , } \\end{array} \\right." + }, + { + "category_id": 13, + "poly": [ + 711, + 955, + 1009, + 955, + 1009, + 989, + 711, + 989 + ], + "score": 0.89, + "latex": "( S , A , 1 / \\epsilon , 1 / \\delta , 1 / ( 1 - \\gamma ) )" + }, + { + "category_id": 13, + "poly": [ + 1347, + 1689, + 1402, + 1689, + 1402, + 1725, + 1347, + 1725 + ], + "score": 0.88, + "latex": "4 { \\sqrt { 2 } }" + }, + { + "category_id": 13, + "poly": [ + 933, + 1123, + 1371, + 1123, + 1371, + 1158, + 933, + 1158 + ], + "score": 0.87, + "latex": "\\left[ \\mathbb { P } V ^ { \\pi _ { t } } \\right] ( s , a ) : = \\mathbb { E } _ { s ^ { \\prime } \\sim p ( \\cdot \\vert s , a ) } V ^ { \\pi _ { t + 1 } } ( s ^ { \\prime } ) ." + }, + { + "category_id": 13, + "poly": [ + 451, + 1466, + 722, + 1466, + 722, + 1511, + 451, + 1511 + ], + "score": 0.87, + "latex": "\\begin{array} { r } { Q ( s , a ) , \\hat { Q } ( s , a ) \\gets \\frac { 1 } { 1 - \\gamma } } \\end{array}" + }, + { + "category_id": 13, + "poly": [ + 1153, + 509, + 1407, + 509, + 1407, + 540, + 1153, + 540 + ], + "score": 0.86, + "latex": "Q ^ { \\pi _ { t } } ( s , a ) = r ( s , a ) +" + }, + { + "category_id": 13, + "poly": [ + 888, + 421, + 918, + 421, + 918, + 447, + 888, + 447 + ], + "score": 0.86, + "latex": "\\pi _ { t }" + }, + { + "category_id": 13, + "poly": [ + 533, + 314, + 561, + 314, + 561, + 339, + 533, + 339 + ], + "score": 0.86, + "latex": "s _ { 1 }" + }, + { + "category_id": 13, + "poly": [ + 447, + 476, + 1002, + 476, + 1002, + 512, + 447, + 512 + ], + "score": 0.85, + "latex": "\\begin{array} { r } { V ^ { \\pi _ { t } } ( s ) = \\mathbb { E } \\bigl [ \\sum _ { i = 1 } ^ { \\infty } \\gamma ^ { i - 1 } r ( s _ { i } , \\pi _ { t + i - 1 } ( s _ { i } ) ) | s _ { 1 } = s \\bigr ] } \\end{array}" + }, + { + "category_id": 13, + "poly": [ + 1326, + 343, + 1351, + 343, + 1351, + 369, + 1326, + 369 + ], + "score": 0.85, + "latex": "r _ { t }" + }, + { + "category_id": 13, + "poly": [ + 1295, + 956, + 1358, + 956, + 1358, + 985, + 1295, + 985 + ], + "score": 0.85, + "latex": "1 - \\delta" + }, + { + "category_id": 13, + "poly": [ + 633, + 572, + 665, + 572, + 665, + 596, + 633, + 596 + ], + "score": 0.84, + "latex": "\\pi ^ { * }" + }, + { + "category_id": 13, + "poly": [ + 842, + 748, + 871, + 748, + 871, + 774, + 842, + 774 + ], + "score": 0.84, + "latex": "\\pi _ { t }" + }, + { + "category_id": 13, + "poly": [ + 563, + 1622, + 589, + 1622, + 589, + 1647, + 563, + 1647 + ], + "score": 0.82, + "latex": "r _ { t }" + }, + { + "category_id": 13, + "poly": [ + 1288, + 452, + 1316, + 452, + 1316, + 476, + 1288, + 476 + ], + "score": 0.82, + "latex": "\\pi _ { t }" + }, + { + "category_id": 13, + "poly": [ + 745, + 1624, + 798, + 1624, + 798, + 1650, + 745, + 1650 + ], + "score": 0.8, + "latex": "s _ { t + 1 }" + }, + { + "category_id": 13, + "poly": [ + 1181, + 1928, + 1214, + 1928, + 1214, + 1955, + 1181, + 1955 + ], + "score": 0.8, + "latex": "M" + }, + { + "category_id": 13, + "poly": [ + 1333, + 749, + 1358, + 749, + 1358, + 774, + 1333, + 774 + ], + "score": 0.8, + "latex": "s _ { t }" + }, + { + "category_id": 13, + "poly": [ + 298, + 2002, + 326, + 2002, + 326, + 2030, + 298, + 2030 + ], + "score": 0.79, + "latex": "H" + }, + { + "category_id": 13, + "poly": [ + 426, + 1515, + 930, + 1515, + 930, + 1555, + 426, + 1555 + ], + "score": 0.78, + "latex": "\\begin{array} { r } { \\iota ( k ) = \\ln ( S A ( k + 1 ) ( k + 2 ) / \\delta ) , \\alpha _ { k } = \\frac { H + 1 } { H + k } , } \\end{array}" + }, + { + "category_id": 13, + "poly": [ + 451, + 1964, + 752, + 1964, + 752, + 1998, + 451, + 1998 + ], + "score": 0.75, + "latex": "{ \\cal { \\left( M = 0 \\left( \\ln 1 / ( 1 - \\gamma ) \\epsilon \\right) \\right) } }" + }, + { + "category_id": 13, + "poly": [ + 520, + 1582, + 814, + 1582, + 814, + 1619, + 520, + 1619 + ], + "score": 0.73, + "latex": "a _ { t } \\gets \\arg \\operatorname* { m a x } _ { a ^ { \\prime } } \\hat { Q } ( s _ { t } , a ^ { \\prime } )" + }, + { + "category_id": 14, + "poly": [ + 432, + 1462, + 1332, + 1462, + 1332, + 1562, + 432, + 1562 + ], + "score": 0.69, + "latex": "\\begin{array} { r l } & { \\textnormal { \\texttt { e } } Q ( s , a ) , \\hat { Q } ( s , a ) \\gets \\frac { 1 } { 1 - \\gamma } , N ( s , a ) \\gets 0 , \\epsilon _ { 1 } \\gets \\frac { \\epsilon } { 2 4 R M \\ln \\frac { 1 } { 1 - \\gamma } } , H \\gets \\frac { \\ln 1 / ( ( 1 - \\gamma ) \\epsilon _ { 1 } ) } { \\ln 1 / \\gamma } . } \\\\ & { \\cdot ( k ) = \\ln ( S A ( k + 1 ) ( k + 2 ) / \\delta ) , \\alpha _ { k } = \\frac { H + 1 } { H + k } . } \\end{array}" + }, + { + "category_id": 13, + "poly": [ + 957, + 748, + 971, + 748, + 971, + 771, + 957, + 771 + ], + "score": 0.68, + "latex": "t" + }, + { + "category_id": 13, + "poly": [ + 621, + 894, + 684, + 894, + 684, + 924, + 621, + 924 + ], + "score": 0.67, + "latex": "\\mathcal { A L G }" + }, + { + "category_id": 13, + "poly": [ + 628, + 927, + 653, + 927, + 653, + 957, + 628, + 957 + ], + "score": 0.67, + "latex": "i f ," + }, + { + "category_id": 13, + "poly": [ + 386, + 1553, + 548, + 1553, + 548, + 1583, + 386, + 1583 + ], + "score": 0.66, + "latex": "t = 1 , 2 , \\dots \\mathbf { d o }" + }, + { + "category_id": 13, + "poly": [ + 819, + 926, + 834, + 926, + 834, + 952, + 819, + 952 + ], + "score": 0.65, + "latex": "\\delta" + }, + { + "category_id": 13, + "poly": [ + 980, + 1700, + 1007, + 1700, + 1007, + 1724, + 980, + 1724 + ], + "score": 0.65, + "latex": "c _ { 2 }" + }, + { + "category_id": 13, + "poly": [ + 1168, + 542, + 1196, + 542, + 1196, + 569, + 1168, + 569 + ], + "score": 0.64, + "latex": "\\pi _ { t }" + }, + { + "category_id": 13, + "poly": [ + 607, + 449, + 621, + 449, + 621, + 474, + 607, + 474 + ], + "score": 0.62, + "latex": "t" + }, + { + "category_id": 13, + "poly": [ + 1138, + 925, + 1200, + 925, + 1200, + 955, + 1138, + 955 + ], + "score": 0.61, + "latex": "\\mathcal { A L G }" + }, + { + "category_id": 13, + "poly": [ + 1057, + 712, + 1119, + 712, + 1119, + 743, + 1057, + 743 + ], + "score": 0.56, + "latex": "\\mathcal { A L G }" + }, + { + "category_id": 14, + "poly": [ + 382, + 1640, + 1142, + 1640, + 1142, + 1863, + 382, + 1863 + ], + "score": 0.48, + "latex": "\\begin{array} { r l r } & { N ( s _ { t } , a _ { t } ) \\gets N ( s _ { t } , a _ { t } ) + 1 } & \\\\ & { N ( s _ { t } , a _ { t } ) \\gets N ( s _ { t } , a _ { t } ) + 1 } & \\\\ & { k \\gets N ( s _ { t } , a _ { t } ) , b _ { k } \\gets \\frac { c _ { 2 } } { 1 - \\gamma } \\sqrt { \\frac { H ( k ) } { k } } } & \\\\ & { \\hat { V } ( s _ { t + 1 } ) \\gets \\operatorname* { m a x } _ { a \\in A } \\hat { Q } ( s _ { t + 1 } , a ) } & \\\\ & { Q ( s _ { t } , a _ { t } ) \\gets ( 1 - \\alpha _ { k } ) Q ( s _ { t } , a _ { t } ) + \\alpha _ { k } \\left[ r ( s _ { t } , a _ { t } ) + b _ { k } + \\gamma \\hat { V } ( s _ { t + 1 } ) \\right] } \\\\ & { \\hat { Q } ( s _ { t } , a _ { t } ) \\gets \\operatorname* { m i n } ( \\hat { Q } ( s _ { t } , a _ { t } ) , Q ( s _ { t } , a _ { t } ) ) } & \\end{array}" + }, + { + "category_id": 13, + "poly": [ + 1040, + 750, + 1055, + 750, + 1055, + 771, + 1040, + 771 + ], + "score": 0.47, + "latex": "\\epsilon" + }, + { + "category_id": 13, + "poly": [ + 709, + 1582, + 812, + 1582, + 812, + 1619, + 709, + 1619 + ], + "score": 0.42, + "latex": "\\hat { Q } ( s _ { t } , a ^ { \\prime } )" + }, + { + "category_id": 13, + "poly": [ + 385, + 1647, + 695, + 1647, + 695, + 1682, + 385, + 1682 + ], + "score": 0.34, + "latex": "N ( s _ { t } , a _ { t } ) \\gets N ( s _ { t } , a _ { t } ) + 1" + }, + { + "category_id": 13, + "poly": [ + 457, + 1964, + 551, + 1964, + 551, + 1994, + 457, + 1994 + ], + "score": 0.28, + "latex": "M = \\mathcal { O }" + }, + { + "category_id": 13, + "poly": [ + 976, + 678, + 1001, + 678, + 1001, + 705, + 976, + 705 + ], + "score": 0.28, + "latex": "\\&" + }, + { + "category_id": 13, + "poly": [ + 898, + 539, + 923, + 539, + 923, + 569, + 898, + 569 + ], + "score": 0.26, + "latex": "\\mathrm { Q }" + }, + { + "category_id": 15, + "poly": [ + 291.0, + 1191.0, + 575.0, + 1191.0, + 575.0, + 1238.0, + 291.0, + 1238.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 72.0, + 817.0, + 72.0, + 817.0, + 108.0, + 295.0, + 108.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 1394.0, + 781.0, + 1394.0, + 781.0, + 1436.0, + 294.0, + 1436.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 1329.0, + 521.0, + 1329.0, + 521.0, + 1365.0, + 294.0, + 1365.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 838.0, + 2085.0, + 862.0, + 2085.0, + 862.0, + 2119.0, + 838.0, + 2119.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 837.0, + 2085.0, + 862.0, + 2085.0, + 862.0, + 2119.0, + 837.0, + 2119.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 411.0, + 887.0, + 411.0, + 887.0, + 453.0, + 292.0, + 453.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 919.0, + 411.0, + 1406.0, + 411.0, + 1406.0, + 453.0, + 919.0, + 453.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 443.0, + 606.0, + 443.0, + 606.0, + 483.0, + 294.0, + 483.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 622.0, + 443.0, + 724.0, + 443.0, + 724.0, + 483.0, + 622.0, + 483.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 809.0, + 443.0, + 1287.0, + 443.0, + 1287.0, + 483.0, + 809.0, + 483.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1317.0, + 443.0, + 1407.0, + 443.0, + 1407.0, + 483.0, + 1317.0, + 483.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 286.0, + 463.0, + 446.0, + 463.0, + 446.0, + 524.0, + 286.0, + 524.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1003.0, + 463.0, + 1157.0, + 463.0, + 1157.0, + 524.0, + 1003.0, + 524.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1403.0, + 463.0, + 1415.0, + 463.0, + 1415.0, + 524.0, + 1403.0, + 524.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 290.0, + 503.0, + 1152.0, + 503.0, + 1152.0, + 544.0, + 290.0, + 544.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1408.0, + 503.0, + 1411.0, + 503.0, + 1411.0, + 544.0, + 1408.0, + 544.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 283.0, + 520.0, + 294.0, + 520.0, + 294.0, + 588.0, + 283.0, + 588.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 825.0, + 520.0, + 897.0, + 520.0, + 897.0, + 588.0, + 825.0, + 588.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 924.0, + 520.0, + 1167.0, + 520.0, + 1167.0, + 588.0, + 924.0, + 588.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1197.0, + 520.0, + 1208.0, + 520.0, + 1208.0, + 588.0, + 1197.0, + 588.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1308.0, + 520.0, + 1416.0, + 520.0, + 1416.0, + 588.0, + 1308.0, + 588.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 567.0, + 632.0, + 567.0, + 632.0, + 603.0, + 295.0, + 603.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 666.0, + 567.0, + 677.0, + 567.0, + 677.0, + 603.0, + 666.0, + 603.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 710.0, + 1056.0, + 710.0, + 1056.0, + 748.0, + 294.0, + 748.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1120.0, + 710.0, + 1406.0, + 710.0, + 1406.0, + 748.0, + 1120.0, + 748.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 742.0, + 841.0, + 742.0, + 841.0, + 781.0, + 292.0, + 781.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 872.0, + 742.0, + 956.0, + 742.0, + 956.0, + 781.0, + 872.0, + 781.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 972.0, + 742.0, + 1039.0, + 742.0, + 1039.0, + 781.0, + 972.0, + 781.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1056.0, + 742.0, + 1332.0, + 742.0, + 1332.0, + 781.0, + 1056.0, + 781.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1359.0, + 742.0, + 1409.0, + 742.0, + 1409.0, + 781.0, + 1359.0, + 781.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 769.0, + 297.0, + 769.0, + 297.0, + 811.0, + 294.0, + 811.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 565.0, + 769.0, + 575.0, + 769.0, + 575.0, + 811.0, + 565.0, + 811.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 291.0, + 1918.0, + 359.0, + 1918.0, + 359.0, + 1974.0, + 291.0, + 1974.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 482.0, + 1918.0, + 647.0, + 1918.0, + 647.0, + 1974.0, + 482.0, + 1974.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 942.0, + 1918.0, + 1180.0, + 1918.0, + 1180.0, + 1974.0, + 942.0, + 1974.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1215.0, + 1918.0, + 1410.0, + 1918.0, + 1410.0, + 1974.0, + 1215.0, + 1974.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 1959.0, + 450.0, + 1959.0, + 450.0, + 1999.0, + 293.0, + 1999.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 753.0, + 1959.0, + 1116.0, + 1959.0, + 1116.0, + 1999.0, + 753.0, + 1999.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1394.0, + 1959.0, + 1404.0, + 1959.0, + 1404.0, + 1999.0, + 1394.0, + 1999.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 327.0, + 1984.0, + 469.0, + 1984.0, + 469.0, + 2050.0, + 327.0, + 2050.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 619.0, + 1984.0, + 798.0, + 1984.0, + 798.0, + 2050.0, + 619.0, + 2050.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1011.0, + 1984.0, + 1018.0, + 1984.0, + 1018.0, + 2050.0, + 1011.0, + 2050.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 892.0, + 620.0, + 892.0, + 620.0, + 931.0, + 294.0, + 931.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 685.0, + 892.0, + 1404.0, + 892.0, + 1404.0, + 931.0, + 685.0, + 931.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 923.0, + 627.0, + 923.0, + 627.0, + 960.0, + 292.0, + 960.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 654.0, + 923.0, + 818.0, + 923.0, + 818.0, + 960.0, + 654.0, + 960.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 835.0, + 923.0, + 1137.0, + 923.0, + 1137.0, + 960.0, + 835.0, + 960.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1201.0, + 923.0, + 1404.0, + 923.0, + 1404.0, + 960.0, + 1201.0, + 960.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 955.0, + 710.0, + 955.0, + 710.0, + 993.0, + 292.0, + 993.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1010.0, + 955.0, + 1294.0, + 955.0, + 1294.0, + 993.0, + 1010.0, + 993.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1359.0, + 955.0, + 1370.0, + 955.0, + 1370.0, + 993.0, + 1359.0, + 993.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 306.0, + 532.0, + 306.0, + 532.0, + 345.0, + 293.0, + 345.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 562.0, + 306.0, + 1406.0, + 306.0, + 1406.0, + 345.0, + 562.0, + 345.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 337.0, + 773.0, + 337.0, + 773.0, + 372.0, + 295.0, + 372.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 854.0, + 337.0, + 1004.0, + 337.0, + 1004.0, + 372.0, + 854.0, + 372.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1089.0, + 337.0, + 1325.0, + 337.0, + 1325.0, + 372.0, + 1089.0, + 372.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1352.0, + 337.0, + 1403.0, + 337.0, + 1403.0, + 372.0, + 1352.0, + 372.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 365.0, + 662.0, + 365.0, + 662.0, + 408.0, + 293.0, + 408.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 717.0, + 365.0, + 730.0, + 365.0, + 730.0, + 408.0, + 717.0, + 408.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 611.0, + 1404.0, + 611.0, + 1404.0, + 653.0, + 294.0, + 653.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 296.0, + 645.0, + 1403.0, + 645.0, + 1403.0, + 679.0, + 296.0, + 679.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 296.0, + 677.0, + 975.0, + 677.0, + 975.0, + 711.0, + 296.0, + 711.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1002.0, + 677.0, + 1187.0, + 677.0, + 1187.0, + 711.0, + 1002.0, + 711.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 229.0, + 532.0, + 229.0, + 532.0, + 265.0, + 295.0, + 265.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 654.0, + 229.0, + 1078.0, + 229.0, + 1078.0, + 265.0, + 654.0, + 265.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1172.0, + 229.0, + 1221.0, + 229.0, + 1221.0, + 265.0, + 1172.0, + 265.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1321.0, + 229.0, + 1404.0, + 229.0, + 1404.0, + 265.0, + 1321.0, + 265.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 258.0, + 966.0, + 258.0, + 966.0, + 297.0, + 293.0, + 297.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 823.0, + 1405.0, + 823.0, + 1405.0, + 866.0, + 293.0, + 866.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 296.0, + 855.0, + 942.0, + 855.0, + 942.0, + 891.0, + 296.0, + 891.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 1003.0, + 1014.0, + 1003.0, + 1014.0, + 1047.0, + 293.0, + 1047.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 1260.0, + 1324.0, + 1260.0, + 1324.0, + 1303.0, + 292.0, + 1303.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 291.0, + 1112.0, + 932.0, + 1112.0, + 932.0, + 1165.0, + 291.0, + 1165.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1372.0, + 1112.0, + 1377.0, + 1112.0, + 1377.0, + 1165.0, + 1372.0, + 1165.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 343.0, + 1431.0, + 561.0, + 1431.0, + 561.0, + 1467.0, + 343.0, + 1467.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 339.0, + 1463.0, + 431.0, + 1463.0, + 431.0, + 1510.0, + 339.0, + 1510.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 341.0, + 1508.0, + 425.0, + 1508.0, + 425.0, + 1558.0, + 341.0, + 1558.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 342.0, + 1549.0, + 385.0, + 1549.0, + 385.0, + 1584.0, + 342.0, + 1584.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 549.0, + 1549.0, + 552.0, + 1549.0, + 552.0, + 1584.0, + 549.0, + 1584.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 307.0, + 1584.0, + 342.0, + 1584.0, + 342.0, + 1620.0, + 307.0, + 1620.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 381.0, + 1583.0, + 519.0, + 1583.0, + 519.0, + 1622.0, + 381.0, + 1622.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 377.0, + 1680.0, + 381.0, + 1680.0, + 381.0, + 1740.0, + 377.0, + 1740.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1143.0, + 1691.0, + 1346.0, + 1691.0, + 1346.0, + 1725.0, + 1143.0, + 1725.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 298.0, + 1777.0, + 340.0, + 1777.0, + 340.0, + 1811.0, + 298.0, + 1811.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 340.0, + 1851.0, + 439.0, + 1851.0, + 439.0, + 1888.0, + 340.0, + 1888.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1080.25, + 1452.5, + 1338.25, + 1452.5, + 1338.25, + 1504.0, + 1080.25, + 1504.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 952.75, + 1480.5, + 1093.75, + 1480.5, + 1093.75, + 1517.5, + 952.75, + 1517.5 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 381.75, + 1613.0, + 801.75, + 1613.0, + 801.75, + 1652.0, + 381.75, + 1652.0 + ], + "score": 1.0, + "text": "" + } + ], + "page_info": { + "page_no": 2, + "width": 1700, + "height": 2200 + } + }, + { + "layout_dets": [ + { + "category_id": 1, + "poly": [ + 297, + 1498, + 1404, + 1498, + 1404, + 1806, + 297, + 1806 + ], + "score": 0.983 + }, + { + "category_id": 1, + "poly": [ + 298, + 1130, + 1404, + 1130, + 1404, + 1346, + 298, + 1346 + ], + "score": 0.982 + }, + { + "category_id": 1, + "poly": [ + 297, + 929, + 1406, + 929, + 1406, + 1115, + 297, + 1115 + ], + "score": 0.98 + }, + { + "category_id": 1, + "poly": [ + 297, + 1819, + 1404, + 1819, + 1404, + 2035, + 297, + 2035 + ], + "score": 0.98 + }, + { + "category_id": 1, + "poly": [ + 297, + 228, + 1405, + 228, + 1405, + 426, + 297, + 426 + ], + "score": 0.979 + }, + { + "category_id": 1, + "poly": [ + 297, + 1360, + 1404, + 1360, + 1404, + 1485, + 297, + 1485 + ], + "score": 0.976 + }, + { + "category_id": 1, + "poly": [ + 298, + 577, + 1409, + 577, + 1409, + 670, + 298, + 670 + ], + "score": 0.97 + }, + { + "category_id": 8, + "poly": [ + 738, + 678, + 959, + 678, + 959, + 768, + 738, + 768 + ], + "score": 0.954 + }, + { + "category_id": 1, + "poly": [ + 297, + 853, + 1405, + 853, + 1405, + 917, + 297, + 917 + ], + "score": 0.947 + }, + { + "category_id": 1, + "poly": [ + 298, + 531, + 1117, + 531, + 1117, + 566, + 298, + 566 + ], + "score": 0.93 + }, + { + "category_id": 1, + "poly": [ + 297, + 788, + 1042, + 788, + 1042, + 826, + 297, + 826 + ], + "score": 0.92 + }, + { + "category_id": 2, + "poly": [ + 299, + 75, + 816, + 75, + 816, + 105, + 299, + 105 + ], + "score": 0.907 + }, + { + "category_id": 0, + "poly": [ + 297, + 470, + 851, + 470, + 851, + 504, + 297, + 504 + ], + "score": 0.867 + }, + { + "category_id": 2, + "poly": [ + 840, + 2089, + 857, + 2089, + 857, + 2111, + 840, + 2111 + ], + "score": 0.784 + }, + { + "category_id": 13, + "poly": [ + 346, + 358, + 441, + 358, + 441, + 395, + 346, + 395 + ], + "score": 0.93, + "latex": "\\hat { Q } _ { t } ( s , a )" + }, + { + "category_id": 13, + "poly": [ + 394, + 265, + 480, + 265, + 480, + 298, + 394, + 298 + ], + "score": 0.93, + "latex": "Q ( s , a )" + }, + { + "category_id": 13, + "poly": [ + 1275, + 1160, + 1361, + 1160, + 1361, + 1195, + 1275, + 1195 + ], + "score": 0.92, + "latex": "o ( T ^ { - 1 } )" + }, + { + "category_id": 14, + "poly": [ + 738, + 674, + 959, + 674, + 959, + 768, + 738, + 768 + ], + "score": 0.92, + "latex": "\\tilde { \\mathcal { O } } \\left( \\frac { S A \\ln { 1 / \\delta } } { \\epsilon ^ { 2 } \\left( 1 - \\gamma \\right) ^ { 7 } } \\right) ," + }, + { + "category_id": 13, + "poly": [ + 764, + 1422, + 1028, + 1422, + 1028, + 1455, + 764, + 1455 + ], + "score": 0.92, + "latex": "V ^ { \\ast } ( s _ { t } ) - V ^ { \\pi _ { t } } ( s _ { t } ) \\leq \\epsilon" + }, + { + "category_id": 13, + "poly": [ + 745, + 296, + 852, + 296, + 852, + 329, + 745, + 329 + ], + "score": 0.92, + "latex": "\\tau ( s , a , k )" + }, + { + "category_id": 13, + "poly": [ + 891, + 1881, + 1144, + 1881, + 1144, + 1914, + 891, + 1914 + ], + "score": 0.92, + "latex": "V ^ { \\ast } ( s _ { t ^ { \\prime } } ) - Q ^ { \\ast } ( s _ { t ^ { \\prime } } , a _ { t ^ { \\prime } } )" + }, + { + "category_id": 13, + "poly": [ + 1223, + 295, + 1403, + 295, + 1403, + 328, + 1223, + 328 + ], + "score": 0.91, + "latex": "( s _ { t } , a _ { t } ) = ( s , a )" + }, + { + "category_id": 13, + "poly": [ + 467, + 1973, + 698, + 1973, + 698, + 2006, + 467, + 2006 + ], + "score": 0.91, + "latex": "V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } )" + }, + { + "category_id": 13, + "poly": [ + 789, + 362, + 851, + 362, + 851, + 395, + 789, + 395 + ], + "score": 0.91, + "latex": "( s , a )" + }, + { + "category_id": 13, + "poly": [ + 580, + 1914, + 681, + 1914, + 681, + 1944, + 580, + 1944 + ], + "score": 0.91, + "latex": "[ t , t + R ]" + }, + { + "category_id": 13, + "poly": [ + 296, + 296, + 358, + 296, + 358, + 328, + 296, + 328 + ], + "score": 0.91, + "latex": "( s , a )" + }, + { + "category_id": 13, + "poly": [ + 1210, + 992, + 1397, + 992, + 1397, + 1026, + 1210, + 1026 + ], + "score": 0.91, + "latex": "( V ^ { * } - V ^ { \\pi } ) ( s _ { 1 } ) )" + }, + { + "category_id": 13, + "poly": [ + 1100, + 1561, + 1167, + 1561, + 1167, + 1590, + 1100, + 1590 + ], + "score": 0.91, + "latex": "h + 1" + }, + { + "category_id": 13, + "poly": [ + 559, + 1882, + 812, + 1882, + 812, + 1915, + 559, + 1915 + ], + "score": 0.91, + "latex": "V ^ { * } ( s _ { t } ) - V ^ { \\pi _ { t } } ( s _ { t } ) \\leq \\epsilon" + }, + { + "category_id": 13, + "poly": [ + 775, + 791, + 942, + 791, + 942, + 825, + 775, + 825 + ], + "score": 0.9, + "latex": "1 / \\epsilon , 1 / ( 1 - \\gamma )" + }, + { + "category_id": 13, + "poly": [ + 1117, + 327, + 1291, + 327, + 1291, + 360, + 1117, + 360 + ], + "score": 0.89, + "latex": "\\tau ( s , a , k ) = \\infty" + }, + { + "category_id": 13, + "poly": [ + 659, + 357, + 685, + 357, + 685, + 395, + 659, + 395 + ], + "score": 0.87, + "latex": "\\hat { Q }" + }, + { + "category_id": 13, + "poly": [ + 1063, + 1657, + 1089, + 1657, + 1089, + 1682, + 1063, + 1682 + ], + "score": 0.86, + "latex": "s _ { t }" + }, + { + "category_id": 13, + "poly": [ + 846, + 260, + 932, + 260, + 932, + 298, + 846, + 298 + ], + "score": 0.86, + "latex": "\\hat { Q } ( s , a )" + }, + { + "category_id": 13, + "poly": [ + 897, + 614, + 925, + 614, + 925, + 640, + 897, + 640 + ], + "score": 0.86, + "latex": "\\pi _ { t }" + }, + { + "category_id": 13, + "poly": [ + 1153, + 1197, + 1181, + 1197, + 1181, + 1223, + 1153, + 1223 + ], + "score": 0.85, + "latex": "s _ { 1 }" + }, + { + "category_id": 13, + "poly": [ + 944, + 264, + 1040, + 264, + 1040, + 299, + 944, + 299 + ], + "score": 0.85, + "latex": "N _ { t } ( s , a )" + }, + { + "category_id": 13, + "poly": [ + 487, + 1854, + 515, + 1854, + 515, + 1881, + 487, + 1881 + ], + "score": 0.85, + "latex": "\\pi _ { t }" + }, + { + "category_id": 13, + "poly": [ + 824, + 1166, + 853, + 1166, + 853, + 1192, + 824, + 1192 + ], + "score": 0.85, + "latex": "s _ { 1 }" + }, + { + "category_id": 13, + "poly": [ + 588, + 1625, + 614, + 1625, + 614, + 1652, + 588, + 1652 + ], + "score": 0.85, + "latex": "s _ { t }" + }, + { + "category_id": 13, + "poly": [ + 1217, + 1165, + 1245, + 1165, + 1245, + 1193, + 1217, + 1193 + ], + "score": 0.85, + "latex": "s _ { 1 }" + }, + { + "category_id": 13, + "poly": [ + 581, + 362, + 607, + 362, + 607, + 395, + 581, + 395 + ], + "score": 0.85, + "latex": "Q" + }, + { + "category_id": 13, + "poly": [ + 1064, + 1227, + 1093, + 1227, + 1093, + 1253, + 1064, + 1253 + ], + "score": 0.85, + "latex": "s _ { 1 }" + }, + { + "category_id": 13, + "poly": [ + 803, + 1625, + 830, + 1625, + 830, + 1652, + 803, + 1652 + ], + "score": 0.84, + "latex": "a _ { t }" + }, + { + "category_id": 13, + "poly": [ + 675, + 1425, + 701, + 1425, + 701, + 1452, + 675, + 1452 + ], + "score": 0.84, + "latex": "s _ { t }" + }, + { + "category_id": 13, + "poly": [ + 1375, + 369, + 1400, + 369, + 1400, + 393, + 1375, + 393 + ], + "score": 0.84, + "latex": "s _ { t }" + }, + { + "category_id": 13, + "poly": [ + 1307, + 328, + 1403, + 328, + 1403, + 360, + 1307, + 360 + ], + "score": 0.84, + "latex": "Q _ { t } ( s , a )" + }, + { + "category_id": 13, + "poly": [ + 1119, + 996, + 1148, + 996, + 1148, + 1023, + 1119, + 1023 + ], + "score": 0.83, + "latex": "s _ { 1 }" + }, + { + "category_id": 13, + "poly": [ + 358, + 1911, + 379, + 1911, + 379, + 1939, + 358, + 1939 + ], + "score": 0.83, + "latex": "t ^ { \\prime }" + }, + { + "category_id": 13, + "poly": [ + 298, + 1686, + 324, + 1686, + 324, + 1713, + 298, + 1713 + ], + "score": 0.83, + "latex": "a _ { t }" + }, + { + "category_id": 13, + "poly": [ + 1140, + 614, + 1167, + 614, + 1167, + 640, + 1140, + 640 + ], + "score": 0.82, + "latex": "s _ { t . }" + }, + { + "category_id": 13, + "poly": [ + 380, + 328, + 399, + 328, + 399, + 354, + 380, + 354 + ], + "score": 0.82, + "latex": "k" + }, + { + "category_id": 13, + "poly": [ + 997, + 1562, + 1016, + 1562, + 1016, + 1588, + 997, + 1588 + ], + "score": 0.81, + "latex": "k" + }, + { + "category_id": 13, + "poly": [ + 619, + 1225, + 643, + 1225, + 643, + 1250, + 619, + 1250 + ], + "score": 0.81, + "latex": "T" + }, + { + "category_id": 13, + "poly": [ + 933, + 1856, + 957, + 1856, + 957, + 1881, + 933, + 1881 + ], + "score": 0.81, + "latex": "s _ { t }" + }, + { + "category_id": 13, + "poly": [ + 297, + 1562, + 316, + 1562, + 316, + 1588, + 297, + 1588 + ], + "score": 0.8, + "latex": "k" + }, + { + "category_id": 13, + "poly": [ + 684, + 1854, + 697, + 1854, + 697, + 1878, + 684, + 1878 + ], + "score": 0.8, + "latex": "t" + }, + { + "category_id": 13, + "poly": [ + 420, + 1562, + 441, + 1562, + 441, + 1588, + 420, + 1588 + ], + "score": 0.79, + "latex": "h" + }, + { + "category_id": 13, + "poly": [ + 371, + 787, + 398, + 787, + 398, + 820, + 371, + 820 + ], + "score": 0.79, + "latex": "\\tilde { \\mathcal { O } }" + }, + { + "category_id": 13, + "poly": [ + 349, + 994, + 373, + 994, + 373, + 1020, + 349, + 1020 + ], + "score": 0.79, + "latex": "T" + }, + { + "category_id": 13, + "poly": [ + 927, + 1915, + 951, + 1915, + 951, + 1939, + 927, + 1939 + ], + "score": 0.78, + "latex": "R" + }, + { + "category_id": 13, + "poly": [ + 540, + 581, + 606, + 581, + 606, + 609, + 540, + 609 + ], + "score": 0.77, + "latex": "\\epsilon > 0" + }, + { + "category_id": 13, + "poly": [ + 995, + 791, + 1037, + 791, + 1037, + 820, + 995, + 820 + ], + "score": 0.77, + "latex": "S A" + }, + { + "category_id": 13, + "poly": [ + 921, + 1194, + 946, + 1194, + 946, + 1220, + 921, + 1220 + ], + "score": 0.76, + "latex": "T" + }, + { + "category_id": 13, + "poly": [ + 1042, + 580, + 1107, + 580, + 1107, + 609, + 1042, + 609 + ], + "score": 0.76, + "latex": "1 - \\delta" + }, + { + "category_id": 13, + "poly": [ + 353, + 1623, + 368, + 1623, + 368, + 1649, + 353, + 1649 + ], + "score": 0.75, + "latex": "t" + }, + { + "category_id": 13, + "poly": [ + 727, + 1857, + 740, + 1857, + 740, + 1878, + 727, + 1878 + ], + "score": 0.75, + "latex": "\\epsilon" + }, + { + "category_id": 13, + "poly": [ + 1100, + 299, + 1114, + 299, + 1114, + 324, + 1100, + 324 + ], + "score": 0.75, + "latex": "t" + }, + { + "category_id": 13, + "poly": [ + 1133, + 1624, + 1147, + 1624, + 1147, + 1648, + 1133, + 1648 + ], + "score": 0.74, + "latex": "t" + }, + { + "category_id": 13, + "poly": [ + 438, + 1715, + 452, + 1715, + 452, + 1741, + 438, + 1741 + ], + "score": 0.74, + "latex": "t" + }, + { + "category_id": 13, + "poly": [ + 547, + 1425, + 561, + 1425, + 561, + 1449, + 547, + 1449 + ], + "score": 0.72, + "latex": "t" + }, + { + "category_id": 13, + "poly": [ + 298, + 1428, + 312, + 1428, + 312, + 1449, + 298, + 1449 + ], + "score": 0.67, + "latex": "\\epsilon" + }, + { + "category_id": 13, + "poly": [ + 683, + 1685, + 697, + 1685, + 697, + 1709, + 683, + 1709 + ], + "score": 0.64, + "latex": "t" + }, + { + "category_id": 13, + "poly": [ + 616, + 579, + 844, + 579, + 844, + 613, + 616, + 613 + ], + "score": 0.6, + "latex": "\\delta > 0 , 1 / 2 < \\gamma < 1" + }, + { + "category_id": 13, + "poly": [ + 998, + 617, + 1012, + 617, + 1012, + 637, + 998, + 637 + ], + "score": 0.55, + "latex": "\\epsilon" + }, + { + "category_id": 13, + "poly": [ + 719, + 298, + 734, + 298, + 734, + 325, + 719, + 325 + ], + "score": 0.48, + "latex": "t" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 73.0, + 817.0, + 73.0, + 817.0, + 108.0, + 295.0, + 108.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 467.0, + 854.0, + 467.0, + 854.0, + 509.0, + 292.0, + 509.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 838.0, + 2086.0, + 862.0, + 2086.0, + 862.0, + 2118.0, + 838.0, + 2118.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 1496.0, + 1405.0, + 1496.0, + 1405.0, + 1533.0, + 294.0, + 1533.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 1527.0, + 1404.0, + 1527.0, + 1404.0, + 1564.0, + 292.0, + 1564.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 1558.0, + 296.0, + 1558.0, + 296.0, + 1596.0, + 292.0, + 1596.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 317.0, + 1558.0, + 419.0, + 1558.0, + 419.0, + 1596.0, + 317.0, + 1596.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 442.0, + 1558.0, + 996.0, + 1558.0, + 996.0, + 1596.0, + 442.0, + 1596.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1017.0, + 1558.0, + 1099.0, + 1558.0, + 1099.0, + 1596.0, + 1017.0, + 1596.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1168.0, + 1558.0, + 1404.0, + 1558.0, + 1404.0, + 1596.0, + 1168.0, + 1596.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 1590.0, + 1406.0, + 1590.0, + 1406.0, + 1625.0, + 294.0, + 1625.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 1619.0, + 352.0, + 1619.0, + 352.0, + 1656.0, + 294.0, + 1656.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 369.0, + 1619.0, + 587.0, + 1619.0, + 587.0, + 1656.0, + 369.0, + 1656.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 615.0, + 1619.0, + 802.0, + 1619.0, + 802.0, + 1656.0, + 615.0, + 1656.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 831.0, + 1619.0, + 1132.0, + 1619.0, + 1132.0, + 1656.0, + 831.0, + 1656.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1148.0, + 1619.0, + 1406.0, + 1619.0, + 1406.0, + 1656.0, + 1148.0, + 1656.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 1652.0, + 1062.0, + 1652.0, + 1062.0, + 1686.0, + 292.0, + 1686.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1090.0, + 1652.0, + 1406.0, + 1652.0, + 1406.0, + 1686.0, + 1090.0, + 1686.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 291.0, + 1680.0, + 297.0, + 1680.0, + 297.0, + 1717.0, + 291.0, + 1717.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 325.0, + 1680.0, + 682.0, + 1680.0, + 682.0, + 1717.0, + 325.0, + 1717.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 698.0, + 1680.0, + 1407.0, + 1680.0, + 1407.0, + 1717.0, + 698.0, + 1717.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 1712.0, + 437.0, + 1712.0, + 437.0, + 1748.0, + 294.0, + 1748.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 453.0, + 1712.0, + 1407.0, + 1712.0, + 1407.0, + 1748.0, + 453.0, + 1748.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 1743.0, + 1406.0, + 1743.0, + 1406.0, + 1778.0, + 294.0, + 1778.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 1770.0, + 599.0, + 1770.0, + 599.0, + 1812.0, + 294.0, + 1812.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 1131.0, + 1408.0, + 1131.0, + 1408.0, + 1165.0, + 294.0, + 1165.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 289.0, + 1158.0, + 823.0, + 1158.0, + 823.0, + 1198.0, + 289.0, + 1198.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 854.0, + 1158.0, + 1216.0, + 1158.0, + 1216.0, + 1198.0, + 854.0, + 1198.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1246.0, + 1158.0, + 1274.0, + 1158.0, + 1274.0, + 1198.0, + 1246.0, + 1198.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1362.0, + 1158.0, + 1406.0, + 1158.0, + 1406.0, + 1198.0, + 1362.0, + 1198.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 1191.0, + 920.0, + 1191.0, + 920.0, + 1228.0, + 293.0, + 1228.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 947.0, + 1191.0, + 1152.0, + 1191.0, + 1152.0, + 1228.0, + 947.0, + 1228.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1182.0, + 1191.0, + 1405.0, + 1191.0, + 1405.0, + 1228.0, + 1182.0, + 1228.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 1223.0, + 618.0, + 1223.0, + 618.0, + 1258.0, + 294.0, + 1258.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 644.0, + 1223.0, + 1063.0, + 1223.0, + 1063.0, + 1258.0, + 644.0, + 1258.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1094.0, + 1223.0, + 1406.0, + 1223.0, + 1406.0, + 1258.0, + 1094.0, + 1258.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 1249.0, + 1405.0, + 1249.0, + 1405.0, + 1290.0, + 292.0, + 1290.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 1282.0, + 1405.0, + 1282.0, + 1405.0, + 1319.0, + 293.0, + 1319.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 1313.0, + 679.0, + 1313.0, + 679.0, + 1352.0, + 294.0, + 1352.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 929.0, + 1404.0, + 929.0, + 1404.0, + 966.0, + 294.0, + 966.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 961.0, + 1404.0, + 961.0, + 1404.0, + 996.0, + 294.0, + 996.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 291.0, + 985.0, + 348.0, + 985.0, + 348.0, + 1031.0, + 291.0, + 1031.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 374.0, + 985.0, + 1118.0, + 985.0, + 1118.0, + 1031.0, + 374.0, + 1031.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1149.0, + 985.0, + 1209.0, + 985.0, + 1209.0, + 1031.0, + 1149.0, + 1031.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1398.0, + 985.0, + 1408.0, + 985.0, + 1408.0, + 1031.0, + 1398.0, + 1031.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 1022.0, + 1406.0, + 1022.0, + 1406.0, + 1059.0, + 292.0, + 1059.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 1054.0, + 1406.0, + 1054.0, + 1406.0, + 1088.0, + 292.0, + 1088.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 1086.0, + 379.0, + 1086.0, + 379.0, + 1119.0, + 294.0, + 1119.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 1820.0, + 1406.0, + 1820.0, + 1406.0, + 1854.0, + 295.0, + 1854.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 1850.0, + 486.0, + 1850.0, + 486.0, + 1885.0, + 295.0, + 1885.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 516.0, + 1850.0, + 683.0, + 1850.0, + 683.0, + 1885.0, + 516.0, + 1885.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 698.0, + 1850.0, + 726.0, + 1850.0, + 726.0, + 1885.0, + 698.0, + 1885.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 741.0, + 1850.0, + 932.0, + 1850.0, + 932.0, + 1885.0, + 741.0, + 1885.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 958.0, + 1850.0, + 1407.0, + 1850.0, + 1407.0, + 1885.0, + 958.0, + 1885.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 1878.0, + 558.0, + 1878.0, + 558.0, + 1918.0, + 292.0, + 1918.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 813.0, + 1878.0, + 890.0, + 1878.0, + 890.0, + 1918.0, + 813.0, + 1918.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1145.0, + 1878.0, + 1406.0, + 1878.0, + 1406.0, + 1918.0, + 1145.0, + 1918.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 1911.0, + 357.0, + 1911.0, + 357.0, + 1946.0, + 295.0, + 1946.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 380.0, + 1911.0, + 579.0, + 1911.0, + 579.0, + 1946.0, + 380.0, + 1946.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 682.0, + 1911.0, + 926.0, + 1911.0, + 926.0, + 1946.0, + 682.0, + 1946.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 952.0, + 1911.0, + 1405.0, + 1911.0, + 1405.0, + 1946.0, + 952.0, + 1946.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 1942.0, + 1406.0, + 1942.0, + 1406.0, + 1976.0, + 295.0, + 1976.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 1969.0, + 466.0, + 1969.0, + 466.0, + 2008.0, + 292.0, + 2008.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 699.0, + 1969.0, + 1407.0, + 1969.0, + 1407.0, + 2008.0, + 699.0, + 2008.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 2000.0, + 1250.0, + 2000.0, + 1250.0, + 2037.0, + 294.0, + 2037.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 296.0, + 227.0, + 1406.0, + 227.0, + 1406.0, + 264.0, + 296.0, + 264.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 263.0, + 393.0, + 263.0, + 393.0, + 300.0, + 295.0, + 300.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 481.0, + 263.0, + 845.0, + 263.0, + 845.0, + 300.0, + 481.0, + 300.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 933.0, + 263.0, + 943.0, + 263.0, + 943.0, + 300.0, + 933.0, + 300.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1041.0, + 263.0, + 1406.0, + 263.0, + 1406.0, + 300.0, + 1041.0, + 300.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 359.0, + 295.0, + 718.0, + 295.0, + 718.0, + 332.0, + 359.0, + 332.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 735.0, + 295.0, + 744.0, + 295.0, + 744.0, + 332.0, + 735.0, + 332.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 853.0, + 295.0, + 1099.0, + 295.0, + 1099.0, + 332.0, + 853.0, + 332.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1115.0, + 295.0, + 1222.0, + 295.0, + 1222.0, + 332.0, + 1115.0, + 332.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 322.0, + 379.0, + 322.0, + 379.0, + 363.0, + 292.0, + 363.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 400.0, + 322.0, + 1116.0, + 322.0, + 1116.0, + 363.0, + 400.0, + 363.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1292.0, + 322.0, + 1306.0, + 322.0, + 1306.0, + 363.0, + 1292.0, + 363.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1404.0, + 322.0, + 1407.0, + 322.0, + 1407.0, + 363.0, + 1404.0, + 363.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 356.0, + 345.0, + 356.0, + 345.0, + 402.0, + 292.0, + 402.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 442.0, + 356.0, + 580.0, + 356.0, + 580.0, + 402.0, + 442.0, + 402.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 608.0, + 356.0, + 658.0, + 356.0, + 658.0, + 402.0, + 608.0, + 402.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 686.0, + 356.0, + 788.0, + 356.0, + 788.0, + 402.0, + 686.0, + 402.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 852.0, + 356.0, + 1374.0, + 356.0, + 1374.0, + 402.0, + 852.0, + 402.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1401.0, + 356.0, + 1407.0, + 356.0, + 1407.0, + 402.0, + 1401.0, + 402.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 387.0, + 442.0, + 387.0, + 442.0, + 432.0, + 293.0, + 432.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 1358.0, + 1405.0, + 1358.0, + 1405.0, + 1396.0, + 292.0, + 1396.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 1387.0, + 1405.0, + 1387.0, + 1405.0, + 1430.0, + 292.0, + 1430.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 1421.0, + 297.0, + 1421.0, + 297.0, + 1458.0, + 294.0, + 1458.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 313.0, + 1421.0, + 546.0, + 1421.0, + 546.0, + 1458.0, + 313.0, + 1458.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 562.0, + 1421.0, + 674.0, + 1421.0, + 674.0, + 1458.0, + 562.0, + 1458.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 702.0, + 1421.0, + 763.0, + 1421.0, + 763.0, + 1458.0, + 702.0, + 1458.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1029.0, + 1421.0, + 1406.0, + 1421.0, + 1406.0, + 1458.0, + 1029.0, + 1458.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 1451.0, + 1038.0, + 1451.0, + 1038.0, + 1489.0, + 292.0, + 1489.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 574.0, + 539.0, + 574.0, + 539.0, + 616.0, + 294.0, + 616.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 607.0, + 574.0, + 615.0, + 574.0, + 615.0, + 616.0, + 607.0, + 616.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 845.0, + 574.0, + 1041.0, + 574.0, + 1041.0, + 616.0, + 845.0, + 616.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1108.0, + 574.0, + 1409.0, + 574.0, + 1409.0, + 616.0, + 1108.0, + 616.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 296.0, + 610.0, + 896.0, + 610.0, + 896.0, + 644.0, + 296.0, + 644.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 926.0, + 610.0, + 997.0, + 610.0, + 997.0, + 644.0, + 926.0, + 644.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1013.0, + 610.0, + 1139.0, + 610.0, + 1139.0, + 644.0, + 1013.0, + 644.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1168.0, + 610.0, + 1406.0, + 610.0, + 1406.0, + 644.0, + 1168.0, + 644.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 640.0, + 360.0, + 640.0, + 360.0, + 673.0, + 292.0, + 673.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 853.0, + 1408.0, + 853.0, + 1408.0, + 889.0, + 295.0, + 889.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 884.0, + 1408.0, + 884.0, + 1408.0, + 920.0, + 295.0, + 920.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 528.0, + 1119.0, + 528.0, + 1119.0, + 572.0, + 295.0, + 572.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 785.0, + 370.0, + 785.0, + 370.0, + 830.0, + 295.0, + 830.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 399.0, + 785.0, + 774.0, + 785.0, + 774.0, + 830.0, + 399.0, + 830.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 943.0, + 785.0, + 994.0, + 785.0, + 994.0, + 830.0, + 943.0, + 830.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1038.0, + 785.0, + 1047.0, + 785.0, + 1047.0, + 830.0, + 1038.0, + 830.0 + ], + "score": 1.0, + "text": "" + } + ], + "page_info": { + "page_no": 3, + "width": 1700, + "height": 2200 + } + }, + { + "layout_dets": [ + { + "category_id": 1, + "poly": [ + 298, + 464, + 1406, + 464, + 1406, + 564, + 298, + 564 + ], + "score": 0.969 + }, + { + "category_id": 1, + "poly": [ + 297, + 228, + 1405, + 228, + 1405, + 324, + 297, + 324 + ], + "score": 0.968 + }, + { + "category_id": 8, + "poly": [ + 402, + 1718, + 1297, + 1718, + 1297, + 1909, + 402, + 1909 + ], + "score": 0.968 + }, + { + "category_id": 8, + "poly": [ + 350, + 579, + 1349, + 579, + 1349, + 1028, + 350, + 1028 + ], + "score": 0.967 + }, + { + "category_id": 1, + "poly": [ + 300, + 1616, + 1404, + 1616, + 1404, + 1703, + 300, + 1703 + ], + "score": 0.967 + }, + { + "category_id": 8, + "poly": [ + 565, + 1207, + 1131, + 1207, + 1131, + 1303, + 565, + 1303 + ], + "score": 0.954 + }, + { + "category_id": 1, + "poly": [ + 297, + 1114, + 1399, + 1114, + 1399, + 1191, + 297, + 1191 + ], + "score": 0.949 + }, + { + "category_id": 1, + "poly": [ + 297, + 1516, + 1404, + 1516, + 1404, + 1581, + 297, + 1581 + ], + "score": 0.939 + }, + { + "category_id": 1, + "poly": [ + 297, + 1378, + 1088, + 1378, + 1088, + 1437, + 297, + 1437 + ], + "score": 0.933 + }, + { + "category_id": 8, + "poly": [ + 764, + 1456, + 934, + 1456, + 934, + 1504, + 764, + 1504 + ], + "score": 0.93 + }, + { + "category_id": 1, + "poly": [ + 295, + 1046, + 1298, + 1046, + 1298, + 1095, + 295, + 1095 + ], + "score": 0.925 + }, + { + "category_id": 1, + "poly": [ + 295, + 1332, + 1202, + 1332, + 1202, + 1369, + 295, + 1369 + ], + "score": 0.925 + }, + { + "category_id": 2, + "poly": [ + 298, + 74, + 817, + 74, + 817, + 106, + 298, + 106 + ], + "score": 0.916 + }, + { + "category_id": 0, + "poly": [ + 297, + 360, + 886, + 360, + 886, + 393, + 297, + 393 + ], + "score": 0.909 + }, + { + "category_id": 1, + "poly": [ + 295, + 416, + 1344, + 416, + 1344, + 453, + 295, + 453 + ], + "score": 0.903 + }, + { + "category_id": 9, + "poly": [ + 1364, + 1467, + 1401, + 1467, + 1401, + 1499, + 1364, + 1499 + ], + "score": 0.882 + }, + { + "category_id": 1, + "poly": [ + 289, + 1924, + 1285, + 1924, + 1285, + 1974, + 289, + 1974 + ], + "score": 0.881 + }, + { + "category_id": 9, + "poly": [ + 1364, + 942, + 1402, + 942, + 1402, + 973, + 1364, + 973 + ], + "score": 0.866 + }, + { + "category_id": 9, + "poly": [ + 1364, + 1239, + 1401, + 1239, + 1401, + 1270, + 1364, + 1270 + ], + "score": 0.864 + }, + { + "category_id": 2, + "poly": [ + 1374, + 1999, + 1404, + 1999, + 1404, + 2028, + 1374, + 2028 + ], + "score": 0.779 + }, + { + "category_id": 2, + "poly": [ + 840, + 2087, + 860, + 2087, + 860, + 2113, + 840, + 2113 + ], + "score": 0.742 + }, + { + "category_id": 1, + "poly": [ + 285, + 1986, + 1324, + 1986, + 1324, + 2044, + 285, + 2044 + ], + "score": 0.529 + }, + { + "category_id": 8, + "poly": [ + 285, + 1986, + 1324, + 1986, + 1324, + 2044, + 285, + 2044 + ], + "score": 0.502 + }, + { + "category_id": 2, + "poly": [ + 840, + 2087, + 860, + 2087, + 860, + 2113, + 840, + 2113 + ], + "score": 0.142 + }, + { + "category_id": 13, + "poly": [ + 703, + 527, + 933, + 527, + 933, + 561, + 703, + 561 + ], + "score": 0.94, + "latex": "V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } )" + }, + { + "category_id": 14, + "poly": [ + 346, + 582, + 1348, + 582, + 1348, + 1034, + 346, + 1034 + ], + "score": 0.94, + "latex": "\\begin{array} { r l } & { \\quad V ^ { * } ( s _ { t } ) - V ^ { \\pi } ( s _ { t } ) } \\\\ & { = V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) + Q ^ { * } ( s _ { t } , a _ { t } ) - V ^ { \\pi } ( s _ { t } ) } \\\\ & { = V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) + \\gamma \\mathbb { P } ( V ^ { * } - V ^ { \\pi } ) ( s _ { t } , \\pi _ { t } ( s _ { t } ) ) } \\\\ & { = V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) + \\gamma \\sum _ { s + 1 } ^ { \\infty } p ( s _ { t + 1 } | s _ { t } , \\pi _ { t } ( s _ { t } ) ) \\cdot [ V ^ { * } ( s _ { t + 1 } ) - Q ^ { * } ( s _ { t + 1 } , a _ { t + 1 } ) ] + } \\\\ & { \\quad \\Big . \\Big . \\Big . \\Big . \\Big . \\Big . } \\\\ & { \\quad \\quad \\Big . \\gamma _ { s + 1 , s ^ { * } + 2 } \\mathrm { ~ } p ( s _ { t + 2 } | s _ { t + 1 } , \\pi _ { t + 1 } ( s _ { t + 1 } ) ) \\cdot p ( s _ { t + 1 } | s _ { t } , \\pi _ { t } ( s _ { t } ) ) \\big [ V ^ { * } ( s _ { t + 2 } ) - Q ^ { * } ( s _ { t + 2 } , a _ { t + 2 } ) \\Big ] } \\\\ & { \\quad \\quad \\cdot \\dots } \\\\ & { \\le \\epsilon _ { 2 } + \\displaystyle \\sum _ { s ^ { \\prime } = s ^ { \\prime } } p ( t r a _ { t } ) \\cdot [ \\frac { n - 1 } { \\lambda _ { 2 } } \\gamma ^ { 2 } \\Delta _ { t + 2 } ] , } \\\\ & { \\quad \\quad \\pi _ { s \\lambda ^ { ( 2 ) } ( L ) } ^ { R , a } } \\end{array}" + }, + { + "category_id": 13, + "poly": [ + 738, + 1046, + 847, + 1046, + 847, + 1096, + 738, + 1096 + ], + "score": 0.94, + "latex": "\\frac { \\gamma ^ { R } } { 1 - \\gamma } \\leq \\epsilon _ { 2 }" + }, + { + "category_id": 13, + "poly": [ + 863, + 1924, + 1125, + 1924, + 1125, + 1975, + 863, + 1975 + ], + "score": 0.93, + "latex": "\\begin{array} { r } { \\sum _ { i = 1 } ^ { \\infty } \\frac { \\gamma ^ { i - 1 } } { i } = \\frac { 1 } { \\gamma } \\ln \\frac { 1 } { 1 - \\gamma } } \\end{array}" + }, + { + "category_id": 13, + "poly": [ + 1124, + 1115, + 1292, + 1115, + 1292, + 1157, + 1124, + 1157 + ], + "score": 0.93, + "latex": "\\left( \\Delta _ { t ^ { \\prime } } \\right) _ { t \\leq t ^ { \\prime } < t + R }" + }, + { + "category_id": 13, + "poly": [ + 1269, + 1616, + 1404, + 1616, + 1404, + 1660, + 1269, + 1660 + ], + "score": 0.93, + "latex": "E [ X _ { t } ^ { ( i ) } ] \\ \\leq" + }, + { + "category_id": 14, + "poly": [ + 564, + 1206, + 1134, + 1206, + 1134, + 1303, + 564, + 1303 + ], + "score": 0.93, + "latex": "V ^ { \\ast } ( s _ { t } ) - V ^ { \\pi _ { t } } ( s _ { t } ) \\leq \\epsilon _ { 2 } + E _ { t r a j } \\left[ \\sum _ { i = 1 } ^ { R } \\gamma ^ { i - 1 } X _ { t } ^ { ( i ) } \\right] ." + }, + { + "category_id": 13, + "poly": [ + 297, + 525, + 602, + 525, + 602, + 568, + 297, + 568 + ], + "score": 0.93, + "latex": "\\begin{array} { r } { R : = \\lceil \\ln \\frac { 1 } { \\epsilon _ { 2 } ( 1 - \\gamma ) } / ( 1 - \\gamma ) \\rceil } \\end{array}" + }, + { + "category_id": 13, + "poly": [ + 298, + 1656, + 458, + 1656, + 458, + 1702, + 298, + 1702 + ], + "score": 0.93, + "latex": "E [ X _ { t } ^ { ( 2 ^ { \\lfloor \\log _ { 2 } i \\rfloor } ) } ]" + }, + { + "category_id": 13, + "poly": [ + 502, + 1617, + 557, + 1617, + 557, + 1659, + 502, + 1659 + ], + "score": 0.93, + "latex": "X _ { t } ^ { ( i ) }" + }, + { + "category_id": 14, + "poly": [ + 401, + 1716, + 1296, + 1716, + 1296, + 1911, + 401, + 1911 + ], + "score": 0.93, + "latex": "\\begin{array} { r l } & { E \\left[ \\displaystyle \\sum _ { i = 1 } ^ { R } \\gamma ^ { i - 1 } X _ { t } ^ { ( i ) } \\right] = \\displaystyle \\sum _ { i = 1 } ^ { R } \\gamma ^ { i - 1 } E [ X _ { t } ^ { ( i ) } ] \\leq \\displaystyle \\sum _ { i = 1 } ^ { R } \\gamma ^ { i - 1 } E [ X _ { t } ^ { ( 2 ^ { \\lfloor \\log _ { 2 } i \\rfloor } ) } ] } \\\\ & { \\leq \\displaystyle \\sum _ { i = 1 } ^ { R } \\gamma ^ { i - 1 } 2 ^ { - \\lfloor \\log _ { 2 } i \\rfloor - 2 } \\epsilon _ { 2 } \\left( \\ln \\frac { 1 } { 1 - \\gamma } \\right) ^ { - 1 } \\leq \\displaystyle \\sum _ { i = 1 } ^ { R } \\frac { \\gamma ^ { i - 1 } } { i } \\epsilon _ { 2 } \\left( \\ln \\frac { 1 } { 1 - \\gamma } \\right) ^ { - 1 } \\leq 2 \\epsilon _ { 2 } , } \\end{array}" + }, + { + "category_id": 13, + "poly": [ + 586, + 1153, + 753, + 1153, + 753, + 1192, + 586, + 1192 + ], + "score": 0.93, + "latex": "\\left( \\Delta _ { t ^ { \\prime } } \\right) _ { t \\leq t ^ { \\prime } < t + R }" + }, + { + "category_id": 13, + "poly": [ + 500, + 1376, + 783, + 1376, + 783, + 1438, + 500, + 1438 + ], + "score": 0.92, + "latex": "\\begin{array} { r } { \\xi _ { i } : = \\frac { 1 } { 2 ^ { i + 2 } } \\epsilon _ { 2 } \\left( \\ln \\frac { 1 } { 1 - \\gamma } \\right) ^ { - 1 } } \\end{array}" + }, + { + "category_id": 13, + "poly": [ + 1093, + 1334, + 1195, + 1334, + 1195, + 1368, + 1093, + 1368 + ], + "score": 0.92, + "latex": "\\epsilon _ { 2 } = \\epsilon / 3" + }, + { + "category_id": 13, + "poly": [ + 1235, + 499, + 1316, + 499, + 1316, + 528, + 1235, + 528 + ], + "score": 0.91, + "latex": "\\epsilon _ { 2 } > 0" + }, + { + "category_id": 13, + "poly": [ + 732, + 1667, + 881, + 1667, + 881, + 1702, + 732, + 1702 + ], + "score": 0.91, + "latex": "1 / 2 < \\gamma < 1" + }, + { + "category_id": 13, + "poly": [ + 1291, + 1516, + 1404, + 1516, + 1404, + 1551, + 1291, + 1551 + ], + "score": 0.91, + "latex": "V ^ { \\ast } ( s _ { t } ) -" + }, + { + "category_id": 13, + "poly": [ + 298, + 1548, + 438, + 1548, + 438, + 1581, + 298, + 1581 + ], + "score": 0.91, + "latex": "V ^ { \\pi _ { t } } ( s _ { t } ) \\leq \\epsilon" + }, + { + "category_id": 13, + "poly": [ + 1346, + 1110, + 1400, + 1110, + 1400, + 1151, + 1346, + 1151 + ], + "score": 0.91, + "latex": "X _ { t } ^ { ( i ) }" + }, + { + "category_id": 13, + "poly": [ + 1176, + 1933, + 1273, + 1933, + 1273, + 1969, + 1176, + 1969 + ], + "score": 0.91, + "latex": "\\gamma > 1 / 2" + }, + { + "category_id": 14, + "poly": [ + 763, + 1452, + 936, + 1452, + 936, + 1502, + 763, + 1502 + ], + "score": 0.9, + "latex": "E [ X _ { t } ^ { ( 2 ^ { i } ) } ] \\leq \\xi _ { i } ." + }, + { + "category_id": 13, + "poly": [ + 880, + 1392, + 1077, + 1392, + 1077, + 1428, + 880, + 1428 + ], + "score": 0.88, + "latex": "0 \\leq i \\leq \\lfloor \\log _ { 2 } R \\rfloor" + }, + { + "category_id": 13, + "poly": [ + 972, + 528, + 1007, + 528, + 1007, + 558, + 972, + 558 + ], + "score": 0.88, + "latex": "\\Delta _ { t }" + }, + { + "category_id": 13, + "poly": [ + 663, + 1987, + 1322, + 1987, + 1322, + 2045, + 663, + 2045 + ], + "score": 0.87, + "latex": "\\begin{array} { r } { V ^ { \\ast } ( s _ { t } ) - V ^ { \\pi _ { t } } ( s _ { t } ) \\leq \\epsilon _ { 2 } + E \\left[ \\sum _ { i = 1 } ^ { R } \\gamma ^ { i - 1 } X _ { t } ^ { ( i ) } \\right] \\leq 3 \\epsilon _ { 2 } = \\epsilon . } \\end{array}" + }, + { + "category_id": 13, + "poly": [ + 840, + 1124, + 866, + 1124, + 866, + 1149, + 840, + 1149 + ], + "score": 0.85, + "latex": "s _ { t }" + }, + { + "category_id": 13, + "poly": [ + 959, + 1523, + 988, + 1523, + 988, + 1548, + 959, + 1548 + ], + "score": 0.85, + "latex": "\\pi _ { t }" + }, + { + "category_id": 13, + "poly": [ + 628, + 502, + 656, + 502, + 656, + 528, + 628, + 528 + ], + "score": 0.85, + "latex": "\\pi _ { t }" + }, + { + "category_id": 13, + "poly": [ + 1268, + 1059, + 1290, + 1059, + 1290, + 1084, + 1268, + 1084 + ], + "score": 0.84, + "latex": "R" + }, + { + "category_id": 13, + "poly": [ + 425, + 471, + 451, + 471, + 451, + 497, + 425, + 497 + ], + "score": 0.83, + "latex": "s _ { t }" + }, + { + "category_id": 13, + "poly": [ + 1213, + 1524, + 1239, + 1524, + 1239, + 1548, + 1213, + 1548 + ], + "score": 0.83, + "latex": "s _ { t }" + }, + { + "category_id": 13, + "poly": [ + 1150, + 473, + 1175, + 473, + 1175, + 497, + 1150, + 497 + ], + "score": 0.83, + "latex": "s _ { t }" + }, + { + "category_id": 13, + "poly": [ + 665, + 1119, + 689, + 1119, + 689, + 1145, + 665, + 1145 + ], + "score": 0.82, + "latex": "R" + }, + { + "category_id": 13, + "poly": [ + 837, + 468, + 861, + 468, + 861, + 494, + 837, + 494 + ], + "score": 0.8, + "latex": "R" + }, + { + "category_id": 13, + "poly": [ + 1009, + 1338, + 1023, + 1338, + 1023, + 1362, + 1009, + 1362 + ], + "score": 0.77, + "latex": "t" + }, + { + "category_id": 13, + "poly": [ + 734, + 1341, + 748, + 1341, + 748, + 1362, + 734, + 1362 + ], + "score": 0.76, + "latex": "\\epsilon" + }, + { + "category_id": 13, + "poly": [ + 962, + 500, + 975, + 500, + 975, + 525, + 962, + 525 + ], + "score": 0.75, + "latex": "t" + }, + { + "category_id": 13, + "poly": [ + 371, + 1156, + 384, + 1156, + 384, + 1181, + 371, + 1181 + ], + "score": 0.74, + "latex": "i" + }, + { + "category_id": 13, + "poly": [ + 1094, + 1628, + 1108, + 1628, + 1108, + 1653, + 1094, + 1653 + ], + "score": 0.73, + "latex": "i" + }, + { + "category_id": 13, + "poly": [ + 1014, + 503, + 1029, + 503, + 1029, + 524, + 1014, + 524 + ], + "score": 0.72, + "latex": "\\epsilon" + }, + { + "category_id": 13, + "poly": [ + 1321, + 423, + 1334, + 423, + 1334, + 447, + 1321, + 447 + ], + "score": 0.71, + "latex": "t" + }, + { + "category_id": 13, + "poly": [ + 551, + 1520, + 566, + 1520, + 566, + 1545, + 551, + 1545 + ], + "score": 0.7, + "latex": "^ { l }" + }, + { + "category_id": 13, + "poly": [ + 1017, + 1524, + 1031, + 1524, + 1031, + 1545, + 1017, + 1545 + ], + "score": 0.68, + "latex": "\\epsilon" + }, + { + "category_id": 14, + "poly": [ + 354, + 903, + 816, + 903, + 816, + 1028, + 354, + 1028 + ], + "score": 0.68, + "latex": "\\leq \\epsilon _ { 2 } + \\sum _ { \\stackrel { t r a j \\in \\epsilon } { \\mathrm { T R A J } ( R ) } } p ( t r a j ) \\cdot \\left[ \\sum _ { j = 0 } ^ { R - 1 } \\gamma ^ { j } \\Delta _ { t + j } \\right] ," + }, + { + "category_id": 13, + "poly": [ + 711, + 368, + 725, + 368, + 725, + 389, + 711, + 389 + ], + "score": 0.67, + "latex": "\\epsilon" + }, + { + "category_id": 13, + "poly": [ + 568, + 468, + 608, + 468, + 608, + 498, + 568, + 498 + ], + "score": 0.66, + "latex": "( R )" + }, + { + "category_id": 13, + "poly": [ + 1046, + 427, + 1059, + 427, + 1059, + 447, + 1046, + 447 + ], + "score": 0.65, + "latex": "\\epsilon" + }, + { + "category_id": 13, + "poly": [ + 298, + 268, + 312, + 268, + 312, + 289, + 298, + 289 + ], + "score": 0.64, + "latex": "\\epsilon" + }, + { + "category_id": 13, + "poly": [ + 822, + 1521, + 836, + 1521, + 836, + 1546, + 822, + 1546 + ], + "score": 0.51, + "latex": "t" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 72.0, + 817.0, + 72.0, + 817.0, + 109.0, + 295.0, + 109.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 360.0, + 710.0, + 360.0, + 710.0, + 396.0, + 295.0, + 396.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 726.0, + 360.0, + 887.0, + 360.0, + 887.0, + 396.0, + 726.0, + 396.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1380.0, + 2004.0, + 1402.0, + 2004.0, + 1402.0, + 2027.0, + 1380.0, + 2027.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 839.0, + 2086.0, + 860.0, + 2086.0, + 860.0, + 2119.0, + 839.0, + 2119.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 839.0, + 2086.0, + 860.0, + 2086.0, + 860.0, + 2119.0, + 839.0, + 2119.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 461.0, + 424.0, + 461.0, + 424.0, + 504.0, + 292.0, + 504.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 452.0, + 461.0, + 567.0, + 461.0, + 567.0, + 504.0, + 452.0, + 504.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 609.0, + 461.0, + 836.0, + 461.0, + 836.0, + 504.0, + 609.0, + 504.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 862.0, + 461.0, + 1149.0, + 461.0, + 1149.0, + 504.0, + 862.0, + 504.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1176.0, + 461.0, + 1406.0, + 461.0, + 1406.0, + 504.0, + 1176.0, + 504.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 496.0, + 627.0, + 496.0, + 627.0, + 531.0, + 293.0, + 531.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 657.0, + 496.0, + 961.0, + 496.0, + 961.0, + 531.0, + 657.0, + 531.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 976.0, + 496.0, + 1013.0, + 496.0, + 1013.0, + 531.0, + 976.0, + 531.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1030.0, + 496.0, + 1234.0, + 496.0, + 1234.0, + 531.0, + 1030.0, + 531.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1317.0, + 496.0, + 1404.0, + 496.0, + 1404.0, + 531.0, + 1317.0, + 531.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 522.0, + 296.0, + 522.0, + 296.0, + 573.0, + 292.0, + 573.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 603.0, + 522.0, + 702.0, + 522.0, + 702.0, + 573.0, + 603.0, + 573.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 934.0, + 522.0, + 971.0, + 522.0, + 971.0, + 573.0, + 934.0, + 573.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1008.0, + 522.0, + 1129.0, + 522.0, + 1129.0, + 573.0, + 1008.0, + 573.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 229.0, + 1405.0, + 229.0, + 1405.0, + 264.0, + 295.0, + 264.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 313.0, + 261.0, + 1405.0, + 261.0, + 1405.0, + 296.0, + 313.0, + 296.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 291.0, + 465.0, + 291.0, + 465.0, + 323.0, + 295.0, + 323.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 288.0, + 1609.0, + 501.0, + 1609.0, + 501.0, + 1667.0, + 288.0, + 1667.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 558.0, + 1609.0, + 1093.0, + 1609.0, + 1093.0, + 1667.0, + 558.0, + 1667.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1109.0, + 1609.0, + 1268.0, + 1609.0, + 1268.0, + 1667.0, + 1109.0, + 1667.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1405.0, + 1609.0, + 1409.0, + 1609.0, + 1409.0, + 1667.0, + 1405.0, + 1667.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 275.0, + 1635.0, + 297.0, + 1635.0, + 297.0, + 1719.0, + 275.0, + 1719.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 459.0, + 1635.0, + 731.0, + 1635.0, + 731.0, + 1719.0, + 459.0, + 1719.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 882.0, + 1635.0, + 910.0, + 1635.0, + 910.0, + 1719.0, + 882.0, + 1719.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 288.0, + 1107.0, + 664.0, + 1107.0, + 664.0, + 1163.0, + 288.0, + 1163.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 690.0, + 1107.0, + 839.0, + 1107.0, + 839.0, + 1163.0, + 690.0, + 1163.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 867.0, + 1107.0, + 1123.0, + 1107.0, + 1123.0, + 1163.0, + 867.0, + 1163.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1293.0, + 1107.0, + 1345.0, + 1107.0, + 1345.0, + 1163.0, + 1293.0, + 1163.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1401.0, + 1107.0, + 1405.0, + 1107.0, + 1405.0, + 1163.0, + 1401.0, + 1163.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 1148.0, + 370.0, + 1148.0, + 370.0, + 1197.0, + 292.0, + 1197.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 385.0, + 1148.0, + 585.0, + 1148.0, + 585.0, + 1197.0, + 385.0, + 1197.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 754.0, + 1148.0, + 1118.0, + 1148.0, + 1118.0, + 1197.0, + 754.0, + 1197.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 1510.0, + 550.0, + 1510.0, + 550.0, + 1556.0, + 292.0, + 1556.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 567.0, + 1510.0, + 821.0, + 1510.0, + 821.0, + 1556.0, + 567.0, + 1556.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 837.0, + 1510.0, + 958.0, + 1510.0, + 958.0, + 1556.0, + 837.0, + 1556.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 989.0, + 1510.0, + 1016.0, + 1510.0, + 1016.0, + 1556.0, + 989.0, + 1556.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1032.0, + 1510.0, + 1212.0, + 1510.0, + 1212.0, + 1556.0, + 1032.0, + 1556.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1240.0, + 1510.0, + 1290.0, + 1510.0, + 1290.0, + 1556.0, + 1240.0, + 1556.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 1539.0, + 297.0, + 1539.0, + 297.0, + 1588.0, + 293.0, + 1588.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 439.0, + 1539.0, + 454.0, + 1539.0, + 454.0, + 1588.0, + 439.0, + 1588.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 286.0, + 1373.0, + 499.0, + 1373.0, + 499.0, + 1440.0, + 286.0, + 1440.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 784.0, + 1373.0, + 879.0, + 1373.0, + 879.0, + 1440.0, + 784.0, + 1440.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1078.0, + 1373.0, + 1096.0, + 1373.0, + 1096.0, + 1440.0, + 1078.0, + 1440.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 1026.0, + 737.0, + 1026.0, + 737.0, + 1115.0, + 292.0, + 1115.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 848.0, + 1026.0, + 1267.0, + 1026.0, + 1267.0, + 1115.0, + 848.0, + 1115.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1291.0, + 1026.0, + 1317.0, + 1026.0, + 1317.0, + 1115.0, + 1291.0, + 1115.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 1329.0, + 733.0, + 1329.0, + 733.0, + 1374.0, + 292.0, + 1374.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 749.0, + 1329.0, + 1008.0, + 1329.0, + 1008.0, + 1374.0, + 749.0, + 1374.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1024.0, + 1329.0, + 1092.0, + 1329.0, + 1092.0, + 1374.0, + 1024.0, + 1374.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1196.0, + 1329.0, + 1207.0, + 1329.0, + 1207.0, + 1374.0, + 1196.0, + 1374.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 412.0, + 1045.0, + 412.0, + 1045.0, + 459.0, + 292.0, + 459.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1060.0, + 412.0, + 1320.0, + 412.0, + 1320.0, + 459.0, + 1060.0, + 459.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1335.0, + 412.0, + 1347.0, + 412.0, + 1347.0, + 459.0, + 1335.0, + 459.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 285.0, + 1914.0, + 862.0, + 1914.0, + 862.0, + 1988.0, + 285.0, + 1988.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1126.0, + 1914.0, + 1175.0, + 1914.0, + 1175.0, + 1988.0, + 1126.0, + 1988.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1274.0, + 1914.0, + 1293.0, + 1914.0, + 1293.0, + 1988.0, + 1274.0, + 1988.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 288.0, + 1979.0, + 662.0, + 1979.0, + 662.0, + 2048.0, + 288.0, + 2048.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1323.0, + 1979.0, + 1334.0, + 1979.0, + 1334.0, + 2048.0, + 1323.0, + 2048.0 + ], + "score": 1.0, + "text": "" + } + ], + "page_info": { + "page_no": 4, + "width": 1700, + "height": 2200 + } + }, + { + "layout_dets": [ + { + "category_id": 1, + "poly": [ + 296, + 855, + 1406, + 855, + 1406, + 1014, + 296, + 1014 + ], + "score": 0.977 + }, + { + "category_id": 1, + "poly": [ + 296, + 1107, + 1406, + 1107, + 1406, + 1237, + 296, + 1237 + ], + "score": 0.976 + }, + { + "category_id": 8, + "poly": [ + 520, + 1340, + 1177, + 1340, + 1177, + 1425, + 520, + 1425 + ], + "score": 0.95 + }, + { + "category_id": 1, + "poly": [ + 291, + 449, + 1408, + 449, + 1408, + 519, + 291, + 519 + ], + "score": 0.949 + }, + { + "category_id": 8, + "poly": [ + 385, + 537, + 1310, + 537, + 1310, + 630, + 385, + 630 + ], + "score": 0.949 + }, + { + "category_id": 1, + "poly": [ + 295, + 272, + 1408, + 272, + 1408, + 373, + 295, + 373 + ], + "score": 0.948 + }, + { + "category_id": 8, + "poly": [ + 691, + 775, + 1007, + 775, + 1007, + 840, + 691, + 840 + ], + "score": 0.947 + }, + { + "category_id": 8, + "poly": [ + 356, + 1716, + 1339, + 1716, + 1339, + 1812, + 356, + 1812 + ], + "score": 0.945 + }, + { + "category_id": 1, + "poly": [ + 293, + 1241, + 1403, + 1241, + 1403, + 1318, + 293, + 1318 + ], + "score": 0.945 + }, + { + "category_id": 1, + "poly": [ + 299, + 1444, + 690, + 1444, + 690, + 1480, + 299, + 1480 + ], + "score": 0.924 + }, + { + "category_id": 0, + "poly": [ + 298, + 1050, + 536, + 1050, + 536, + 1083, + 298, + 1083 + ], + "score": 0.92 + }, + { + "category_id": 1, + "poly": [ + 293, + 1546, + 1402, + 1546, + 1402, + 1616, + 293, + 1616 + ], + "score": 0.919 + }, + { + "category_id": 1, + "poly": [ + 298, + 1847, + 805, + 1847, + 805, + 1892, + 298, + 1892 + ], + "score": 0.919 + }, + { + "category_id": 2, + "poly": [ + 298, + 73, + 817, + 73, + 817, + 106, + 298, + 106 + ], + "score": 0.918 + }, + { + "category_id": 1, + "poly": [ + 293, + 720, + 1404, + 720, + 1404, + 758, + 293, + 758 + ], + "score": 0.918 + }, + { + "category_id": 1, + "poly": [ + 295, + 378, + 973, + 378, + 973, + 413, + 295, + 413 + ], + "score": 0.906 + }, + { + "category_id": 1, + "poly": [ + 290, + 1914, + 1300, + 1914, + 1300, + 1951, + 290, + 1951 + ], + "score": 0.903 + }, + { + "category_id": 1, + "poly": [ + 297, + 1503, + 1223, + 1503, + 1223, + 1538, + 297, + 1538 + ], + "score": 0.903 + }, + { + "category_id": 1, + "poly": [ + 297, + 227, + 939, + 227, + 939, + 264, + 297, + 264 + ], + "score": 0.901 + }, + { + "category_id": 1, + "poly": [ + 293, + 1624, + 1349, + 1624, + 1349, + 1662, + 293, + 1662 + ], + "score": 0.881 + }, + { + "category_id": 9, + "poly": [ + 1365, + 793, + 1400, + 793, + 1400, + 824, + 1365, + 824 + ], + "score": 0.879 + }, + { + "category_id": 9, + "poly": [ + 1364, + 1366, + 1401, + 1366, + 1401, + 1397, + 1364, + 1397 + ], + "score": 0.846 + }, + { + "category_id": 2, + "poly": [ + 839, + 2088, + 859, + 2088, + 859, + 2113, + 839, + 2113 + ], + "score": 0.815 + }, + { + "category_id": 2, + "poly": [ + 1374, + 648, + 1403, + 648, + 1403, + 678, + 1374, + 678 + ], + "score": 0.812 + }, + { + "category_id": 2, + "poly": [ + 296, + 1973, + 1411, + 1973, + 1411, + 2036, + 296, + 2036 + ], + "score": 0.812 + }, + { + "category_id": 14, + "poly": [ + 690, + 771, + 1010, + 771, + 1010, + 840, + 690, + 840 + ], + "score": 0.93, + "latex": "\\eta _ { j } \\mathrm { P r } [ X _ { t } ^ { ( 2 ^ { i } ) } > \\eta _ { j - 1 } ] > \\frac { \\xi _ { i } } { M } ." + }, + { + "category_id": 13, + "poly": [ + 914, + 723, + 1110, + 723, + 1110, + 757, + 914, + 757 + ], + "score": 0.93, + "latex": "0 \\leq i < \\lfloor \\log _ { 2 } R \\rfloor" + }, + { + "category_id": 14, + "poly": [ + 387, + 533, + 1309, + 533, + 1309, + 632, + 387, + 632 + ], + "score": 0.93, + "latex": "E \\left[ { X _ { t } ^ { ( 2 ^ { i } ) } } \\right] = \\int _ { 0 } ^ { 1 / ( 1 - \\gamma ) } \\operatorname* { P r } \\left[ { X _ { t } ^ { ( 2 ^ { i } ) } } > x \\right] d x \\le \\eta _ { 1 } + \\sum _ { j = 2 } ^ { M } \\eta _ { j } \\operatorname* { P r } [ { X _ { t } ^ { ( 2 ^ { i } ) } } > \\eta _ { j - 1 } ] \\le \\xi _ { i } ." + }, + { + "category_id": 13, + "poly": [ + 663, + 919, + 953, + 919, + 953, + 971, + 663, + 971 + ], + "score": 0.93, + "latex": "\\begin{array} { r } { \\operatorname* { P r } [ X _ { t } ^ { ( 2 ^ { i } ) } > \\eta _ { j - 1 } ] > \\frac { \\xi _ { i } } { M \\eta _ { j } } } \\end{array}" + }, + { + "category_id": 13, + "poly": [ + 1199, + 1972, + 1404, + 1972, + 1404, + 2008, + 1199, + 2008 + ], + "score": 0.93, + "latex": "2 ^ { M / 2 - 1 } > ( M + 1 )" + }, + { + "category_id": 13, + "poly": [ + 661, + 485, + 794, + 485, + 794, + 517, + 661, + 517 + ], + "score": 0.92, + "latex": "1 \\leq j \\leq M" + }, + { + "category_id": 13, + "poly": [ + 297, + 967, + 454, + 967, + 454, + 1014, + 297, + 1014 + ], + "score": 0.92, + "latex": "X _ { t } ^ { ( 2 ^ { i } ) } > \\eta _ { j - 1 }" + }, + { + "category_id": 14, + "poly": [ + 355, + 1716, + 1342, + 1716, + 1342, + 1810, + 355, + 1810 + ], + "score": 0.92, + "latex": "\\sum _ { t \\ge 1 } w _ { t } ( \\hat { Q } _ { t } - Q ^ { * } ) ( s _ { t } , a _ { t } ) \\le \\frac { C \\epsilon _ { 1 } } { 1 - \\gamma } + \\mathcal { O } \\left( \\frac { \\sqrt { w S A C \\ell ( C ) } } { ( 1 - \\gamma ) ^ { 2 . 5 } } + \\frac { w S A \\ln C } { ( 1 - \\gamma ) ^ { 3 } } \\ln \\frac { 1 } { ( 1 - \\gamma ) \\epsilon _ { 1 } } \\right) ." + }, + { + "category_id": 13, + "poly": [ + 1001, + 857, + 1080, + 857, + 1080, + 890, + 1001, + 890 + ], + "score": 0.92, + "latex": "( t , i , j )" + }, + { + "category_id": 13, + "poly": [ + 536, + 1170, + 720, + 1170, + 720, + 1208, + 536, + 1208 + ], + "score": 0.92, + "latex": "( \\hat { Q } _ { t } - Q ^ { * } ) ( s , a )" + }, + { + "category_id": 13, + "poly": [ + 929, + 1973, + 1154, + 1973, + 1154, + 2009, + 929, + 2009 + ], + "score": 0.92, + "latex": "\\xi _ { i } \\cdot 2 ^ { M / 2 } \\geq 1 / ( 1 - \\gamma )" + }, + { + "category_id": 14, + "poly": [ + 519, + 1333, + 1176, + 1333, + 1176, + 1430, + 519, + 1430 + ], + "score": 0.92, + "latex": "\\sum _ { t = 1 } ^ { t = \\infty } I \\left[ B _ { \\eta } ^ { ( t ) } \\right] \\leq \\frac { S A \\ln S A \\ln 1 / \\delta } { \\eta ^ { 2 } ( 1 - \\gamma ) ^ { 3 } } \\cdot p o l y l o g \\left( \\frac { 1 } { \\epsilon _ { 1 } } , \\frac { 1 } { 1 - \\gamma } \\right) ," + }, + { + "category_id": 13, + "poly": [ + 735, + 1626, + 825, + 1626, + 825, + 1661, + 735, + 1661 + ], + "score": 0.92, + "latex": "( w _ { t } ) _ { t \\geq 1 }" + }, + { + "category_id": 13, + "poly": [ + 458, + 1580, + 619, + 1580, + 619, + 1618, + 458, + 1618 + ], + "score": 0.92, + "latex": "\\begin{array} { r } { \\sum _ { t \\geq 1 } w _ { t } \\leq C } \\end{array}" + }, + { + "category_id": 13, + "poly": [ + 936, + 888, + 993, + 888, + 993, + 921, + 936, + 921 + ], + "score": 0.92, + "latex": "( i , j )" + }, + { + "category_id": 13, + "poly": [ + 591, + 1548, + 681, + 1548, + 681, + 1582, + 591, + 1582 + ], + "score": 0.91, + "latex": "( w _ { t } ) _ { t \\geq 1 }" + }, + { + "category_id": 13, + "poly": [ + 543, + 1626, + 618, + 1626, + 618, + 1660, + 543, + 1660 + ], + "score": 0.91, + "latex": "( C , w )" + }, + { + "category_id": 13, + "poly": [ + 1163, + 724, + 1295, + 724, + 1295, + 756, + 1163, + 756 + ], + "score": 0.91, + "latex": "2 \\leq j \\leq M" + }, + { + "category_id": 13, + "poly": [ + 712, + 1240, + 764, + 1240, + 764, + 1282, + 712, + 1282 + ], + "score": 0.91, + "latex": "{ B } _ { \\eta } ^ { ( t ) }" + }, + { + "category_id": 13, + "poly": [ + 957, + 1247, + 1272, + 1247, + 1272, + 1288, + 957, + 1288 + ], + "score": 0.91, + "latex": "\\begin{array} { r } { V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) > \\frac { \\eta } { 1 - \\gamma } } \\end{array}" + }, + { + "category_id": 13, + "poly": [ + 992, + 452, + 1203, + 452, + 1203, + 487, + 992, + 487 + ], + "score": 0.91, + "latex": "\\eta _ { M } > 1 / ( 1 - \\gamma )" + }, + { + "category_id": 13, + "poly": [ + 541, + 283, + 703, + 283, + 703, + 318, + 541, + 318 + ], + "score": 0.91, + "latex": "L = \\lfloor \\log _ { 2 } R \\rfloor" + }, + { + "category_id": 13, + "poly": [ + 371, + 1849, + 636, + 1849, + 636, + 1892, + 371, + 1892 + ], + "score": 0.9, + "latex": "\\begin{array} { r } { \\ell ( C ) = \\iota ( C ) \\ln { \\frac { 1 } { ( 1 - \\gamma ) \\epsilon _ { 1 } } } } \\end{array}" + }, + { + "category_id": 13, + "poly": [ + 1020, + 1626, + 1112, + 1626, + 1112, + 1660, + 1020, + 1660 + ], + "score": 0.9, + "latex": "1 - \\delta / 2" + }, + { + "category_id": 13, + "poly": [ + 726, + 1284, + 816, + 1284, + 816, + 1318, + 726, + 1318 + ], + "score": 0.9, + "latex": "1 - \\delta / 2" + }, + { + "category_id": 13, + "poly": [ + 849, + 1548, + 924, + 1548, + 924, + 1582, + 849, + 1582 + ], + "score": 0.9, + "latex": "( C , w )" + }, + { + "category_id": 13, + "poly": [ + 297, + 1285, + 389, + 1285, + 389, + 1317, + 297, + 1317 + ], + "score": 0.89, + "latex": "\\eta > 2 \\epsilon _ { 1 }" + }, + { + "category_id": 13, + "poly": [ + 598, + 1249, + 667, + 1249, + 667, + 1281, + 598, + 1281 + ], + "score": 0.89, + "latex": "\\eta > 0" + }, + { + "category_id": 13, + "poly": [ + 348, + 1976, + 519, + 1976, + 519, + 2008, + 348, + 2008 + ], + "score": 0.88, + "latex": "\\eta _ { M } > 1 / ( 1 - \\gamma )" + }, + { + "category_id": 13, + "poly": [ + 334, + 1580, + 396, + 1580, + 396, + 1611, + 334, + 1611 + ], + "score": 0.88, + "latex": "t \\geq 1" + }, + { + "category_id": 13, + "poly": [ + 761, + 272, + 1158, + 272, + 1158, + 329, + 761, + 329 + ], + "score": 0.87, + "latex": "\\begin{array} { r } { M = \\operatorname* { m a x } \\left\\{ \\lceil 2 \\log _ { 2 } \\frac { 1 } { \\xi _ { L } ( 1 - \\gamma ) } \\rceil , 1 0 \\right\\} } \\end{array}" + }, + { + "category_id": 13, + "poly": [ + 371, + 1446, + 411, + 1446, + 411, + 1480, + 371, + 1480 + ], + "score": 0.87, + "latex": "I [ \\cdot ]" + }, + { + "category_id": 13, + "poly": [ + 1222, + 277, + 1397, + 277, + 1397, + 321, + 1222, + 321 + ], + "score": 0.87, + "latex": "\\begin{array} { r } { \\eta _ { j } = \\frac { \\xi _ { i } } { M } \\cdot 2 ^ { j - 1 } } \\end{array}" + }, + { + "category_id": 13, + "poly": [ + 652, + 729, + 678, + 729, + 678, + 754, + 652, + 754 + ], + "score": 0.85, + "latex": "\\epsilon _ { 2 }" + }, + { + "category_id": 13, + "poly": [ + 760, + 455, + 793, + 455, + 793, + 481, + 760, + 481 + ], + "score": 0.83, + "latex": "M" + }, + { + "category_id": 13, + "poly": [ + 577, + 232, + 612, + 232, + 612, + 262, + 577, + 262 + ], + "score": 0.82, + "latex": "i , t" + }, + { + "category_id": 13, + "poly": [ + 1081, + 1549, + 1187, + 1549, + 1187, + 1580, + 1081, + 1580 + ], + "score": 0.82, + "latex": "C , w > 0" + }, + { + "category_id": 13, + "poly": [ + 468, + 2007, + 498, + 2007, + 498, + 2030, + 468, + 2030 + ], + "score": 0.8, + "latex": "M" + }, + { + "category_id": 13, + "poly": [ + 1200, + 1549, + 1361, + 1549, + 1361, + 1581, + 1200, + 1581 + ], + "score": 0.79, + "latex": "i f 0 \\le w _ { t } \\le w" + }, + { + "category_id": 13, + "poly": [ + 568, + 728, + 581, + 728, + 581, + 751, + 568, + 751 + ], + "score": 0.79, + "latex": "t" + }, + { + "category_id": 13, + "poly": [ + 389, + 325, + 823, + 325, + 823, + 373, + 389, + 373 + ], + "score": 0.75, + "latex": "\\begin{array} { r } { \\because j \\le M , \\eta _ { j } \\operatorname* { P r } [ X _ { t } ^ { ( 2 ^ { i } ) } > \\eta _ { j - 1 } ] \\le \\frac { \\xi _ { i } } { M } , } \\end{array}" + }, + { + "category_id": 13, + "poly": [ + 539, + 933, + 553, + 933, + 553, + 957, + 539, + 957 + ], + "score": 0.74, + "latex": "t" + }, + { + "category_id": 13, + "poly": [ + 1110, + 982, + 1123, + 982, + 1123, + 1006, + 1110, + 1006 + ], + "score": 0.74, + "latex": "t" + }, + { + "category_id": 13, + "poly": [ + 378, + 334, + 510, + 334, + 510, + 370, + 378, + 370 + ], + "score": 0.63, + "latex": "2 \\leq j \\leq M" + }, + { + "category_id": 13, + "poly": [ + 533, + 1251, + 547, + 1251, + 547, + 1276, + 533, + 1276 + ], + "score": 0.25, + "latex": "t" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 1046.0, + 538.0, + 1046.0, + 538.0, + 1087.0, + 293.0, + 1087.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 72.0, + 817.0, + 72.0, + 817.0, + 108.0, + 295.0, + 108.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 840.0, + 2087.0, + 861.0, + 2087.0, + 861.0, + 2117.0, + 840.0, + 2117.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1376.0, + 651.0, + 1404.0, + 651.0, + 1404.0, + 682.0, + 1376.0, + 682.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 331.0, + 1965.0, + 347.0, + 1965.0, + 347.0, + 2013.0, + 331.0, + 2013.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 520.0, + 1965.0, + 928.0, + 1965.0, + 928.0, + 2013.0, + 520.0, + 2013.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1155.0, + 1965.0, + 1198.0, + 1965.0, + 1198.0, + 2013.0, + 1155.0, + 2013.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1405.0, + 1965.0, + 1409.0, + 1965.0, + 1409.0, + 2013.0, + 1405.0, + 2013.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 297.0, + 2003.0, + 467.0, + 2003.0, + 467.0, + 2036.0, + 297.0, + 2036.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 499.0, + 2003.0, + 511.0, + 2003.0, + 511.0, + 2036.0, + 499.0, + 2036.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 855.0, + 1000.0, + 855.0, + 1000.0, + 893.0, + 294.0, + 893.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1081.0, + 855.0, + 1408.0, + 855.0, + 1408.0, + 893.0, + 1081.0, + 893.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 886.0, + 935.0, + 886.0, + 935.0, + 924.0, + 294.0, + 924.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 994.0, + 886.0, + 1404.0, + 886.0, + 1404.0, + 924.0, + 994.0, + 924.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 283.0, + 919.0, + 538.0, + 919.0, + 538.0, + 976.0, + 283.0, + 976.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 554.0, + 919.0, + 662.0, + 919.0, + 662.0, + 976.0, + 554.0, + 976.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 954.0, + 919.0, + 1405.0, + 919.0, + 1405.0, + 976.0, + 954.0, + 976.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 455.0, + 971.0, + 1109.0, + 971.0, + 1109.0, + 1018.0, + 455.0, + 1018.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1124.0, + 971.0, + 1138.0, + 971.0, + 1138.0, + 1018.0, + 1124.0, + 1018.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 288.0, + 966.0, + 378.0, + 966.0, + 378.0, + 1018.0, + 288.0, + 1018.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 1105.0, + 1409.0, + 1105.0, + 1409.0, + 1146.0, + 293.0, + 1146.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 1140.0, + 1404.0, + 1140.0, + 1404.0, + 1173.0, + 295.0, + 1173.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 1172.0, + 535.0, + 1172.0, + 535.0, + 1209.0, + 294.0, + 1209.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 721.0, + 1172.0, + 1406.0, + 1172.0, + 1406.0, + 1209.0, + 721.0, + 1209.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 1204.0, + 680.0, + 1204.0, + 680.0, + 1238.0, + 294.0, + 1238.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 296.0, + 451.0, + 759.0, + 451.0, + 759.0, + 488.0, + 296.0, + 488.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 794.0, + 451.0, + 991.0, + 451.0, + 991.0, + 488.0, + 794.0, + 488.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1204.0, + 451.0, + 1407.0, + 451.0, + 1407.0, + 488.0, + 1204.0, + 488.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 483.0, + 660.0, + 483.0, + 660.0, + 518.0, + 293.0, + 518.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 795.0, + 483.0, + 806.0, + 483.0, + 806.0, + 518.0, + 795.0, + 518.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 288.0, + 265.0, + 540.0, + 265.0, + 540.0, + 335.0, + 288.0, + 335.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 704.0, + 265.0, + 760.0, + 265.0, + 760.0, + 335.0, + 704.0, + 335.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1159.0, + 265.0, + 1221.0, + 265.0, + 1221.0, + 335.0, + 1159.0, + 335.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1398.0, + 265.0, + 1410.0, + 265.0, + 1410.0, + 335.0, + 1398.0, + 335.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 290.0, + 320.0, + 377.0, + 320.0, + 377.0, + 380.0, + 290.0, + 380.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 824.0, + 320.0, + 835.0, + 320.0, + 835.0, + 380.0, + 824.0, + 380.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 289.0, + 1231.0, + 532.0, + 1231.0, + 532.0, + 1293.0, + 289.0, + 1293.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 548.0, + 1231.0, + 597.0, + 1231.0, + 597.0, + 1293.0, + 548.0, + 1293.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 668.0, + 1231.0, + 711.0, + 1231.0, + 711.0, + 1293.0, + 668.0, + 1293.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 765.0, + 1231.0, + 956.0, + 1231.0, + 956.0, + 1293.0, + 765.0, + 1293.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1273.0, + 1231.0, + 1411.0, + 1231.0, + 1411.0, + 1293.0, + 1273.0, + 1293.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 1281.0, + 296.0, + 1281.0, + 296.0, + 1321.0, + 292.0, + 1321.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 390.0, + 1281.0, + 725.0, + 1281.0, + 725.0, + 1321.0, + 390.0, + 1321.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 817.0, + 1281.0, + 829.0, + 1281.0, + 829.0, + 1321.0, + 817.0, + 1321.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 297.0, + 1445.0, + 370.0, + 1445.0, + 370.0, + 1482.0, + 297.0, + 1482.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 412.0, + 1445.0, + 692.0, + 1445.0, + 692.0, + 1482.0, + 412.0, + 1482.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 291.0, + 1541.0, + 590.0, + 1541.0, + 590.0, + 1588.0, + 291.0, + 1588.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 682.0, + 1541.0, + 848.0, + 1541.0, + 848.0, + 1588.0, + 682.0, + 1588.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 925.0, + 1541.0, + 1080.0, + 1541.0, + 1080.0, + 1588.0, + 925.0, + 1588.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1188.0, + 1541.0, + 1199.0, + 1541.0, + 1199.0, + 1588.0, + 1188.0, + 1588.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1362.0, + 1541.0, + 1407.0, + 1541.0, + 1407.0, + 1588.0, + 1362.0, + 1588.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 1576.0, + 333.0, + 1576.0, + 333.0, + 1618.0, + 293.0, + 1618.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 397.0, + 1576.0, + 457.0, + 1576.0, + 457.0, + 1618.0, + 397.0, + 1618.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 620.0, + 1576.0, + 631.0, + 1576.0, + 631.0, + 1618.0, + 620.0, + 1618.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 284.0, + 1824.0, + 370.0, + 1824.0, + 370.0, + 1911.0, + 284.0, + 1911.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 637.0, + 1824.0, + 821.0, + 1824.0, + 821.0, + 1911.0, + 637.0, + 1911.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 717.0, + 567.0, + 717.0, + 567.0, + 761.0, + 293.0, + 761.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 582.0, + 717.0, + 651.0, + 717.0, + 651.0, + 761.0, + 582.0, + 761.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 679.0, + 717.0, + 913.0, + 717.0, + 913.0, + 761.0, + 679.0, + 761.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1111.0, + 717.0, + 1162.0, + 717.0, + 1162.0, + 761.0, + 1111.0, + 761.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1296.0, + 717.0, + 1406.0, + 717.0, + 1406.0, + 761.0, + 1296.0, + 761.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 298.0, + 378.0, + 971.0, + 378.0, + 971.0, + 414.0, + 298.0, + 414.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 1912.0, + 1301.0, + 1912.0, + 1301.0, + 1955.0, + 292.0, + 1955.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 1502.0, + 1224.0, + 1502.0, + 1224.0, + 1543.0, + 292.0, + 1543.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 221.0, + 576.0, + 221.0, + 576.0, + 272.0, + 292.0, + 272.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 613.0, + 221.0, + 942.0, + 221.0, + 942.0, + 272.0, + 613.0, + 272.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 291.0, + 1620.0, + 542.0, + 1620.0, + 542.0, + 1666.0, + 291.0, + 1666.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 619.0, + 1620.0, + 734.0, + 1620.0, + 734.0, + 1666.0, + 619.0, + 1666.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 826.0, + 1620.0, + 1019.0, + 1620.0, + 1019.0, + 1666.0, + 826.0, + 1666.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1113.0, + 1620.0, + 1352.0, + 1620.0, + 1352.0, + 1666.0, + 1113.0, + 1666.0 + ], + "score": 1.0, + "text": "" + } + ], + "page_info": { + "page_no": 5, + "width": 1700, + "height": 2200 + } + }, + { + "layout_dets": [ + { + "category_id": 1, + "poly": [ + 294, + 1128, + 1407, + 1128, + 1407, + 1315, + 294, + 1315 + ], + "score": 0.977 + }, + { + "category_id": 1, + "poly": [ + 295, + 348, + 1407, + 348, + 1407, + 516, + 295, + 516 + ], + "score": 0.975 + }, + { + "category_id": 1, + "poly": [ + 296, + 615, + 1404, + 615, + 1404, + 733, + 296, + 733 + ], + "score": 0.975 + }, + { + "category_id": 1, + "poly": [ + 295, + 1444, + 1407, + 1444, + 1407, + 1657, + 295, + 1657 + ], + "score": 0.974 + }, + { + "category_id": 8, + "poly": [ + 317, + 1669, + 1403, + 1669, + 1403, + 2033, + 317, + 2033 + ], + "score": 0.96 + }, + { + "category_id": 1, + "poly": [ + 295, + 228, + 1405, + 228, + 1405, + 299, + 295, + 299 + ], + "score": 0.951 + }, + { + "category_id": 8, + "poly": [ + 602, + 1323, + 1095, + 1323, + 1095, + 1390, + 602, + 1390 + ], + "score": 0.948 + }, + { + "category_id": 8, + "poly": [ + 408, + 521, + 1286, + 521, + 1286, + 607, + 408, + 607 + ], + "score": 0.945 + }, + { + "category_id": 8, + "poly": [ + 582, + 306, + 1119, + 306, + 1119, + 346, + 582, + 346 + ], + "score": 0.931 + }, + { + "category_id": 1, + "poly": [ + 298, + 1397, + 1077, + 1397, + 1077, + 1434, + 298, + 1434 + ], + "score": 0.925 + }, + { + "category_id": 2, + "poly": [ + 298, + 73, + 817, + 73, + 817, + 106, + 298, + 106 + ], + "score": 0.923 + }, + { + "category_id": 1, + "poly": [ + 296, + 821, + 985, + 821, + 985, + 857, + 296, + 857 + ], + "score": 0.922 + }, + { + "category_id": 0, + "poly": [ + 299, + 765, + 651, + 765, + 651, + 797, + 299, + 797 + ], + "score": 0.92 + }, + { + "category_id": 1, + "poly": [ + 297, + 1061, + 811, + 1061, + 811, + 1114, + 297, + 1114 + ], + "score": 0.919 + }, + { + "category_id": 9, + "poly": [ + 1365, + 997, + 1401, + 997, + 1401, + 1028, + 1365, + 1028 + ], + "score": 0.877 + }, + { + "category_id": 1, + "poly": [ + 298, + 888, + 634, + 888, + 634, + 921, + 298, + 921 + ], + "score": 0.873 + }, + { + "category_id": 9, + "poly": [ + 1365, + 1339, + 1401, + 1339, + 1401, + 1369, + 1365, + 1369 + ], + "score": 0.863 + }, + { + "category_id": 2, + "poly": [ + 841, + 2086, + 858, + 2086, + 858, + 2112, + 841, + 2112 + ], + "score": 0.773 + }, + { + "category_id": 9, + "poly": [ + 1174, + 1975, + 1403, + 1975, + 1403, + 2009, + 1174, + 2009 + ], + "score": 0.588 + }, + { + "category_id": 8, + "poly": [ + 696, + 977, + 1000, + 977, + 1000, + 1053, + 696, + 1053 + ], + "score": 0.549 + }, + { + "category_id": 1, + "poly": [ + 298, + 931, + 1249, + 931, + 1249, + 1053, + 298, + 1053 + ], + "score": 0.228 + }, + { + "category_id": 8, + "poly": [ + 298, + 931, + 1249, + 931, + 1249, + 1053, + 298, + 1053 + ], + "score": 0.114 + }, + { + "category_id": 13, + "poly": [ + 521, + 647, + 644, + 647, + 644, + 701, + 521, + 701 + ], + "score": 0.93, + "latex": "\\tilde { \\mathcal { O } } \\left( \\sqrt { | J | } \\right)" + }, + { + "category_id": 13, + "poly": [ + 885, + 1232, + 1222, + 1232, + 1222, + 1289, + 885, + 1289 + ], + "score": 0.93, + "latex": "\\begin{array} { r } { T = \\mathcal { O } \\left( \\frac { C } { 2 ^ { i } } \\cdot \\frac { M \\eta _ { j } } { \\xi _ { i } } \\ln ( R M L ) \\right) } \\end{array}" + }, + { + "category_id": 13, + "poly": [ + 342, + 1128, + 596, + 1128, + 596, + 1173, + 342, + 1173 + ], + "score": 0.93, + "latex": "A _ { t } = I [ X _ { t } ^ { ( 2 ^ { i } ) } \\geq \\eta _ { j - 1 } ]" + }, + { + "category_id": 14, + "poly": [ + 604, + 1318, + 1094, + 1318, + 1094, + 1392, + 604, + 1392 + ], + "score": 0.93, + "latex": "\\operatorname* { P r } \\left[ X _ { k + t R } ^ { ( 2 ^ { i } ) } \\geq \\eta _ { j - 1 } \\right] = \\mathbb { E } [ A _ { k + t R } ] > \\frac { \\xi _ { i } } { M \\eta _ { j } } ," + }, + { + "category_id": 14, + "poly": [ + 408, + 518, + 1291, + 518, + 1291, + 611, + 408, + 611 + ], + "score": 0.93, + "latex": "| J | \\eta ( 1 - \\gamma ) ^ { - 1 } \\leq \\frac { C \\epsilon _ { 1 } } { 1 - \\gamma } + \\mathcal { O } \\left( \\frac { \\sqrt { S A | J | \\ell ( | J | ) } } { ( 1 - \\gamma ) ^ { 2 . 5 } } + \\frac { w S A \\ln | J | } { ( 1 - \\gamma ) ^ { 3 } } \\ln \\frac { 1 } { ( 1 - \\gamma ) \\epsilon _ { 1 } } \\right) ." + }, + { + "category_id": 13, + "poly": [ + 767, + 261, + 872, + 261, + 872, + 298, + 767, + 298 + ], + "score": 0.93, + "latex": "\\hat { Q } _ { t } \\geq Q ^ { * }" + }, + { + "category_id": 13, + "poly": [ + 394, + 1397, + 611, + 1397, + 611, + 1436, + 394, + 1436 + ], + "score": 0.93, + "latex": "\\textstyle \\sum _ { t } A _ { k + t R } \\geq C / 2 ^ { i }" + }, + { + "category_id": 14, + "poly": [ + 315, + 1678, + 1424, + 1678, + 1424, + 2039, + 315, + 2039 + ], + "score": 0.93, + "latex": "\\begin{array} { r l r } { { \\sum _ { t = 1 } ^ { \\ell - 1 } I [ V ^ { * } ( s _ { t } ) - V ^ { \\pi _ { t } } ( s _ { t } ) > \\epsilon ] } } \\\\ & { \\leq \\sum _ { t = 1 } ^ { \\infty } \\sum _ { i = 0 } ^ { L } \\sum _ { j = 2 } ^ { M } I [ \\eta _ { j } \\operatorname* { P r } [ X _ { t } ^ { ( 2 ^ { i } ) } > \\eta _ { j - 1 } ] > \\frac { \\xi _ { i } } { M } ] = \\sum _ { i = 0 } ^ { L } \\sum _ { j = 2 } ^ { M } \\sum _ { t = 1 } ^ { \\infty } I [ \\operatorname* { P r } [ X _ { t } ^ { ( 2 ^ { i } ) } > \\eta _ { j - 1 } ] > \\frac { \\xi _ { i } } { \\eta _ { j } M } ] } \\\\ & { \\leq \\sum _ { i = 0 } ^ { L } \\sum _ { j = 2 } ^ { M } \\frac { S A M R \\ln 1 / \\delta \\ln S A } { \\eta _ { j } \\xi _ { i } \\cdot 2 ^ { i } ( 1 - \\gamma ) ^ { 5 } } \\tilde { P } \\leq \\sum _ { i = 0 } ^ { L } \\frac { S A \\cdot 2 ^ { i + 4 } \\ln S A \\ln 1 / \\delta } { \\epsilon _ { 2 } ^ { 2 } ( 1 - \\gamma ) ^ { 6 } } \\tilde { P } \\mathrm { ( B y ~ d e f i n i t i o n ~ o f } \\xi _ { i } \\mathrm { ~ a n d } \\eta _ { j } ) } \\\\ & { \\leq \\frac { S A R \\ln S A \\ln 1 / \\delta } { \\epsilon _ { 2 } ^ { 2 } ( 1 - \\gamma ) ^ { 6 } } \\tilde { P } \\leq \\frac { S A \\ln S A \\ln 1 / \\delta } { \\epsilon _ { 2 } ^ { 2 } ( 1 - \\gamma ) ^ { 7 } } \\tilde { P } . } & { \\mathrm { ( B y ~ d e f i n i t i o n ~ o f } \\hbar ) } \\end{array}" + }, + { + "category_id": 13, + "poly": [ + 1010, + 1139, + 1106, + 1139, + 1106, + 1173, + 1010, + 1173 + ], + "score": 0.92, + "latex": "\\{ \\mathcal { F } _ { t } \\} _ { t \\ge 1 }" + }, + { + "category_id": 13, + "poly": [ + 810, + 1571, + 969, + 1571, + 969, + 1605, + 810, + 1605 + ], + "score": 0.92, + "latex": "1 - \\delta / ( 2 M L )" + }, + { + "category_id": 13, + "poly": [ + 1136, + 448, + 1330, + 448, + 1330, + 486, + 1136, + 486 + ], + "score": 0.92, + "latex": "( \\hat { Q } - Q ^ { * } ) ( s _ { t } , a _ { t } )" + }, + { + "category_id": 13, + "poly": [ + 1233, + 410, + 1397, + 410, + 1397, + 445, + 1233, + 445 + ], + "score": 0.92, + "latex": "| J | \\bar { \\eta ( 1 - \\gamma ) } ^ { - 1 }" + }, + { + "category_id": 13, + "poly": [ + 929, + 1509, + 1180, + 1509, + 1180, + 1545, + 929, + 1545 + ], + "score": 0.92, + "latex": "\\textstyle \\sum _ { t = 0 } ^ { \\infty } A _ { k + t R } \\leq C / 2 ^ { i }" + }, + { + "category_id": 13, + "poly": [ + 829, + 1447, + 1135, + 1447, + 1135, + 1479, + 829, + 1479 + ], + "score": 0.92, + "latex": "[ k + t R , k + t R + R - 1 ]" + }, + { + "category_id": 13, + "poly": [ + 1313, + 350, + 1395, + 350, + 1395, + 384, + 1313, + 384 + ], + "score": 0.91, + "latex": "( | J | , 1 )" + }, + { + "category_id": 13, + "poly": [ + 635, + 383, + 817, + 383, + 817, + 414, + 635, + 414 + ], + "score": 0.91, + "latex": "w _ { t } ~ = ~ I \\left[ t \\in J \\right]" + }, + { + "category_id": 13, + "poly": [ + 1309, + 657, + 1344, + 657, + 1344, + 691, + 1309, + 691 + ], + "score": 0.91, + "latex": "| J |" + }, + { + "category_id": 13, + "poly": [ + 563, + 1478, + 896, + 1478, + 896, + 1511, + 563, + 1511 + ], + "score": 0.91, + "latex": "V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) > ^ { \\mathsf { ^ { * } } } \\eta _ { j - 1 }" + }, + { + "category_id": 13, + "poly": [ + 348, + 1511, + 648, + 1511, + 648, + 1544, + 348, + 1544 + ], + "score": 0.9, + "latex": "[ k + t R , k + t R + R - 1 ]" + }, + { + "category_id": 13, + "poly": [ + 551, + 1448, + 630, + 1448, + 630, + 1479, + 551, + 1479 + ], + "score": 0.9, + "latex": "A _ { k + t R }" + }, + { + "category_id": 13, + "poly": [ + 1266, + 1170, + 1397, + 1170, + 1397, + 1201, + 1266, + 1201 + ], + "score": 0.9, + "latex": "0 \\leq k < R" + }, + { + "category_id": 13, + "poly": [ + 298, + 1242, + 427, + 1242, + 427, + 1274, + 298, + 1274 + ], + "score": 0.9, + "latex": "0 \\leq k < R" + }, + { + "category_id": 13, + "poly": [ + 298, + 1572, + 425, + 1572, + 425, + 1602, + 298, + 1602 + ], + "score": 0.9, + "latex": "0 \\leq k < R" + }, + { + "category_id": 14, + "poly": [ + 696, + 976, + 1001, + 976, + 1001, + 1054, + 696, + 1054 + ], + "score": 0.89, + "latex": "C = \\frac { S A \\ln S A \\ln 1 / \\delta } { \\eta _ { j - 1 } ^ { 2 } ( 1 - \\gamma ) ^ { 5 } } \\cdot \\tilde { P } ." + }, + { + "category_id": 13, + "poly": [ + 885, + 1398, + 1067, + 1398, + 1067, + 1433, + 885, + 1433 + ], + "score": 0.89, + "latex": "1 - \\delta / ( 2 M R L )" + }, + { + "category_id": 13, + "poly": [ + 673, + 616, + 708, + 616, + 708, + 649, + 673, + 649 + ], + "score": 0.89, + "latex": "| J |" + }, + { + "category_id": 13, + "poly": [ + 923, + 261, + 1204, + 261, + 1204, + 299, + 923, + 299 + ], + "score": 0.89, + "latex": "a _ { t } = \\arg \\operatorname* { m a x } _ { a } \\hat { Q } _ { t } ( s _ { t } , a )" + }, + { + "category_id": 13, + "poly": [ + 298, + 1200, + 690, + 1200, + 690, + 1235, + 298, + 1235 + ], + "score": 0.88, + "latex": "\\{ \\dot { A } _ { k + t R } - E [ A _ { k + t R } \\ | \\ \\mathcal { F } _ { k + t R } ] \\} _ { t \\geq 0 }" + }, + { + "category_id": 13, + "poly": [ + 884, + 1171, + 917, + 1171, + 917, + 1201, + 884, + 1201 + ], + "score": 0.88, + "latex": "A _ { t }" + }, + { + "category_id": 13, + "poly": [ + 537, + 1170, + 798, + 1170, + 798, + 1203, + 537, + 1203 + ], + "score": 0.88, + "latex": "\\bar { \\{ ( s _ { \\tau } , a _ { \\tau } ) : 1 \\leq \\tau \\leq t \\} }" + }, + { + "category_id": 13, + "poly": [ + 1219, + 616, + 1255, + 616, + 1255, + 650, + 1219, + 650 + ], + "score": 0.88, + "latex": "| J |" + }, + { + "category_id": 13, + "poly": [ + 297, + 410, + 657, + 410, + 657, + 450, + 297, + 450 + ], + "score": 0.87, + "latex": "\\begin{array} { r } { \\sum _ { t \\geq 1 } \\dot { w } _ { t } \\left[ \\bar { V } ^ { \\ast } ( s _ { t } ) - Q ^ { \\ast } ( s _ { t } , \\dot { a } _ { t } ) \\right] , } \\end{array}" + }, + { + "category_id": 13, + "poly": [ + 580, + 701, + 625, + 701, + 625, + 733, + 580, + 733 + ], + "score": 0.87, + "latex": "1 / \\eta" + }, + { + "category_id": 13, + "poly": [ + 358, + 1066, + 384, + 1066, + 384, + 1098, + 358, + 1098 + ], + "score": 0.86, + "latex": "\\tilde { P }" + }, + { + "category_id": 13, + "poly": [ + 1288, + 1888, + 1312, + 1888, + 1312, + 1918, + 1288, + 1918 + ], + "score": 0.86, + "latex": "\\xi _ { i }" + }, + { + "category_id": 13, + "poly": [ + 532, + 934, + 1164, + 934, + 1164, + 971, + 532, + 971 + ], + "score": 0.85, + "latex": "2 \\leq j \\leq M , \\sum _ { t = 1 } ^ { \\infty } I \\left[ V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) > \\eta _ { j - 1 } \\right] \\leq C" + }, + { + "category_id": 13, + "poly": [ + 296, + 1602, + 664, + 1602, + 664, + 1658, + 296, + 1658 + ], + "score": 0.85, + "latex": "\\mathrm { P r } \\left[ X _ { t } ^ { ( 2 ^ { i } ) } \\geq \\eta _ { j - 1 } \\right] > \\xi _ { i } / ( M \\eta _ { j } )" + }, + { + "category_id": 13, + "poly": [ + 562, + 349, + 1104, + 349, + 1104, + 384, + 562, + 384 + ], + "score": 0.85, + "latex": "J = \\{ t : \\ V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) > \\eta ( 1 - \\gamma ) ^ { - 1 } \\}" + }, + { + "category_id": 14, + "poly": [ + 576, + 304, + 1113, + 304, + 1113, + 345, + 576, + 345 + ], + "score": 0.83, + "latex": "V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) \\leq \\hat { Q } _ { t } ( s _ { t } , a _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) ." + }, + { + "category_id": 13, + "poly": [ + 296, + 1476, + 323, + 1476, + 323, + 1506, + 296, + 1506 + ], + "score": 0.83, + "latex": "2 ^ { i }" + }, + { + "category_id": 13, + "poly": [ + 815, + 1543, + 839, + 1543, + 839, + 1569, + 815, + 1569 + ], + "score": 0.83, + "latex": "T" + }, + { + "category_id": 13, + "poly": [ + 1302, + 1479, + 1327, + 1479, + 1327, + 1505, + 1302, + 1505 + ], + "score": 0.81, + "latex": "C" + }, + { + "category_id": 13, + "poly": [ + 1363, + 1890, + 1390, + 1890, + 1390, + 1921, + 1363, + 1921 + ], + "score": 0.81, + "latex": "\\eta _ { j }" + }, + { + "category_id": 13, + "poly": [ + 948, + 1172, + 1015, + 1172, + 1015, + 1203, + 948, + 1203 + ], + "score": 0.8, + "latex": "\\mathcal { F } _ { t + R }" + }, + { + "category_id": 13, + "poly": [ + 1099, + 1546, + 1115, + 1546, + 1115, + 1573, + 1099, + 1573 + ], + "score": 0.8, + "latex": "j" + }, + { + "category_id": 13, + "poly": [ + 1168, + 1572, + 1212, + 1572, + 1212, + 1600, + 1168, + 1600 + ], + "score": 0.78, + "latex": "R T" + }, + { + "category_id": 13, + "poly": [ + 1028, + 1546, + 1042, + 1546, + 1042, + 1569, + 1028, + 1569 + ], + "score": 0.75, + "latex": "i" + }, + { + "category_id": 13, + "poly": [ + 1367, + 1979, + 1391, + 1979, + 1391, + 2004, + 1367, + 2004 + ], + "score": 0.71, + "latex": "R" + }, + { + "category_id": 13, + "poly": [ + 677, + 1059, + 800, + 1059, + 800, + 1115, + 677, + 1115 + ], + "score": 0.69, + "latex": "\\begin{array} { r } { \\left( \\frac { 1 } { \\epsilon _ { 1 } } , \\frac { 1 } { 1 - \\gamma } \\right) } \\end{array}" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 72.0, + 817.0, + 72.0, + 817.0, + 108.0, + 295.0, + 108.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 763.0, + 654.0, + 763.0, + 654.0, + 799.0, + 292.0, + 799.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 839.0, + 2086.0, + 860.0, + 2086.0, + 860.0, + 2119.0, + 839.0, + 2119.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 287.0, + 1120.0, + 341.0, + 1120.0, + 341.0, + 1186.0, + 287.0, + 1186.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 597.0, + 1120.0, + 1009.0, + 1120.0, + 1009.0, + 1186.0, + 597.0, + 1186.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1107.0, + 1120.0, + 1413.0, + 1120.0, + 1413.0, + 1186.0, + 1107.0, + 1186.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 1165.0, + 536.0, + 1165.0, + 536.0, + 1207.0, + 292.0, + 1207.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 799.0, + 1165.0, + 883.0, + 1165.0, + 883.0, + 1207.0, + 799.0, + 1207.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 918.0, + 1165.0, + 947.0, + 1165.0, + 947.0, + 1207.0, + 918.0, + 1207.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1016.0, + 1165.0, + 1265.0, + 1165.0, + 1265.0, + 1207.0, + 1016.0, + 1207.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1398.0, + 1165.0, + 1409.0, + 1165.0, + 1409.0, + 1207.0, + 1398.0, + 1207.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 1195.0, + 297.0, + 1195.0, + 297.0, + 1239.0, + 293.0, + 1239.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 691.0, + 1195.0, + 1408.0, + 1195.0, + 1408.0, + 1239.0, + 691.0, + 1239.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 1231.0, + 297.0, + 1231.0, + 297.0, + 1286.0, + 292.0, + 1286.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 428.0, + 1231.0, + 884.0, + 1231.0, + 884.0, + 1286.0, + 428.0, + 1286.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 1280.0, + 643.0, + 1280.0, + 643.0, + 1316.0, + 293.0, + 1316.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1024.0, + 1228.5, + 1410.0, + 1228.5, + 1410.0, + 1285.0, + 1024.0, + 1285.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 346.0, + 561.0, + 346.0, + 561.0, + 387.0, + 293.0, + 387.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1105.0, + 346.0, + 1312.0, + 346.0, + 1312.0, + 387.0, + 1105.0, + 387.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1396.0, + 346.0, + 1409.0, + 346.0, + 1409.0, + 387.0, + 1396.0, + 387.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 377.0, + 634.0, + 377.0, + 634.0, + 416.0, + 292.0, + 416.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 818.0, + 377.0, + 1408.0, + 377.0, + 1408.0, + 416.0, + 818.0, + 416.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 290.0, + 407.0, + 296.0, + 407.0, + 296.0, + 450.0, + 290.0, + 450.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 658.0, + 407.0, + 1232.0, + 407.0, + 1232.0, + 450.0, + 658.0, + 450.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1398.0, + 407.0, + 1408.0, + 407.0, + 1408.0, + 450.0, + 1398.0, + 450.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 450.0, + 1135.0, + 450.0, + 1135.0, + 487.0, + 294.0, + 487.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1331.0, + 450.0, + 1405.0, + 450.0, + 1405.0, + 487.0, + 1331.0, + 487.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 290.0, + 485.0, + 380.0, + 485.0, + 380.0, + 519.0, + 290.0, + 519.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 614.0, + 672.0, + 614.0, + 672.0, + 652.0, + 295.0, + 652.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 709.0, + 614.0, + 1218.0, + 614.0, + 1218.0, + 652.0, + 709.0, + 652.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1256.0, + 614.0, + 1404.0, + 614.0, + 1404.0, + 652.0, + 1256.0, + 652.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 291.0, + 648.0, + 520.0, + 648.0, + 520.0, + 700.0, + 291.0, + 700.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 645.0, + 648.0, + 1308.0, + 648.0, + 1308.0, + 700.0, + 645.0, + 700.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1345.0, + 648.0, + 1407.0, + 648.0, + 1407.0, + 700.0, + 1345.0, + 700.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 296.0, + 699.0, + 579.0, + 699.0, + 579.0, + 738.0, + 296.0, + 738.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 626.0, + 699.0, + 635.0, + 699.0, + 635.0, + 738.0, + 626.0, + 738.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 1443.0, + 550.0, + 1443.0, + 550.0, + 1484.0, + 293.0, + 1484.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 631.0, + 1443.0, + 828.0, + 1443.0, + 828.0, + 1484.0, + 631.0, + 1484.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1136.0, + 1443.0, + 1408.0, + 1443.0, + 1408.0, + 1484.0, + 1136.0, + 1484.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 291.0, + 1471.0, + 295.0, + 1471.0, + 295.0, + 1516.0, + 291.0, + 1516.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 324.0, + 1471.0, + 562.0, + 1471.0, + 562.0, + 1516.0, + 324.0, + 1516.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 897.0, + 1471.0, + 1301.0, + 1471.0, + 1301.0, + 1516.0, + 897.0, + 1516.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1328.0, + 1471.0, + 1412.0, + 1471.0, + 1412.0, + 1516.0, + 1328.0, + 1516.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 284.0, + 1493.0, + 347.0, + 1493.0, + 347.0, + 1577.0, + 284.0, + 1577.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 649.0, + 1493.0, + 814.0, + 1493.0, + 814.0, + 1577.0, + 649.0, + 1577.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 840.0, + 1493.0, + 928.0, + 1493.0, + 928.0, + 1577.0, + 840.0, + 1577.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1181.0, + 1493.0, + 1417.0, + 1493.0, + 1417.0, + 1577.0, + 1181.0, + 1577.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 1568.0, + 297.0, + 1568.0, + 297.0, + 1607.0, + 293.0, + 1607.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 426.0, + 1568.0, + 809.0, + 1568.0, + 809.0, + 1607.0, + 426.0, + 1607.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 970.0, + 1568.0, + 1167.0, + 1568.0, + 1167.0, + 1607.0, + 970.0, + 1607.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1213.0, + 1568.0, + 1407.0, + 1568.0, + 1407.0, + 1607.0, + 1213.0, + 1607.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 289.0, + 1598.0, + 295.0, + 1598.0, + 295.0, + 1659.0, + 289.0, + 1659.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 665.0, + 1598.0, + 1283.0, + 1598.0, + 1283.0, + 1659.0, + 665.0, + 1659.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 227.0, + 1405.0, + 227.0, + 1405.0, + 265.0, + 295.0, + 265.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 262.0, + 766.0, + 262.0, + 766.0, + 304.0, + 294.0, + 304.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 873.0, + 262.0, + 922.0, + 262.0, + 922.0, + 304.0, + 873.0, + 304.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1205.0, + 262.0, + 1216.0, + 262.0, + 1216.0, + 304.0, + 1205.0, + 304.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 291.0, + 1392.0, + 393.0, + 1392.0, + 393.0, + 1441.0, + 291.0, + 1441.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 612.0, + 1392.0, + 884.0, + 1392.0, + 884.0, + 1441.0, + 612.0, + 1441.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1068.0, + 1392.0, + 1080.0, + 1392.0, + 1080.0, + 1441.0, + 1068.0, + 1441.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 820.0, + 988.0, + 820.0, + 988.0, + 859.0, + 294.0, + 859.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 283.0, + 1051.0, + 357.0, + 1051.0, + 357.0, + 1124.0, + 283.0, + 1124.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 385.0, + 1051.0, + 676.0, + 1051.0, + 676.0, + 1124.0, + 385.0, + 1124.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 801.0, + 1051.0, + 818.0, + 1051.0, + 818.0, + 1124.0, + 801.0, + 1124.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 296.0, + 887.0, + 633.0, + 887.0, + 633.0, + 926.0, + 296.0, + 926.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 926.0, + 531.0, + 926.0, + 531.0, + 977.0, + 293.0, + 977.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1165.0, + 926.0, + 1251.0, + 926.0, + 1251.0, + 977.0, + 1165.0, + 977.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 752.25, + 966.5, + 1008.25, + 966.5, + 1008.25, + 1026.5, + 752.25, + 1026.5 + ], + "score": 1.0, + "text": "" + } + ], + "page_info": { + "page_no": 6, + "width": 1700, + "height": 2200 + } + }, + { + "layout_dets": [ + { + "category_id": 1, + "poly": [ + 296, + 1330, + 1406, + 1330, + 1406, + 1539, + 296, + 1539 + ], + "score": 0.98 + }, + { + "category_id": 1, + "poly": [ + 296, + 226, + 1405, + 226, + 1405, + 378, + 296, + 378 + ], + "score": 0.978 + }, + { + "category_id": 1, + "poly": [ + 296, + 947, + 1406, + 947, + 1406, + 1135, + 296, + 1135 + ], + "score": 0.977 + }, + { + "category_id": 1, + "poly": [ + 297, + 1677, + 1405, + 1677, + 1405, + 1838, + 297, + 1838 + ], + "score": 0.976 + }, + { + "category_id": 1, + "poly": [ + 296, + 787, + 1406, + 787, + 1406, + 936, + 296, + 936 + ], + "score": 0.976 + }, + { + "category_id": 1, + "poly": [ + 298, + 1852, + 1404, + 1852, + 1404, + 1954, + 298, + 1954 + ], + "score": 0.976 + }, + { + "category_id": 1, + "poly": [ + 296, + 1142, + 1405, + 1142, + 1405, + 1260, + 296, + 1260 + ], + "score": 0.966 + }, + { + "category_id": 1, + "poly": [ + 298, + 631, + 1405, + 631, + 1405, + 695, + 298, + 695 + ], + "score": 0.954 + }, + { + "category_id": 8, + "poly": [ + 588, + 1968, + 1105, + 1968, + 1105, + 2047, + 588, + 2047 + ], + "score": 0.954 + }, + { + "category_id": 8, + "poly": [ + 741, + 391, + 956, + 391, + 956, + 469, + 741, + 469 + ], + "score": 0.954 + }, + { + "category_id": 1, + "poly": [ + 297, + 482, + 870, + 482, + 870, + 524, + 297, + 524 + ], + "score": 0.932 + }, + { + "category_id": 1, + "poly": [ + 297, + 1283, + 1202, + 1283, + 1202, + 1319, + 297, + 1319 + ], + "score": 0.925 + }, + { + "category_id": 0, + "poly": [ + 298, + 561, + 531, + 561, + 531, + 598, + 298, + 598 + ], + "score": 0.925 + }, + { + "category_id": 1, + "poly": [ + 295, + 1630, + 1345, + 1630, + 1345, + 1665, + 295, + 1665 + ], + "score": 0.92 + }, + { + "category_id": 2, + "poly": [ + 298, + 74, + 817, + 74, + 817, + 105, + 298, + 105 + ], + "score": 0.916 + }, + { + "category_id": 0, + "poly": [ + 300, + 1575, + 755, + 1575, + 755, + 1606, + 300, + 1606 + ], + "score": 0.911 + }, + { + "category_id": 0, + "poly": [ + 299, + 732, + 836, + 732, + 836, + 763, + 299, + 763 + ], + "score": 0.9 + }, + { + "category_id": 2, + "poly": [ + 1374, + 486, + 1403, + 486, + 1403, + 515, + 1374, + 515 + ], + "score": 0.839 + }, + { + "category_id": 2, + "poly": [ + 840, + 2088, + 859, + 2088, + 859, + 2112, + 840, + 2112 + ], + "score": 0.825 + }, + { + "category_id": 13, + "poly": [ + 325, + 980, + 482, + 980, + 482, + 1034, + 325, + 1034 + ], + "score": 0.95, + "latex": "\\begin{array} { r } { \\tilde { \\mathcal O } \\left( \\frac { S A } { \\epsilon ^ { 4 } ( 1 - \\gamma ) ^ { 8 } } \\right) } \\end{array}" + }, + { + "category_id": 13, + "poly": [ + 906, + 1393, + 1063, + 1393, + 1063, + 1448, + 906, + 1448 + ], + "score": 0.94, + "latex": "\\begin{array} { r } { \\tilde { \\mathcal O } \\left( \\frac { S A } { \\epsilon ^ { 2 } ( 1 - \\gamma ) ^ { 6 } } \\right) } \\end{array}" + }, + { + "category_id": 13, + "poly": [ + 1093, + 1174, + 1227, + 1174, + 1227, + 1229, + 1093, + 1229 + ], + "score": 0.94, + "latex": "\\Omega \\left( \\frac { \\epsilon ^ { - 3 } } { \\ln ( 1 / \\delta ) } \\right)" + }, + { + "category_id": 14, + "poly": [ + 588, + 1968, + 1109, + 1968, + 1109, + 2045, + 588, + 2045 + ], + "score": 0.94, + "latex": "\\mathcal { O } \\left( \\frac { S A \\ln S A \\ln 1 / \\delta } { \\epsilon _ { 2 } ^ { 2 } ( 1 - \\gamma ) ^ { 7 } } \\mathrm { p o l y l o g } \\left( \\frac { 1 } { \\epsilon _ { 1 } } , \\frac { 1 } { 1 - \\gamma } \\right) \\right) ." + }, + { + "category_id": 13, + "poly": [ + 847, + 1852, + 936, + 1852, + 936, + 1890, + 847, + 1890 + ], + "score": 0.93, + "latex": "\\tilde { \\mathcal { O } } ( { \\sqrt { T } } )" + }, + { + "category_id": 13, + "poly": [ + 961, + 1030, + 1046, + 1030, + 1046, + 1075, + 961, + 1075 + ], + "score": 0.93, + "latex": "\\frac { 1 } { \\epsilon ^ { 2 } ( 1 - \\gamma ) }" + }, + { + "category_id": 13, + "poly": [ + 1036, + 1887, + 1262, + 1887, + 1262, + 1925, + 1036, + 1925 + ], + "score": 0.93, + "latex": "\\epsilon _ { 2 } > \\tilde { \\mathcal { O } } ( \\epsilon _ { 1 } / ( 1 - \\gamma ) )" + }, + { + "category_id": 13, + "poly": [ + 1034, + 261, + 1240, + 261, + 1240, + 308, + 1034, + 308 + ], + "score": 0.93, + "latex": "\\begin{array} { r } { \\epsilon _ { 1 } = \\frac { \\epsilon } { 2 4 R M \\ln \\frac { 1 } { 1 - \\gamma } } } \\end{array}" + }, + { + "category_id": 13, + "poly": [ + 457, + 821, + 685, + 821, + 685, + 874, + 457, + 874 + ], + "score": 0.93, + "latex": "\\begin{array} { r } { \\Omega \\left( \\frac { S A } { \\epsilon ^ { 2 } ( 1 - \\gamma ) ^ { 3 } } \\ln { 1 / \\delta } \\right) } \\end{array}" + }, + { + "category_id": 13, + "poly": [ + 809, + 1504, + 904, + 1504, + 904, + 1539, + 809, + 1539 + ], + "score": 0.93, + "latex": "\\Omega ( S ^ { 2 } A )" + }, + { + "category_id": 14, + "poly": [ + 741, + 391, + 955, + 391, + 955, + 468, + 741, + 468 + ], + "score": 0.93, + "latex": "\\tilde { \\mathcal { O } } \\left( \\frac { S A \\ln 1 / \\delta } { \\epsilon ^ { 2 } ( 1 - \\gamma ) ^ { 7 } } \\right) ," + }, + { + "category_id": 13, + "poly": [ + 860, + 870, + 968, + 870, + 968, + 905, + 860, + 905 + ], + "score": 0.93, + "latex": "1 / ( 1 - \\gamma )" + }, + { + "category_id": 13, + "poly": [ + 1084, + 1476, + 1170, + 1476, + 1170, + 1509, + 1084, + 1509 + ], + "score": 0.92, + "latex": "O ( S A )" + }, + { + "category_id": 13, + "poly": [ + 887, + 262, + 973, + 262, + 973, + 298, + 887, + 298 + ], + "score": 0.92, + "latex": "\\epsilon _ { 2 } = \\textstyle { \\frac { \\epsilon } { 3 } }" + }, + { + "category_id": 13, + "poly": [ + 419, + 303, + 741, + 303, + 741, + 345, + 419, + 345 + ], + "score": 0.92, + "latex": "\\ln 1 / \\epsilon _ { 1 } = \\mathrm { p o l y } ( \\ln \\textstyle \\frac { 1 } { \\epsilon } , \\ln \\frac { 1 } { 1 - \\gamma } )" + }, + { + "category_id": 13, + "poly": [ + 490, + 1445, + 576, + 1445, + 576, + 1479, + 490, + 1479 + ], + "score": 0.91, + "latex": "( 1 - \\gamma )" + }, + { + "category_id": 13, + "poly": [ + 298, + 1709, + 392, + 1709, + 392, + 1749, + 298, + 1749 + ], + "score": 0.91, + "latex": "\\tilde { \\mathcal { O } } \\left( \\epsilon ^ { - 2 } \\right)" + }, + { + "category_id": 13, + "poly": [ + 739, + 1709, + 847, + 1709, + 847, + 1749, + 739, + 1749 + ], + "score": 0.9, + "latex": "\\bar { \\mathcal { O } } \\left( T ^ { 1 / 2 } \\right)" + }, + { + "category_id": 13, + "poly": [ + 644, + 344, + 871, + 344, + 871, + 379, + 644, + 379 + ], + "score": 0.9, + "latex": "\\left( V ^ { * } - \\dot { V } ^ { \\pi } \\right) \\left( s _ { t } \\right) > \\epsilon" + }, + { + "category_id": 13, + "poly": [ + 297, + 1224, + 464, + 1224, + 464, + 1261, + 297, + 1261 + ], + "score": 0.89, + "latex": "\\ln ( 1 / \\delta ) < \\epsilon ^ { - 2 }" + }, + { + "category_id": 13, + "poly": [ + 1253, + 869, + 1403, + 869, + 1403, + 905, + 1253, + 905 + ], + "score": 0.88, + "latex": "\\mathrm { { } } ^ { \\mathrm { { 3 } } A , 1 / ( 1 - \\gamma ) }" + }, + { + "category_id": 13, + "poly": [ + 296, + 1070, + 339, + 1070, + 339, + 1105, + 296, + 1105 + ], + "score": 0.87, + "latex": "1 / \\epsilon" + }, + { + "category_id": 13, + "poly": [ + 345, + 903, + 386, + 903, + 386, + 935, + 345, + 935 + ], + "score": 0.87, + "latex": "1 / \\epsilon" + }, + { + "category_id": 13, + "poly": [ + 806, + 226, + 831, + 226, + 831, + 258, + 806, + 258 + ], + "score": 0.87, + "latex": "\\tilde { P }" + }, + { + "category_id": 13, + "poly": [ + 889, + 1892, + 952, + 1892, + 952, + 1921, + 889, + 1921 + ], + "score": 0.86, + "latex": "1 - \\delta" + }, + { + "category_id": 13, + "poly": [ + 733, + 265, + 760, + 265, + 760, + 292, + 733, + 292 + ], + "score": 0.85, + "latex": "\\epsilon _ { 2 }" + }, + { + "category_id": 13, + "poly": [ + 327, + 1926, + 354, + 1926, + 354, + 1953, + 327, + 1953 + ], + "score": 0.85, + "latex": "\\epsilon _ { 2 }" + }, + { + "category_id": 13, + "poly": [ + 813, + 267, + 840, + 267, + 840, + 292, + 813, + 292 + ], + "score": 0.85, + "latex": "\\epsilon _ { 1 }" + }, + { + "category_id": 13, + "poly": [ + 1255, + 1862, + 1282, + 1862, + 1282, + 1887, + 1255, + 1887 + ], + "score": 0.82, + "latex": "\\epsilon _ { 1 }" + }, + { + "category_id": 13, + "poly": [ + 580, + 481, + 860, + 481, + 860, + 527, + 580, + 527 + ], + "score": 0.79, + "latex": "\\begin{array} { r } { \\operatorname { p o l y } ( \\ln { \\frac { 1 } { \\epsilon } } , \\ln { \\frac { 1 } { 1 - \\gamma } } , \\ln S A ) } \\end{array}" + }, + { + "category_id": 13, + "poly": [ + 1288, + 308, + 1352, + 308, + 1352, + 337, + 1288, + 337 + ], + "score": 0.79, + "latex": "1 - \\delta" + }, + { + "category_id": 13, + "poly": [ + 984, + 1145, + 1006, + 1145, + 1006, + 1171, + 984, + 1171 + ], + "score": 0.77, + "latex": "S" + }, + { + "category_id": 13, + "poly": [ + 1066, + 1145, + 1089, + 1145, + 1089, + 1171, + 1066, + 1171 + ], + "score": 0.71, + "latex": "A" + }, + { + "category_id": 13, + "poly": [ + 295, + 1183, + 360, + 1183, + 360, + 1214, + 295, + 1214 + ], + "score": 0.68, + "latex": "1 - \\delta" + }, + { + "category_id": 13, + "poly": [ + 473, + 1185, + 496, + 1185, + 496, + 1215, + 473, + 1215 + ], + "score": 0.66, + "latex": "Q" + }, + { + "category_id": 15, + "poly": [ + 291.0, + 558.0, + 535.0, + 558.0, + 535.0, + 605.0, + 291.0, + 605.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 296.0, + 72.0, + 817.0, + 72.0, + 817.0, + 108.0, + 296.0, + 108.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 1574.0, + 757.0, + 1574.0, + 757.0, + 1609.0, + 295.0, + 1609.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 731.0, + 838.0, + 731.0, + 838.0, + 767.0, + 295.0, + 767.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1378.0, + 490.0, + 1403.0, + 490.0, + 1403.0, + 516.0, + 1378.0, + 516.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 839.0, + 2085.0, + 861.0, + 2085.0, + 861.0, + 2116.0, + 839.0, + 2116.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 1332.0, + 1404.0, + 1332.0, + 1404.0, + 1366.0, + 295.0, + 1366.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 1362.0, + 1406.0, + 1362.0, + 1406.0, + 1396.0, + 294.0, + 1396.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 291.0, + 1402.0, + 905.0, + 1402.0, + 905.0, + 1438.0, + 291.0, + 1438.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1064.0, + 1404.0, + 1404.0, + 1404.0, + 1404.0, + 1438.0, + 1064.0, + 1438.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 1444.0, + 489.0, + 1444.0, + 489.0, + 1482.0, + 294.0, + 1482.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 577.0, + 1444.0, + 1407.0, + 1444.0, + 1407.0, + 1482.0, + 577.0, + 1482.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 1476.0, + 1083.0, + 1476.0, + 1083.0, + 1509.0, + 294.0, + 1509.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1171.0, + 1476.0, + 1404.0, + 1476.0, + 1404.0, + 1509.0, + 1171.0, + 1509.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 296.0, + 1506.0, + 808.0, + 1506.0, + 808.0, + 1540.0, + 296.0, + 1540.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 905.0, + 1506.0, + 1331.0, + 1506.0, + 1331.0, + 1540.0, + 905.0, + 1540.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 291.0, + 223.0, + 805.0, + 223.0, + 805.0, + 267.0, + 291.0, + 267.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 832.0, + 223.0, + 1406.0, + 223.0, + 1406.0, + 267.0, + 832.0, + 267.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1241.0, + 260.0, + 1404.0, + 260.0, + 1404.0, + 292.0, + 1241.0, + 292.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 290.0, + 299.0, + 418.0, + 299.0, + 418.0, + 353.0, + 290.0, + 353.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 742.0, + 299.0, + 1287.0, + 299.0, + 1287.0, + 353.0, + 742.0, + 353.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1353.0, + 299.0, + 1408.0, + 299.0, + 1408.0, + 353.0, + 1353.0, + 353.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 340.0, + 643.0, + 340.0, + 643.0, + 381.0, + 293.0, + 381.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 872.0, + 340.0, + 902.0, + 340.0, + 902.0, + 381.0, + 872.0, + 381.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 289.0, + 255.0, + 1208.0, + 255.0, + 1208.0, + 304.5, + 289.0, + 304.5 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1191.25, + 285.0, + 1229.25, + 285.0, + 1229.25, + 307.0, + 1191.25, + 307.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 291.0, + 945.0, + 1406.0, + 945.0, + 1406.0, + 986.0, + 291.0, + 986.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 290.0, + 978.0, + 324.0, + 978.0, + 324.0, + 1026.0, + 290.0, + 1026.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 484.0, + 987.0, + 1408.0, + 987.0, + 1408.0, + 1026.0, + 484.0, + 1026.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 286.0, + 1026.0, + 960.0, + 1026.0, + 960.0, + 1086.0, + 286.0, + 1086.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1047.0, + 1026.0, + 1412.0, + 1026.0, + 1412.0, + 1086.0, + 1047.0, + 1086.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 340.0, + 1071.0, + 1406.0, + 1071.0, + 1406.0, + 1107.0, + 340.0, + 1107.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 1100.0, + 1025.0, + 1100.0, + 1025.0, + 1141.0, + 294.0, + 1141.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 1676.0, + 1405.0, + 1676.0, + 1405.0, + 1717.0, + 292.0, + 1717.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 1704.0, + 297.0, + 1704.0, + 297.0, + 1753.0, + 292.0, + 1753.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 393.0, + 1704.0, + 738.0, + 1704.0, + 738.0, + 1753.0, + 393.0, + 1753.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 848.0, + 1704.0, + 1408.0, + 1704.0, + 1408.0, + 1753.0, + 848.0, + 1753.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 1745.0, + 1405.0, + 1745.0, + 1405.0, + 1779.0, + 295.0, + 1779.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 291.0, + 1771.0, + 1408.0, + 1771.0, + 1408.0, + 1815.0, + 291.0, + 1815.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 1804.0, + 445.0, + 1804.0, + 445.0, + 1843.0, + 294.0, + 1843.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 788.0, + 1404.0, + 788.0, + 1404.0, + 824.0, + 295.0, + 824.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 825.0, + 456.0, + 825.0, + 456.0, + 867.0, + 295.0, + 867.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 871.0, + 859.0, + 871.0, + 859.0, + 907.0, + 294.0, + 907.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 969.0, + 871.0, + 1252.0, + 871.0, + 1252.0, + 907.0, + 969.0, + 907.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 899.0, + 344.0, + 899.0, + 344.0, + 938.0, + 293.0, + 938.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 387.0, + 899.0, + 400.0, + 899.0, + 400.0, + 938.0, + 387.0, + 938.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 482.75, + 815.5, + 1411.75, + 815.5, + 1411.75, + 876.5, + 482.75, + 876.5 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 1852.0, + 846.0, + 1852.0, + 846.0, + 1892.0, + 294.0, + 1892.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 937.0, + 1852.0, + 1254.0, + 1852.0, + 1254.0, + 1892.0, + 937.0, + 1892.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1283.0, + 1852.0, + 1404.0, + 1852.0, + 1404.0, + 1892.0, + 1283.0, + 1892.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 1890.0, + 888.0, + 1890.0, + 888.0, + 1926.0, + 294.0, + 1926.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 953.0, + 1890.0, + 1035.0, + 1890.0, + 1035.0, + 1926.0, + 953.0, + 1926.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1263.0, + 1890.0, + 1405.0, + 1890.0, + 1405.0, + 1926.0, + 1263.0, + 1926.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 296.0, + 1922.0, + 326.0, + 1922.0, + 326.0, + 1957.0, + 296.0, + 1957.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 355.0, + 1922.0, + 713.0, + 1922.0, + 713.0, + 1957.0, + 355.0, + 1957.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 1138.0, + 983.0, + 1138.0, + 983.0, + 1179.0, + 294.0, + 1179.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1007.0, + 1138.0, + 1065.0, + 1138.0, + 1065.0, + 1179.0, + 1007.0, + 1179.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1090.0, + 1138.0, + 1403.0, + 1138.0, + 1403.0, + 1179.0, + 1090.0, + 1179.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 291.0, + 1175.0, + 294.0, + 1175.0, + 294.0, + 1221.0, + 291.0, + 1221.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 361.0, + 1175.0, + 472.0, + 1175.0, + 472.0, + 1221.0, + 361.0, + 1221.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 497.0, + 1175.0, + 1092.0, + 1175.0, + 1092.0, + 1221.0, + 497.0, + 1221.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1233.0, + 1183.0, + 1403.0, + 1183.0, + 1403.0, + 1219.0, + 1233.0, + 1219.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 1223.0, + 296.0, + 1223.0, + 296.0, + 1259.0, + 292.0, + 1259.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 465.0, + 1223.0, + 473.0, + 1223.0, + 473.0, + 1259.0, + 465.0, + 1259.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1140.0, + 1173.0, + 1203.0, + 1173.0, + 1203.0, + 1202.5, + 1140.0, + 1202.5 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 630.0, + 1406.0, + 630.0, + 1406.0, + 669.0, + 293.0, + 669.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 662.0, + 875.0, + 662.0, + 875.0, + 698.0, + 293.0, + 698.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 477.0, + 579.0, + 477.0, + 579.0, + 530.0, + 292.0, + 530.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 861.0, + 477.0, + 873.0, + 477.0, + 873.0, + 530.0, + 861.0, + 530.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 1281.0, + 1204.0, + 1281.0, + 1204.0, + 1322.0, + 293.0, + 1322.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 1627.0, + 1348.0, + 1627.0, + 1348.0, + 1672.0, + 292.0, + 1672.0 + ], + "score": 1.0, + "text": "" + } + ], + "page_info": { + "page_no": 7, + "width": 1700, + "height": 2200 + } + }, + { + "layout_dets": [ + { + "category_id": 1, + "poly": [ + 298, + 405, + 1405, + 405, + 1405, + 612, + 298, + 612 + ], + "score": 0.98 + }, + { + "category_id": 1, + "poly": [ + 299, + 723, + 1401, + 723, + 1401, + 818, + 299, + 818 + ], + "score": 0.95 + }, + { + "category_id": 1, + "poly": [ + 296, + 229, + 1402, + 229, + 1402, + 294, + 296, + 294 + ], + "score": 0.947 + }, + { + "category_id": 1, + "poly": [ + 300, + 1744, + 1405, + 1744, + 1405, + 1839, + 300, + 1839 + ], + "score": 0.909 + }, + { + "category_id": 1, + "poly": [ + 297, + 1221, + 1402, + 1221, + 1402, + 1315, + 297, + 1315 + ], + "score": 0.903 + }, + { + "category_id": 0, + "poly": [ + 300, + 335, + 544, + 335, + 544, + 372, + 300, + 372 + ], + "score": 0.898 + }, + { + "category_id": 2, + "poly": [ + 300, + 75, + 816, + 75, + 816, + 105, + 300, + 105 + ], + "score": 0.895 + }, + { + "category_id": 1, + "poly": [ + 295, + 1333, + 1401, + 1333, + 1401, + 1397, + 295, + 1397 + ], + "score": 0.894 + }, + { + "category_id": 1, + "poly": [ + 293, + 1663, + 1402, + 1663, + 1402, + 1728, + 293, + 1728 + ], + "score": 0.89 + }, + { + "category_id": 1, + "poly": [ + 295, + 1416, + 1402, + 1416, + 1402, + 1481, + 295, + 1481 + ], + "score": 0.89 + }, + { + "category_id": 1, + "poly": [ + 299, + 914, + 1401, + 914, + 1401, + 977, + 299, + 977 + ], + "score": 0.887 + }, + { + "category_id": 1, + "poly": [ + 299, + 1077, + 1406, + 1077, + 1406, + 1201, + 299, + 1201 + ], + "score": 0.881 + }, + { + "category_id": 1, + "poly": [ + 297, + 1581, + 1404, + 1581, + 1404, + 1645, + 297, + 1645 + ], + "score": 0.878 + }, + { + "category_id": 1, + "poly": [ + 296, + 995, + 1402, + 995, + 1402, + 1059, + 296, + 1059 + ], + "score": 0.87 + }, + { + "category_id": 0, + "poly": [ + 300, + 656, + 674, + 656, + 674, + 691, + 300, + 691 + ], + "score": 0.868 + }, + { + "category_id": 1, + "poly": [ + 296, + 1498, + 1401, + 1498, + 1401, + 1564, + 296, + 1564 + ], + "score": 0.864 + }, + { + "category_id": 0, + "poly": [ + 299, + 862, + 489, + 862, + 489, + 897, + 299, + 897 + ], + "score": 0.824 + }, + { + "category_id": 1, + "poly": [ + 297, + 1971, + 1397, + 1971, + 1397, + 2035, + 297, + 2035 + ], + "score": 0.811 + }, + { + "category_id": 2, + "poly": [ + 840, + 2088, + 859, + 2088, + 859, + 2111, + 840, + 2111 + ], + "score": 0.777 + }, + { + "category_id": 1, + "poly": [ + 297, + 1858, + 1402, + 1858, + 1402, + 1953, + 297, + 1953 + ], + "score": 0.374 + }, + { + "category_id": 13, + "poly": [ + 1065, + 467, + 1206, + 467, + 1206, + 513, + 1065, + 513 + ], + "score": 0.94, + "latex": "\\tilde { \\cal O } \\big ( { \\textstyle \\frac { S A } { \\epsilon ^ { 4 } ( 1 - \\gamma _ { _ { - } } ) ^ { 8 } } } \\big )" + }, + { + "category_id": 13, + "poly": [ + 1059, + 538, + 1199, + 538, + 1199, + 582, + 1059, + 582 + ], + "score": 0.94, + "latex": "\\begin{array} { r } { \\tilde { \\mathcal { O } } \\big ( \\frac { S A } { \\epsilon ^ { 2 } ( 1 - \\gamma ) ^ { 7 } } \\big ) } \\end{array}" + }, + { + "category_id": 13, + "poly": [ + 774, + 578, + 889, + 578, + 889, + 613, + 774, + 613 + ], + "score": 0.93, + "latex": "1 / ( 1 - \\gamma )" + }, + { + "category_id": 13, + "poly": [ + 615, + 267, + 642, + 267, + 642, + 292, + 615, + 292 + ], + "score": 0.84, + "latex": "\\epsilon _ { 1 }" + }, + { + "category_id": 13, + "poly": [ + 1242, + 236, + 1268, + 236, + 1268, + 261, + 1242, + 261 + ], + "score": 0.84, + "latex": "\\epsilon _ { 1 }" + }, + { + "category_id": 15, + "poly": [ + 291.0, + 332.0, + 550.0, + 332.0, + 550.0, + 380.0, + 291.0, + 380.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 296.0, + 73.0, + 817.0, + 73.0, + 817.0, + 108.0, + 296.0, + 108.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 657.0, + 676.0, + 657.0, + 676.0, + 697.0, + 294.0, + 697.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 297.0, + 865.0, + 490.0, + 865.0, + 490.0, + 898.0, + 297.0, + 898.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 839.0, + 2087.0, + 861.0, + 2087.0, + 861.0, + 2117.0, + 839.0, + 2117.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 297.0, + 408.0, + 1405.0, + 408.0, + 1405.0, + 438.0, + 297.0, + 438.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 283.0, + 437.0, + 1064.0, + 437.0, + 1064.0, + 530.0, + 283.0, + 530.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1207.0, + 437.0, + 1406.0, + 437.0, + 1406.0, + 530.0, + 1207.0, + 530.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 506.0, + 1406.0, + 506.0, + 1406.0, + 543.0, + 295.0, + 543.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 285.0, + 523.0, + 1058.0, + 523.0, + 1058.0, + 596.0, + 285.0, + 596.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1200.0, + 523.0, + 1414.0, + 523.0, + 1414.0, + 596.0, + 1200.0, + 596.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 576.0, + 773.0, + 576.0, + 773.0, + 616.0, + 292.0, + 616.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 890.0, + 576.0, + 1165.0, + 576.0, + 1165.0, + 616.0, + 890.0, + 616.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 723.0, + 1405.0, + 723.0, + 1405.0, + 761.0, + 293.0, + 761.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 752.0, + 1406.0, + 752.0, + 1406.0, + 790.0, + 293.0, + 790.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 784.0, + 1181.0, + 784.0, + 1181.0, + 823.0, + 293.0, + 823.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 227.0, + 1241.0, + 227.0, + 1241.0, + 267.0, + 292.0, + 267.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1269.0, + 227.0, + 1404.0, + 227.0, + 1404.0, + 267.0, + 1269.0, + 267.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 259.0, + 614.0, + 259.0, + 614.0, + 299.0, + 295.0, + 299.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 643.0, + 259.0, + 653.0, + 259.0, + 653.0, + 299.0, + 643.0, + 299.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 296.0, + 1744.0, + 1405.0, + 1744.0, + 1405.0, + 1782.0, + 296.0, + 1782.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 322.0, + 1776.0, + 1404.0, + 1776.0, + 1404.0, + 1813.0, + 322.0, + 1813.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 323.0, + 1809.0, + 596.0, + 1809.0, + 596.0, + 1838.0, + 323.0, + 1838.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 296.0, + 1221.0, + 1406.0, + 1221.0, + 1406.0, + 1258.0, + 296.0, + 1258.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 321.0, + 1249.0, + 1408.0, + 1249.0, + 1408.0, + 1291.0, + 321.0, + 1291.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 324.0, + 1284.0, + 533.0, + 1284.0, + 533.0, + 1314.0, + 324.0, + 1314.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 1329.0, + 1405.0, + 1329.0, + 1405.0, + 1373.0, + 293.0, + 1373.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 322.0, + 1365.0, + 661.0, + 1365.0, + 661.0, + 1397.0, + 322.0, + 1397.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 1659.0, + 1404.0, + 1659.0, + 1404.0, + 1701.0, + 295.0, + 1701.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 320.0, + 1693.0, + 992.0, + 1693.0, + 992.0, + 1728.0, + 320.0, + 1728.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 297.0, + 1416.0, + 1404.0, + 1416.0, + 1404.0, + 1452.0, + 297.0, + 1452.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 322.0, + 1447.0, + 1184.0, + 1447.0, + 1184.0, + 1482.0, + 322.0, + 1482.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 909.0, + 1405.0, + 909.0, + 1405.0, + 953.0, + 293.0, + 953.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 323.0, + 944.0, + 1137.0, + 944.0, + 1137.0, + 979.0, + 323.0, + 979.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 1076.0, + 1406.0, + 1076.0, + 1406.0, + 1113.0, + 294.0, + 1113.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 319.0, + 1109.0, + 1406.0, + 1109.0, + 1406.0, + 1142.0, + 319.0, + 1142.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 322.0, + 1140.0, + 1406.0, + 1140.0, + 1406.0, + 1173.0, + 322.0, + 1173.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 322.0, + 1171.0, + 640.0, + 1171.0, + 640.0, + 1203.0, + 322.0, + 1203.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 1580.0, + 1408.0, + 1580.0, + 1408.0, + 1618.0, + 295.0, + 1618.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 326.0, + 1612.0, + 843.0, + 1612.0, + 843.0, + 1644.0, + 326.0, + 1644.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 991.0, + 1407.0, + 991.0, + 1407.0, + 1033.0, + 294.0, + 1033.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 323.0, + 1027.0, + 947.0, + 1027.0, + 947.0, + 1062.0, + 323.0, + 1062.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 296.0, + 1499.0, + 1405.0, + 1499.0, + 1405.0, + 1535.0, + 296.0, + 1535.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 324.0, + 1530.0, + 1196.0, + 1530.0, + 1196.0, + 1562.0, + 324.0, + 1562.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 1968.0, + 1403.0, + 1968.0, + 1403.0, + 2009.0, + 293.0, + 2009.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 322.0, + 2002.0, + 1377.0, + 2002.0, + 1377.0, + 2036.0, + 322.0, + 2036.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 296.0, + 1857.0, + 1403.0, + 1857.0, + 1403.0, + 1896.0, + 296.0, + 1896.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 324.0, + 1890.0, + 1403.0, + 1890.0, + 1403.0, + 1924.0, + 324.0, + 1924.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 321.0, + 1919.0, + 1236.0, + 1919.0, + 1236.0, + 1955.0, + 321.0, + 1955.0 + ], + "score": 1.0, + "text": "" + } + ], + "page_info": { + "page_no": 8, + "width": 1700, + "height": 2200 + } + }, + { + "layout_dets": [ + { + "category_id": 8, + "poly": [ + 390, + 1268, + 1310, + 1268, + 1310, + 1643, + 390, + 1643 + ], + "score": 0.97 + }, + { + "category_id": 8, + "poly": [ + 360, + 1777, + 1342, + 1777, + 1342, + 2035, + 360, + 2035 + ], + "score": 0.967 + }, + { + "category_id": 8, + "poly": [ + 520, + 996, + 1177, + 996, + 1177, + 1082, + 520, + 1082 + ], + "score": 0.948 + }, + { + "category_id": 1, + "poly": [ + 298, + 683, + 1405, + 683, + 1405, + 780, + 298, + 780 + ], + "score": 0.945 + }, + { + "category_id": 1, + "poly": [ + 292, + 899, + 1404, + 899, + 1404, + 977, + 292, + 977 + ], + "score": 0.94 + }, + { + "category_id": 1, + "poly": [ + 298, + 342, + 1404, + 342, + 1404, + 467, + 298, + 467 + ], + "score": 0.933 + }, + { + "category_id": 1, + "poly": [ + 298, + 1098, + 690, + 1098, + 690, + 1133, + 298, + 1133 + ], + "score": 0.922 + }, + { + "category_id": 1, + "poly": [ + 301, + 228, + 1401, + 228, + 1401, + 324, + 301, + 324 + ], + "score": 0.922 + }, + { + "category_id": 1, + "poly": [ + 297, + 1714, + 1355, + 1714, + 1355, + 1762, + 297, + 1762 + ], + "score": 0.921 + }, + { + "category_id": 1, + "poly": [ + 298, + 568, + 1406, + 568, + 1406, + 665, + 298, + 665 + ], + "score": 0.913 + }, + { + "category_id": 2, + "poly": [ + 299, + 75, + 817, + 75, + 817, + 105, + 299, + 105 + ], + "score": 0.898 + }, + { + "category_id": 1, + "poly": [ + 296, + 1210, + 1196, + 1210, + 1196, + 1252, + 296, + 1252 + ], + "score": 0.891 + }, + { + "category_id": 1, + "poly": [ + 296, + 1163, + 1198, + 1163, + 1198, + 1200, + 296, + 1200 + ], + "score": 0.888 + }, + { + "category_id": 1, + "poly": [ + 294, + 486, + 1399, + 486, + 1399, + 551, + 294, + 551 + ], + "score": 0.871 + }, + { + "category_id": 2, + "poly": [ + 835, + 2087, + 865, + 2087, + 865, + 2114, + 835, + 2114 + ], + "score": 0.854 + }, + { + "category_id": 9, + "poly": [ + 1364, + 1022, + 1401, + 1022, + 1401, + 1053, + 1364, + 1053 + ], + "score": 0.839 + }, + { + "category_id": 0, + "poly": [ + 301, + 835, + 646, + 835, + 646, + 872, + 301, + 872 + ], + "score": 0.562 + }, + { + "category_id": 1, + "poly": [ + 301, + 835, + 646, + 835, + 646, + 872, + 301, + 872 + ], + "score": 0.395 + }, + { + "category_id": 14, + "poly": [ + 386, + 1272, + 1313, + 1272, + 1313, + 1645, + 386, + 1645 + ], + "score": 0.95, + "latex": "\\begin{array} { r l } & { \\frac { \\eta | I | } { 1 - \\gamma } \\leq \\displaystyle \\sum _ { t \\in I } \\left( V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) \\right) \\leq \\displaystyle \\sum _ { t \\in I } \\left[ \\left( \\hat { Q } _ { t } - Q ^ { * } \\right) ( s _ { t } , a _ { t } ) \\right] } \\\\ & { \\qquad \\leq \\displaystyle \\frac { | I | \\epsilon _ { 1 } } { 1 - \\gamma } + \\mathcal { O } \\left( \\frac { 1 } { ( 1 - \\gamma ) ^ { 5 / 2 } } \\sqrt { S A | I | \\ell | ( I | ) } + \\frac { S A } { ( 1 - \\gamma ) ^ { 3 } } \\ln | I | \\ln \\frac { 1 } { \\epsilon _ { 1 } ( 1 - \\gamma ) } \\right) } \\\\ & { \\qquad \\leq \\displaystyle \\frac { | I | \\epsilon _ { 1 } } { 1 - \\gamma } + \\mathcal { O } \\left( \\ln \\frac { 1 } { \\epsilon _ { 1 } ( 1 - \\gamma ) } \\cdot \\left( \\frac { \\sqrt { S A | I | \\ln \\frac { S A | I | } { \\delta } } } { ( 1 - \\gamma ) ^ { 5 / 2 } } + \\frac { S A \\ln | I | } { ( 1 - \\gamma ) ^ { 3 } } \\right) \\right) } \\\\ & { \\qquad \\leq \\displaystyle \\frac { | I | \\epsilon _ { 1 } } { 1 - \\gamma } + \\mathcal { O } \\left( \\sqrt { \\ln \\frac { 1 } { \\delta } } \\ln \\frac { 1 } { \\epsilon _ { 1 } ( 1 - \\gamma ) } \\cdot \\left( \\frac { \\sqrt { S A | I | \\ln S A | I | } } { ( 1 - \\gamma ) ^ { 5 / 2 } } + \\frac { S A \\ln | I | } { ( 1 - \\gamma ) ^ { 3 } } \\right) \\right) } \\end{array}" + }, + { + "category_id": 14, + "poly": [ + 356, + 1775, + 1344, + 1775, + 1344, + 2038, + 356, + 2038 + ], + "score": 0.95, + "latex": "\\begin{array} { r l } & { \\frac { \\eta | I | } { 1 - \\gamma } = \\cfrac { k ^ { 2 } S A \\ln S A } { ( 1 - \\gamma ) ^ { 4 } \\eta } \\leq 2 \\cfrac { ( \\eta - \\epsilon _ { 1 } ) | I | } { 1 - \\gamma } } \\\\ & { \\qquad \\leq C _ { 1 } \\sqrt { \\ln \\frac { 1 } { \\delta } } \\ln \\cfrac { 1 } { \\epsilon _ { 1 } ( 1 - \\gamma ) } \\left( \\cfrac { \\sqrt { S A | I | \\ln \\left( S A | I | \\right) } } { ( 1 - \\gamma ) ^ { 5 / 2 } } + \\cfrac { S A \\ln | I | } { ( 1 - \\gamma ) ^ { 3 } } \\right) } \\\\ & { \\qquad \\leq C _ { 1 } \\sqrt { \\ln \\frac { 1 } { \\delta } } \\ln \\cfrac { 1 } { \\epsilon _ { 1 } ( 1 - \\gamma ) } \\left( \\cfrac { S A k } { \\eta ( 1 - \\gamma ) ^ { 4 } } \\sqrt { \\ln S A \\cdot ( \\ln S A + \\ln | I | ) } + \\cfrac { S A \\ln | I | } { ( 1 - \\gamma ) ^ { 3 } } \\right) . } \\end{array}" + }, + { + "category_id": 13, + "poly": [ + 447, + 1714, + 687, + 1714, + 687, + 1763, + 447, + 1763 + ], + "score": 0.94, + "latex": "\\begin{array} { r } { | I | = \\frac { S A k ^ { 2 } } { \\eta ^ { 2 } ( 1 - \\gamma ) ^ { 3 } } \\ln S A } \\end{array}" + }, + { + "category_id": 13, + "poly": [ + 957, + 905, + 1272, + 905, + 1272, + 946, + 957, + 946 + ], + "score": 0.93, + "latex": "\\begin{array} { r } { V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) > \\frac { \\eta } { 1 - \\gamma } } \\end{array}" + }, + { + "category_id": 14, + "poly": [ + 519, + 990, + 1176, + 990, + 1176, + 1086, + 519, + 1086 + ], + "score": 0.92, + "latex": "\\sum _ { t = 1 } ^ { t = \\infty } I \\left[ B _ { \\eta } ^ { ( t ) } \\right] \\leq \\frac { S A \\ln S A \\ln 1 / \\delta } { \\eta ^ { 2 } ( 1 - \\gamma ) ^ { 3 } } \\cdot p o l y l o g \\left( \\frac { 1 } { \\epsilon _ { 1 } } , \\frac { 1 } { 1 - \\gamma } \\right) ," + }, + { + "category_id": 13, + "poly": [ + 341, + 1211, + 777, + 1211, + 777, + 1254, + 341, + 1254 + ], + "score": 0.92, + "latex": "\\begin{array} { r } { I = \\{ t \\colon V ^ { * } ( s _ { t } ) - Q ^ { * } ( s _ { t } , a _ { t } ) > \\frac { \\eta } { 1 - \\gamma } \\} } \\end{array}" + }, + { + "category_id": 13, + "poly": [ + 599, + 907, + 667, + 907, + 667, + 939, + 599, + 939 + ], + "score": 0.92, + "latex": "\\eta > 0" + }, + { + "category_id": 13, + "poly": [ + 712, + 899, + 764, + 899, + 764, + 940, + 712, + 940 + ], + "score": 0.92, + "latex": "B _ { \\eta } ^ { ( t ) }" + }, + { + "category_id": 13, + "poly": [ + 453, + 1168, + 522, + 1168, + 522, + 1199, + 453, + 1199 + ], + "score": 0.91, + "latex": "\\eta > 1" + }, + { + "category_id": 13, + "poly": [ + 1121, + 1168, + 1189, + 1168, + 1189, + 1199, + 1121, + 1199 + ], + "score": 0.91, + "latex": "\\eta \\leq 1" + }, + { + "category_id": 13, + "poly": [ + 726, + 943, + 817, + 943, + 817, + 977, + 726, + 977 + ], + "score": 0.9, + "latex": "1 - \\delta / 2" + }, + { + "category_id": 13, + "poly": [ + 298, + 944, + 388, + 944, + 388, + 976, + 298, + 976 + ], + "score": 0.9, + "latex": "\\eta > 2 \\epsilon _ { 1 }" + }, + { + "category_id": 13, + "poly": [ + 802, + 1722, + 871, + 1722, + 871, + 1750, + 802, + 1750 + ], + "score": 0.9, + "latex": "k > 1" + }, + { + "category_id": 13, + "poly": [ + 1312, + 1723, + 1345, + 1723, + 1345, + 1753, + 1312, + 1753 + ], + "score": 0.88, + "latex": "C _ { 1 }" + }, + { + "category_id": 13, + "poly": [ + 371, + 1099, + 411, + 1099, + 411, + 1133, + 371, + 1133 + ], + "score": 0.87, + "latex": "I [ \\cdot ]" + }, + { + "category_id": 13, + "poly": [ + 1124, + 1214, + 1187, + 1214, + 1187, + 1243, + 1124, + 1243 + ], + "score": 0.84, + "latex": "1 - \\delta" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 73.0, + 817.0, + 73.0, + 817.0, + 108.0, + 295.0, + 108.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 831.0, + 2085.0, + 869.0, + 2085.0, + 869.0, + 2123.0, + 831.0, + 2123.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 833.0, + 649.0, + 833.0, + 649.0, + 877.0, + 295.0, + 877.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 685.0, + 1402.0, + 685.0, + 1402.0, + 719.0, + 295.0, + 719.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 321.0, + 712.0, + 1405.0, + 712.0, + 1405.0, + 754.0, + 321.0, + 754.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 322.0, + 746.0, + 706.0, + 746.0, + 706.0, + 781.0, + 322.0, + 781.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 290.0, + 892.0, + 598.0, + 892.0, + 598.0, + 951.0, + 290.0, + 951.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 668.0, + 892.0, + 711.0, + 892.0, + 711.0, + 951.0, + 668.0, + 951.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 765.0, + 892.0, + 956.0, + 892.0, + 956.0, + 951.0, + 765.0, + 951.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1273.0, + 892.0, + 1411.0, + 892.0, + 1411.0, + 951.0, + 1273.0, + 951.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 941.0, + 297.0, + 941.0, + 297.0, + 981.0, + 292.0, + 981.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 389.0, + 941.0, + 725.0, + 941.0, + 725.0, + 981.0, + 389.0, + 981.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 818.0, + 941.0, + 826.0, + 941.0, + 826.0, + 981.0, + 818.0, + 981.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 296.0, + 345.0, + 1405.0, + 345.0, + 1405.0, + 378.0, + 296.0, + 378.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 322.0, + 374.0, + 1404.0, + 374.0, + 1404.0, + 407.0, + 322.0, + 407.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 317.0, + 403.0, + 1405.0, + 403.0, + 1405.0, + 443.0, + 317.0, + 443.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 321.0, + 436.0, + 563.0, + 436.0, + 563.0, + 469.0, + 321.0, + 469.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 296.0, + 1098.0, + 370.0, + 1098.0, + 370.0, + 1134.0, + 296.0, + 1134.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 412.0, + 1098.0, + 693.0, + 1098.0, + 693.0, + 1134.0, + 412.0, + 1134.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 227.0, + 1406.0, + 227.0, + 1406.0, + 269.0, + 295.0, + 269.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 325.0, + 264.0, + 1404.0, + 264.0, + 1404.0, + 294.0, + 325.0, + 294.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 320.0, + 288.0, + 1039.0, + 288.0, + 1039.0, + 329.0, + 320.0, + 329.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 1712.0, + 446.0, + 1712.0, + 446.0, + 1764.0, + 295.0, + 1764.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 688.0, + 1712.0, + 801.0, + 1712.0, + 801.0, + 1764.0, + 688.0, + 1764.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 872.0, + 1712.0, + 1311.0, + 1712.0, + 1311.0, + 1764.0, + 872.0, + 1764.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1346.0, + 1712.0, + 1357.0, + 1712.0, + 1357.0, + 1764.0, + 1346.0, + 1764.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 296.0, + 571.0, + 1408.0, + 571.0, + 1408.0, + 605.0, + 296.0, + 605.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 324.0, + 603.0, + 1404.0, + 603.0, + 1404.0, + 637.0, + 324.0, + 637.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 323.0, + 631.0, + 730.0, + 631.0, + 730.0, + 666.0, + 323.0, + 666.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 1205.0, + 340.0, + 1205.0, + 340.0, + 1258.0, + 292.0, + 1258.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 778.0, + 1205.0, + 1123.0, + 1205.0, + 1123.0, + 1258.0, + 778.0, + 1258.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1188.0, + 1205.0, + 1202.0, + 1205.0, + 1202.0, + 1258.0, + 1188.0, + 1258.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 1163.0, + 452.0, + 1163.0, + 452.0, + 1203.0, + 294.0, + 1203.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 523.0, + 1163.0, + 1120.0, + 1163.0, + 1120.0, + 1203.0, + 523.0, + 1203.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1190.0, + 1163.0, + 1201.0, + 1163.0, + 1201.0, + 1203.0, + 1190.0, + 1203.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 298.0, + 489.0, + 1403.0, + 489.0, + 1403.0, + 521.0, + 298.0, + 521.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 322.0, + 519.0, + 1392.0, + 519.0, + 1392.0, + 552.0, + 322.0, + 552.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 833.0, + 649.0, + 833.0, + 649.0, + 877.0, + 295.0, + 877.0 + ], + "score": 1.0, + "text": "" + } + ], + "page_info": { + "page_no": 9, + "width": 1700, + "height": 2200 + } + }, + { + "layout_dets": [ + { + "category_id": 8, + "poly": [ + 417, + 272, + 1279, + 272, + 1279, + 603, + 417, + 603 + ], + "score": 0.968 + }, + { + "category_id": 8, + "poly": [ + 581, + 788, + 1114, + 788, + 1114, + 871, + 581, + 871 + ], + "score": 0.959 + }, + { + "category_id": 8, + "poly": [ + 356, + 1483, + 1341, + 1483, + 1341, + 1579, + 356, + 1579 + ], + "score": 0.95 + }, + { + "category_id": 8, + "poly": [ + 534, + 934, + 1159, + 934, + 1159, + 1004, + 534, + 1004 + ], + "score": 0.944 + }, + { + "category_id": 8, + "poly": [ + 696, + 1818, + 1002, + 1818, + 1002, + 1864, + 696, + 1864 + ], + "score": 0.943 + }, + { + "category_id": 8, + "poly": [ + 699, + 1713, + 998, + 1713, + 998, + 1758, + 699, + 1758 + ], + "score": 0.941 + }, + { + "category_id": 8, + "poly": [ + 744, + 688, + 951, + 688, + 951, + 728, + 744, + 728 + ], + "score": 0.938 + }, + { + "category_id": 1, + "poly": [ + 297, + 1017, + 603, + 1017, + 603, + 1049, + 297, + 1049 + ], + "score": 0.936 + }, + { + "category_id": 1, + "poly": [ + 294, + 619, + 843, + 619, + 843, + 672, + 294, + 672 + ], + "score": 0.932 + }, + { + "category_id": 1, + "poly": [ + 297, + 884, + 906, + 884, + 906, + 919, + 297, + 919 + ], + "score": 0.929 + }, + { + "category_id": 1, + "poly": [ + 297, + 740, + 561, + 740, + 561, + 774, + 297, + 774 + ], + "score": 0.928 + }, + { + "category_id": 1, + "poly": [ + 297, + 1769, + 770, + 1769, + 770, + 1802, + 297, + 1802 + ], + "score": 0.926 + }, + { + "category_id": 1, + "poly": [ + 296, + 1890, + 1167, + 1890, + 1167, + 1927, + 296, + 1927 + ], + "score": 0.922 + }, + { + "category_id": 1, + "poly": [ + 298, + 1612, + 804, + 1612, + 804, + 1657, + 298, + 1657 + ], + "score": 0.919 + }, + { + "category_id": 2, + "poly": [ + 297, + 73, + 817, + 73, + 817, + 106, + 297, + 106 + ], + "score": 0.918 + }, + { + "category_id": 1, + "poly": [ + 287, + 1393, + 1347, + 1393, + 1347, + 1432, + 287, + 1432 + ], + "score": 0.916 + }, + { + "category_id": 1, + "poly": [ + 296, + 229, + 411, + 229, + 411, + 262, + 296, + 262 + ], + "score": 0.915 + }, + { + "category_id": 0, + "poly": [ + 300, + 1325, + 648, + 1325, + 648, + 1362, + 300, + 1362 + ], + "score": 0.913 + }, + { + "category_id": 1, + "poly": [ + 296, + 1663, + 1059, + 1663, + 1059, + 1697, + 296, + 1697 + ], + "score": 0.91 + }, + { + "category_id": 1, + "poly": [ + 293, + 1959, + 992, + 1959, + 992, + 1995, + 293, + 1995 + ], + "score": 0.905 + }, + { + "category_id": 9, + "poly": [ + 1351, + 950, + 1401, + 950, + 1401, + 982, + 1351, + 982 + ], + "score": 0.893 + }, + { + "category_id": 9, + "poly": [ + 1351, + 1165, + 1401, + 1165, + 1401, + 1197, + 1351, + 1197 + ], + "score": 0.887 + }, + { + "category_id": 9, + "poly": [ + 1351, + 1087, + 1401, + 1087, + 1401, + 1119, + 1351, + 1119 + ], + "score": 0.885 + }, + { + "category_id": 2, + "poly": [ + 835, + 2087, + 862, + 2087, + 862, + 2114, + 835, + 2114 + ], + "score": 0.849 + }, + { + "category_id": 9, + "poly": [ + 1364, + 693, + 1402, + 693, + 1402, + 724, + 1364, + 724 + ], + "score": 0.847 + }, + { + "category_id": 2, + "poly": [ + 1373, + 1892, + 1404, + 1892, + 1404, + 1923, + 1373, + 1923 + ], + "score": 0.845 + }, + { + "category_id": 1, + "poly": [ + 298, + 2001, + 849, + 2001, + 849, + 2036, + 298, + 2036 + ], + "score": 0.843 + }, + { + "category_id": 8, + "poly": [ + 585, + 1066, + 863, + 1066, + 863, + 1140, + 585, + 1140 + ], + "score": 0.836 + }, + { + "category_id": 8, + "poly": [ + 624, + 1144, + 1111, + 1144, + 1111, + 1221, + 624, + 1221 + ], + "score": 0.82 + }, + { + "category_id": 2, + "poly": [ + 1374, + 1249, + 1404, + 1249, + 1404, + 1279, + 1374, + 1279 + ], + "score": 0.817 + }, + { + "category_id": 8, + "poly": [ + 585, + 1065, + 1113, + 1065, + 1113, + 1221, + 585, + 1221 + ], + "score": 0.118 + }, + { + "category_id": 14, + "poly": [ + 418, + 271, + 1281, + 271, + 1281, + 604, + 418, + 604 + ], + "score": 0.95, + "latex": "\\begin{array} { r l } & { k ^ { 2 } \\ln ( S A ) \\le C _ { 1 } \\sqrt { \\ln \\displaystyle \\frac { 1 } { \\delta } } \\ln \\frac { 1 } { \\epsilon _ { 1 } ( 1 - \\gamma ) } \\left( k \\left( \\ln S A + \\ln | I | \\right) + \\eta ( 1 - \\gamma ) \\ln | I | \\right) } \\\\ & { \\qquad \\le k C _ { 1 } \\sqrt { \\ln \\displaystyle \\frac { 1 } { \\delta } } \\ln \\frac { 1 } { \\epsilon _ { 1 } ( 1 - \\gamma ) } \\cdot \\left( \\ln S A + 2 \\ln | I | \\right) } \\\\ & { \\qquad \\le k C _ { 1 } \\sqrt { \\ln \\displaystyle \\frac { 1 } { \\delta } } \\ln \\frac { 1 } { \\epsilon _ { 1 } ( 1 - \\gamma ) } \\cdot \\left( 3 \\ln S A + 4 \\ln k + 6 \\ln \\frac { 1 } { \\eta ( 1 - \\gamma ) } \\right) } \\\\ & { \\qquad \\le 6 k C _ { 1 } \\sqrt { \\ln \\displaystyle \\frac { 1 } { \\delta } } \\ln ^ { 2 } \\frac { 1 } { \\epsilon _ { 1 } ( 1 - \\gamma ) } \\left( \\ln S A + \\ln \\epsilon k \\right) . } \\end{array}" + }, + { + "category_id": 13, + "poly": [ + 342, + 618, + 765, + 618, + 765, + 675, + 342, + 675 + ], + "score": 0.94, + "latex": "\\begin{array} { r } { C ^ { \\prime } = \\operatorname* { m a x } \\lbrace 2 , 6 C _ { 1 } \\sqrt { \\ln \\frac { 1 } { \\delta } } \\ln ^ { 2 } \\frac { 1 } { \\epsilon _ { 1 } ( 1 - \\gamma ) } \\rbrace } \\end{array}" + }, + { + "category_id": 14, + "poly": [ + 584, + 1063, + 1115, + 1063, + 1115, + 1223, + 584, + 1223 + ], + "score": 0.93, + "latex": "\\begin{array} { r l r } { { \\vert I \\vert = \\frac { S A k ^ { 2 } } { \\eta ^ { 2 } ( 1 - \\gamma ) ^ { 3 } } \\ln S A } } \\\\ & { \\leq \\frac { S A \\ln S A } { \\eta ^ { 2 } ( 1 - \\gamma ) ^ { 5 } } \\cdot \\ln \\frac { 1 } { \\delta } \\cdot \\mathcal { O } ( \\ln ^ { 8 } \\frac { 1 } { \\epsilon _ { 1 } ( 1 - \\gamma ) } ) . } \\end{array}" + }, + { + "category_id": 14, + "poly": [ + 356, + 1484, + 1340, + 1484, + 1340, + 1579, + 356, + 1579 + ], + "score": 0.93, + "latex": "\\sum _ { t \\ge 1 } w _ { t } ( \\hat { Q } _ { t } - Q ^ { * } ) ( s _ { t } , a _ { t } ) \\le \\frac { C \\epsilon _ { 1 } } { 1 - \\gamma } + \\mathcal { O } \\left( \\frac { \\sqrt { w S A C \\ell ( C ) } } { ( 1 - \\gamma ) ^ { 2 . 5 } } + \\frac { w S A \\ln C } { ( 1 - \\gamma ) ^ { 3 } } \\ln \\frac { 1 } { ( 1 - \\gamma ) \\epsilon _ { 1 } } \\right) ." + }, + { + "category_id": 13, + "poly": [ + 586, + 1769, + 662, + 1769, + 662, + 1802, + 586, + 1802 + ], + "score": 0.92, + "latex": "p ^ { \\prime } \\leq p" + }, + { + "category_id": 13, + "poly": [ + 372, + 1613, + 636, + 1613, + 636, + 1658, + 372, + 1658 + ], + "score": 0.92, + "latex": "\\begin{array} { r } { \\ell ( C ) = \\iota ( C ) \\ln { \\frac { 1 } { ( 1 - \\gamma ) \\epsilon _ { 1 } } } } \\end{array}" + }, + { + "category_id": 13, + "poly": [ + 324, + 742, + 496, + 742, + 496, + 773, + 324, + 773 + ], + "score": 0.91, + "latex": "k \\geq 1 0 C ^ { \\prime } \\ln C ^ { \\prime }" + }, + { + "category_id": 13, + "poly": [ + 543, + 1396, + 619, + 1396, + 619, + 1430, + 543, + 1430 + ], + "score": 0.91, + "latex": "( C , w )" + }, + { + "category_id": 13, + "poly": [ + 735, + 1396, + 825, + 1396, + 825, + 1431, + 735, + 1431 + ], + "score": 0.91, + "latex": "( w _ { t } ) _ { t \\geq 1 }" + }, + { + "category_id": 14, + "poly": [ + 696, + 1816, + 1002, + 1816, + 1002, + 1861, + 696, + 1861 + ], + "score": 0.91, + "latex": "{ \\hat { Q } } _ { p + 1 } ( s , a ) \\geq Q _ { p ^ { \\prime } + 1 } ( s , a ) ." + }, + { + "category_id": 14, + "poly": [ + 699, + 1711, + 998, + 1711, + 998, + 1756, + 699, + 1756 + ], + "score": 0.91, + "latex": "\\hat { Q } _ { p + 1 } ( s , a ) \\leq Q _ { p + 1 } ( s , a ) ." + }, + { + "category_id": 13, + "poly": [ + 818, + 885, + 903, + 885, + 903, + 917, + 818, + 917 + ], + "score": 0.91, + "latex": "C ^ { \\prime } \\geq 2" + }, + { + "category_id": 14, + "poly": [ + 537, + 930, + 1161, + 930, + 1161, + 1004, + 537, + 1004 + ], + "score": 0.9, + "latex": "k \\leq 1 0 C ^ { \\prime } \\ln C ^ { \\prime } \\leq 3 6 0 C _ { 1 } ^ { 2 } \\operatorname* { m a x } \\{ \\ln ^ { 4 } { \\frac { 1 } { \\epsilon _ { 1 } ( 1 - \\gamma ) } } , 2 0 \\ln 2 \\} ." + }, + { + "category_id": 14, + "poly": [ + 582, + 786, + 1114, + 786, + 1114, + 875, + 582, + 875 + ], + "score": 0.9, + "latex": "\\begin{array} { c } { k - C ^ { \\prime } \\left( 2 + \\ln k \\right) \\geq 8 C ^ { \\prime } \\ln C ^ { \\prime } - ( 2 + \\ln 1 0 ) C ^ { \\prime } } \\\\ { \\geq 4 C ^ { \\prime } \\left( 2 \\ln C ^ { \\prime } - 4 \\right) \\geq 0 , } \\end{array}" + }, + { + "category_id": 14, + "poly": [ + 745, + 686, + 954, + 686, + 954, + 728, + 745, + 728 + ], + "score": 0.89, + "latex": "k \\leq C ^ { \\prime } ( 2 + \\ln k ) ." + }, + { + "category_id": 13, + "poly": [ + 1020, + 1396, + 1111, + 1396, + 1111, + 1430, + 1020, + 1430 + ], + "score": 0.89, + "latex": "1 - \\delta / 2" + }, + { + "category_id": 13, + "poly": [ + 805, + 2002, + 835, + 2002, + 835, + 2036, + 805, + 2036 + ], + "score": 0.86, + "latex": "\\alpha _ { t } ^ { i }" + }, + { + "category_id": 13, + "poly": [ + 427, + 1776, + 444, + 1776, + 444, + 1802, + 427, + 1802 + ], + "score": 0.54, + "latex": "p" + }, + { + "category_id": 15, + "poly": [ + 296.0, + 72.0, + 818.0, + 72.0, + 818.0, + 108.0, + 296.0, + 108.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 1323.0, + 649.0, + 1323.0, + 649.0, + 1367.0, + 293.0, + 1367.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 831.0, + 2085.0, + 867.0, + 2085.0, + 867.0, + 2124.0, + 831.0, + 2124.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1379.0, + 1898.0, + 1402.0, + 1898.0, + 1402.0, + 1921.0, + 1379.0, + 1921.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1378.0, + 1254.0, + 1403.0, + 1254.0, + 1403.0, + 1282.0, + 1378.0, + 1282.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 1012.0, + 605.0, + 1012.0, + 605.0, + 1054.0, + 294.0, + 1054.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 280.0, + 612.0, + 341.0, + 612.0, + 341.0, + 686.0, + 280.0, + 686.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 766.0, + 612.0, + 854.0, + 612.0, + 854.0, + 686.0, + 766.0, + 686.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 883.0, + 817.0, + 883.0, + 817.0, + 923.0, + 294.0, + 923.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 904.0, + 883.0, + 908.0, + 883.0, + 908.0, + 923.0, + 904.0, + 923.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 738.0, + 323.0, + 738.0, + 323.0, + 778.0, + 294.0, + 778.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 497.0, + 738.0, + 563.0, + 738.0, + 563.0, + 778.0, + 497.0, + 778.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 1766.0, + 426.0, + 1766.0, + 426.0, + 1805.0, + 292.0, + 1805.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 445.0, + 1766.0, + 585.0, + 1766.0, + 585.0, + 1805.0, + 445.0, + 1805.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 663.0, + 1766.0, + 774.0, + 1766.0, + 774.0, + 1805.0, + 663.0, + 1805.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 1889.0, + 1169.0, + 1889.0, + 1169.0, + 1930.0, + 295.0, + 1930.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 284.0, + 1603.0, + 371.0, + 1603.0, + 371.0, + 1672.0, + 284.0, + 1672.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 637.0, + 1603.0, + 819.0, + 1603.0, + 819.0, + 1672.0, + 637.0, + 1672.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 1393.0, + 542.0, + 1393.0, + 542.0, + 1434.0, + 294.0, + 1434.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 620.0, + 1393.0, + 734.0, + 1393.0, + 734.0, + 1434.0, + 620.0, + 1434.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 826.0, + 1393.0, + 1019.0, + 1393.0, + 1019.0, + 1434.0, + 826.0, + 1434.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1112.0, + 1393.0, + 1350.0, + 1393.0, + 1350.0, + 1434.0, + 1112.0, + 1434.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 296.0, + 229.0, + 412.0, + 229.0, + 412.0, + 263.0, + 296.0, + 263.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 1659.0, + 1061.0, + 1659.0, + 1061.0, + 1704.0, + 293.0, + 1704.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 1956.0, + 994.0, + 1956.0, + 994.0, + 2000.0, + 293.0, + 2000.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 1998.0, + 804.0, + 1998.0, + 804.0, + 2042.0, + 295.0, + 2042.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 836.0, + 1998.0, + 855.0, + 1998.0, + 855.0, + 2042.0, + 836.0, + 2042.0 + ], + "score": 1.0, + "text": "" + } + ], + "page_info": { + "page_no": 10, + "width": 1700, + "height": 2200 + } + }, + { + "layout_dets": [ + { + "category_id": 8, + "poly": [ + 587, + 1518, + 1108, + 1518, + 1108, + 1609, + 587, + 1609 + ], + "score": 0.958 + }, + { + "category_id": 8, + "poly": [ + 497, + 546, + 1200, + 546, + 1200, + 638, + 497, + 638 + ], + "score": 0.954 + }, + { + "category_id": 8, + "poly": [ + 610, + 723, + 1087, + 723, + 1087, + 813, + 610, + 813 + ], + "score": 0.953 + }, + { + "category_id": 1, + "poly": [ + 297, + 863, + 1404, + 863, + 1404, + 927, + 297, + 927 + ], + "score": 0.949 + }, + { + "category_id": 8, + "poly": [ + 433, + 1086, + 1265, + 1086, + 1265, + 1166, + 433, + 1166 + ], + "score": 0.949 + }, + { + "category_id": 8, + "poly": [ + 344, + 939, + 1354, + 939, + 1354, + 1032, + 344, + 1032 + ], + "score": 0.945 + }, + { + "category_id": 8, + "poly": [ + 473, + 1270, + 1224, + 1270, + 1224, + 1356, + 473, + 1356 + ], + "score": 0.942 + }, + { + "category_id": 8, + "poly": [ + 390, + 1808, + 1307, + 1808, + 1307, + 1894, + 390, + 1894 + ], + "score": 0.934 + }, + { + "category_id": 1, + "poly": [ + 297, + 1759, + 690, + 1759, + 690, + 1794, + 297, + 1794 + ], + "score": 0.934 + }, + { + "category_id": 1, + "poly": [ + 294, + 1615, + 1270, + 1615, + 1270, + 1649, + 294, + 1649 + ], + "score": 0.932 + }, + { + "category_id": 1, + "poly": [ + 295, + 1043, + 1226, + 1043, + 1226, + 1078, + 295, + 1078 + ], + "score": 0.931 + }, + { + "category_id": 1, + "poly": [ + 299, + 1903, + 697, + 1903, + 697, + 1938, + 299, + 1938 + ], + "score": 0.928 + }, + { + "category_id": 1, + "poly": [ + 294, + 1219, + 1126, + 1219, + 1126, + 1257, + 294, + 1257 + ], + "score": 0.927 + }, + { + "category_id": 8, + "poly": [ + 298, + 1952, + 1536, + 1952, + 1536, + 2039, + 298, + 2039 + ], + "score": 0.926 + }, + { + "category_id": 1, + "poly": [ + 297, + 648, + 1167, + 648, + 1167, + 683, + 297, + 683 + ], + "score": 0.923 + }, + { + "category_id": 1, + "poly": [ + 296, + 817, + 850, + 817, + 850, + 851, + 296, + 851 + ], + "score": 0.923 + }, + { + "category_id": 1, + "poly": [ + 296, + 500, + 505, + 500, + 505, + 534, + 296, + 534 + ], + "score": 0.917 + }, + { + "category_id": 2, + "poly": [ + 297, + 73, + 817, + 73, + 817, + 106, + 297, + 106 + ], + "score": 0.913 + }, + { + "category_id": 1, + "poly": [ + 297, + 1485, + 504, + 1485, + 504, + 1518, + 297, + 1518 + ], + "score": 0.911 + }, + { + "category_id": 9, + "poly": [ + 1351, + 1295, + 1401, + 1295, + 1401, + 1328, + 1351, + 1328 + ], + "score": 0.881 + }, + { + "category_id": 9, + "poly": [ + 1351, + 1369, + 1402, + 1369, + 1402, + 1401, + 1351, + 1401 + ], + "score": 0.879 + }, + { + "category_id": 1, + "poly": [ + 297, + 696, + 490, + 696, + 490, + 728, + 297, + 728 + ], + "score": 0.872 + }, + { + "category_id": 1, + "poly": [ + 299, + 1417, + 1073, + 1417, + 1073, + 1458, + 299, + 1458 + ], + "score": 0.866 + }, + { + "category_id": 8, + "poly": [ + 506, + 1664, + 1189, + 1664, + 1189, + 1750, + 506, + 1750 + ], + "score": 0.842 + }, + { + "category_id": 2, + "poly": [ + 1374, + 1174, + 1403, + 1174, + 1403, + 1202, + 1374, + 1202 + ], + "score": 0.813 + }, + { + "category_id": 1, + "poly": [ + 360, + 296, + 1041, + 296, + 1041, + 343, + 360, + 343 + ], + "score": 0.796 + }, + { + "category_id": 1, + "poly": [ + 360, + 357, + 819, + 357, + 819, + 397, + 360, + 397 + ], + "score": 0.739 + }, + { + "category_id": 2, + "poly": [ + 835, + 2087, + 864, + 2087, + 864, + 2114, + 835, + 2114 + ], + "score": 0.72 + }, + { + "category_id": 1, + "poly": [ + 361, + 222, + 982, + 222, + 982, + 282, + 361, + 282 + ], + "score": 0.669 + }, + { + "category_id": 8, + "poly": [ + 361, + 412, + 1400, + 412, + 1400, + 473, + 361, + 473 + ], + "score": 0.49 + }, + { + "category_id": 1, + "poly": [ + 361, + 412, + 1400, + 412, + 1400, + 473, + 361, + 473 + ], + "score": 0.446 + }, + { + "category_id": 8, + "poly": [ + 476, + 1363, + 729, + 1363, + 729, + 1406, + 476, + 1406 + ], + "score": 0.446 + }, + { + "category_id": 2, + "poly": [ + 835, + 2087, + 865, + 2087, + 865, + 2114, + 835, + 2114 + ], + "score": 0.313 + }, + { + "category_id": 8, + "poly": [ + 506, + 1664, + 1190, + 1664, + 1190, + 1750, + 506, + 1750 + ], + "score": 0.197 + }, + { + "category_id": 14, + "poly": [ + 609, + 721, + 1085, + 721, + 1085, + 815, + 609, + 815 + ], + "score": 0.95, + "latex": "\\sum _ { i = 1 } ^ { t } \\alpha _ { t } ^ { i } \\sqrt { \\frac { \\iota ( i ) } { i } } \\leq \\sum _ { i = 1 } ^ { t } \\alpha _ { t } ^ { i } \\sqrt { \\frac { \\iota ( t ) } { i } } \\leq 2 \\sqrt { \\frac { \\iota ( t ) } { t } } ," + }, + { + "category_id": 14, + "poly": [ + 508, + 1657, + 1192, + 1657, + 1192, + 1752, + 508, + 1752 + ], + "score": 0.94, + "latex": "Q _ { p } ( s , a ) = \\alpha _ { t } ^ { 0 } \\frac { 1 } { 1 - \\gamma } + \\sum _ { i = 1 } ^ { t } \\alpha _ { t } ^ { i } \\left[ r ( s , a ) + b _ { i } + \\gamma \\hat { V } _ { t _ { i } } ( s _ { t _ { i } + 1 } ) \\right] ." + }, + { + "category_id": 13, + "poly": [ + 466, + 1043, + 618, + 1043, + 618, + 1078, + 466, + 1078 + ], + "score": 0.94, + "latex": "f ( t ) = \\iota ( t ) / t" + }, + { + "category_id": 14, + "poly": [ + 499, + 542, + 1200, + 542, + 1200, + 641, + 499, + 641 + ], + "score": 0.94, + "latex": "\\alpha _ { t } = \\frac { H + 1 } { H + t } , \\quad \\alpha _ { t } ^ { 0 } = \\prod _ { j = 1 } ^ { t } ( 1 - \\alpha _ { j } ) , \\quad \\alpha _ { t } ^ { i } = \\alpha _ { i } \\prod _ { j = i + 1 } ^ { t } ( 1 - \\alpha _ { j } ) ." + }, + { + "category_id": 14, + "poly": [ + 433, + 1086, + 1264, + 1086, + 1264, + 1165, + 433, + 1165 + ], + "score": 0.93, + "latex": "\\alpha _ { t } \\sqrt { \\frac { \\iota ( t ) } { t } } + ( 1 - \\alpha _ { t } ) \\sqrt { \\frac { \\iota ( t - 1 ) } { t - 1 } } \\geq \\alpha _ { t } \\sqrt { \\frac { \\iota ( t ) } { t } } + ( 1 - \\alpha _ { t } ) \\sqrt { \\frac { \\iota ( t ) } { t } } \\geq \\sqrt { \\frac { \\iota ( t ) } { t } } ." + }, + { + "category_id": 14, + "poly": [ + 591, + 1512, + 1108, + 1512, + 1108, + 1611, + 591, + 1611 + ], + "score": 0.93, + "latex": "\\alpha _ { t } ^ { 0 } = \\prod _ { j = 1 } ^ { t } ( 1 - \\alpha _ { j } ) , \\quad \\alpha _ { t } ^ { i } = \\alpha _ { i } \\prod _ { j = i + 1 } ^ { t } ( 1 - \\alpha _ { j } ) ." + }, + { + "category_id": 14, + "poly": [ + 341, + 938, + 1353, + 938, + 1353, + 1034, + 341, + 1034 + ], + "score": 0.93, + "latex": "\\sum _ { i = 1 } ^ { t } \\alpha _ { t } ^ { i } \\sqrt { \\frac { \\iota ( i ) } { i } } = \\alpha _ { t } \\sqrt { \\frac { \\iota ( t ) } { t } } + ( 1 - \\alpha _ { t } ) \\sum _ { i = 1 } ^ { t - 1 } \\alpha _ { t - 1 } ^ { i } \\sqrt { \\frac { \\iota ( i ) } { i } } \\geq \\alpha _ { t } \\sqrt { \\frac { \\iota ( t ) } { t } } + ( 1 - \\alpha _ { t } ) \\sqrt { \\frac { \\iota ( t - 1 ) } { t - 1 } } ." + }, + { + "category_id": 14, + "poly": [ + 391, + 1802, + 1308, + 1802, + 1308, + 1896, + 391, + 1896 + ], + "score": 0.93, + "latex": "Q ^ { * } ( s , a ) = r ( s , a ) + \\gamma \\mathbb { P } V ^ { * } ( s , a ) = \\alpha _ { t } ^ { 0 } Q ^ { * } ( s , a ) + \\sum _ { i = 1 } ^ { t } \\alpha _ { t } ^ { i } \\left[ r ( s , a ) + \\gamma \\mathbb { P } V ^ { * } ( s , a ) \\right] ." + }, + { + "category_id": 13, + "poly": [ + 357, + 893, + 575, + 893, + 575, + 931, + 357, + 931 + ], + "score": 0.93, + "latex": "\\alpha _ { t } ^ { i } = ( 1 - \\alpha _ { t } ) \\dot { \\alpha _ { t - 1 } ^ { i } }" + }, + { + "category_id": 13, + "poly": [ + 979, + 1046, + 1117, + 1046, + 1117, + 1077, + 979, + 1077 + ], + "score": 0.92, + "latex": "t \\geq 1 , c \\geq 1" + }, + { + "category_id": 13, + "poly": [ + 882, + 1223, + 950, + 1223, + 950, + 1255, + 882, + 1255 + ], + "score": 0.92, + "latex": "p \\geq 0" + }, + { + "category_id": 13, + "poly": [ + 1176, + 1615, + 1261, + 1615, + 1261, + 1649, + 1176, + 1649 + ], + "score": 0.92, + "latex": "Q ( s , a )" + }, + { + "category_id": 13, + "poly": [ + 1003, + 1223, + 1065, + 1223, + 1065, + 1256, + 1003, + 1256 + ], + "score": 0.91, + "latex": "( s , a )" + }, + { + "category_id": 13, + "poly": [ + 1080, + 864, + 1234, + 864, + 1234, + 898, + 1080, + 898 + ], + "score": 0.91, + "latex": "t = 1 , \\alpha _ { t } ^ { t } = 1" + }, + { + "category_id": 14, + "poly": [ + 473, + 1265, + 1222, + 1265, + 1222, + 1407, + 473, + 1407 + ], + "score": 0.91, + "latex": "\\begin{array} { r l } & { 0 \\le ( Q _ { p } - Q ^ { * } ) ( s , a ) \\le \\displaystyle \\frac { \\alpha _ { t } ^ { 0 } } { 1 - \\gamma } + \\displaystyle \\sum _ { i = 1 } ^ { t } \\gamma \\alpha _ { t } ^ { i } ( { \\hat { V } } _ { t _ { i } } - V ^ { * } ) ( s _ { t _ { i } + 1 } ) + \\beta _ { t } , } \\\\ & { 0 \\le ( { \\hat { Q } } _ { p } - Q ^ { * } ) ( s , a ) , } \\end{array}" + }, + { + "category_id": 13, + "poly": [ + 704, + 1222, + 796, + 1222, + 796, + 1256, + 704, + 1256 + ], + "score": 0.91, + "latex": "1 - \\delta / 2" + }, + { + "category_id": 13, + "poly": [ + 619, + 895, + 777, + 895, + 777, + 925, + 619, + 925 + ], + "score": 0.9, + "latex": "1 \\leq i \\leq t - 1" + }, + { + "category_id": 13, + "poly": [ + 396, + 359, + 634, + 359, + 634, + 397, + 396, + 397 + ], + "score": 0.9, + "latex": "\\textstyle \\sum _ { t = i } ^ { \\infty } \\alpha _ { t } ^ { i } = 1 + 1 / H" + }, + { + "category_id": 14, + "poly": [ + 310, + 1946, + 1428, + 1946, + 1428, + 2040, + 310, + 2040 + ], + "score": 0.9, + "latex": "Q _ { p } - Q ^ { * } ) ( s , a ) = \\alpha _ { t } ^ { 0 } ( \\frac { 1 } { 1 - \\gamma } - Q ^ { * } ( s , a ) ) + \\sum _ { i = 1 } ^ { t } \\alpha _ { t } ^ { i } \\left[ b _ { i } + \\gamma \\left( V _ { t _ { i } } - V ^ { * } \\right) \\left( s _ { t _ { i } + 1 } \\right) + \\gamma \\left( V ^ { * } \\left( s _ { t _ { i } + 1 } \\right) - \\mathbb { P } V ^ { * } \\right) \\right] ," + }, + { + "category_id": 13, + "poly": [ + 737, + 1416, + 1064, + 1416, + 1064, + 1457, + 737, + 1457 + ], + "score": 0.89, + "latex": "\\beta _ { t } = c _ { 3 } \\sqrt { H \\iota ( t ) / ( ( 1 - \\gamma ) ^ { 2 } t ) }" + }, + { + "category_id": 13, + "poly": [ + 371, + 1420, + 684, + 1420, + 684, + 1456, + 371, + 1456 + ], + "score": 0.89, + "latex": "t = N _ { p } ( s , a ) , t _ { i } = \\tau ( s , a , i )" + }, + { + "category_id": 13, + "poly": [ + 397, + 223, + 722, + 223, + 722, + 282, + 397, + 282 + ], + "score": 0.89, + "latex": "\\begin{array} { r } { \\sqrt { \\frac { 1 } { t } } \\leq \\sum _ { i = 1 } ^ { t } \\alpha _ { t } ^ { i } \\sqrt { \\frac { 1 } { i } } \\leq 2 \\sqrt { \\frac { 1 } { t } } } \\end{array}" + }, + { + "category_id": 13, + "poly": [ + 1291, + 865, + 1355, + 865, + 1355, + 895, + 1291, + 895 + ], + "score": 0.88, + "latex": "t \\geq 2" + }, + { + "category_id": 13, + "poly": [ + 1254, + 431, + 1393, + 431, + 1393, + 463, + 1254, + 463 + ], + "score": 0.88, + "latex": "t \\geq 1 , c \\geq 1" + }, + { + "category_id": 13, + "poly": [ + 656, + 298, + 861, + 298, + 861, + 341, + 656, + 341 + ], + "score": 0.87, + "latex": "\\begin{array} { r } { \\sum _ { i = 1 } ^ { t } ( \\alpha _ { t } ^ { i } ) ^ { 2 } \\le \\frac { 2 H } { t } } \\end{array}" + }, + { + "category_id": 13, + "poly": [ + 396, + 300, + 602, + 300, + 602, + 341, + 396, + 341 + ], + "score": 0.84, + "latex": "\\begin{array} { r } { \\operatorname* { m a x } _ { i \\in [ t ] } \\alpha _ { t } ^ { i } \\leq \\frac { 2 H } { t } } \\end{array}" + }, + { + "category_id": 13, + "poly": [ + 749, + 362, + 812, + 362, + 812, + 394, + 749, + 394 + ], + "score": 0.83, + "latex": "i \\geq 1" + }, + { + "category_id": 13, + "poly": [ + 787, + 868, + 801, + 868, + 801, + 892, + 787, + 892 + ], + "score": 0.7, + "latex": "t" + }, + { + "category_id": 13, + "poly": [ + 396, + 413, + 792, + 413, + 792, + 473, + 396, + 473 + ], + "score": 0.7, + "latex": "\\begin{array} { r } { \\sqrt { \\frac { \\iota ( t ) } { t } } \\leq \\sum _ { i = 1 } ^ { t } \\alpha _ { t } ^ { i } \\sqrt { \\frac { \\iota ( i ) } { i } } \\leq 2 \\sqrt { \\frac { \\iota ( t ) } { t } } } \\end{array}" + }, + { + "category_id": 13, + "poly": [ + 969, + 304, + 1034, + 304, + 1034, + 337, + 969, + 337 + ], + "score": 0.68, + "latex": "t \\geq 1" + }, + { + "category_id": 13, + "poly": [ + 866, + 427, + 1141, + 427, + 1141, + 466, + 866, + 466 + ], + "score": 0.63, + "latex": "\\iota ( t ) = \\ln ( c ( t + 1 ) ( t + 2 ) )" + }, + { + "category_id": 13, + "poly": [ + 831, + 235, + 971, + 235, + 971, + 272, + 831, + 272 + ], + "score": 0.58, + "latex": "t \\geq 1 , c > 0" + }, + { + "category_id": 15, + "poly": [ + 296.0, + 72.0, + 818.0, + 72.0, + 818.0, + 108.0, + 296.0, + 108.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1377.0, + 1177.0, + 1403.0, + 1177.0, + 1403.0, + 1205.0, + 1377.0, + 1205.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 831.0, + 2085.0, + 869.0, + 2085.0, + 869.0, + 2124.0, + 831.0, + 2124.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 831.0, + 2085.0, + 868.0, + 2085.0, + 868.0, + 2124.0, + 831.0, + 2124.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 858.0, + 786.0, + 858.0, + 786.0, + 901.0, + 292.0, + 901.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 802.0, + 858.0, + 1079.0, + 858.0, + 1079.0, + 901.0, + 802.0, + 901.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1235.0, + 858.0, + 1290.0, + 858.0, + 1290.0, + 901.0, + 1235.0, + 901.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1356.0, + 858.0, + 1405.0, + 858.0, + 1405.0, + 901.0, + 1356.0, + 901.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 891.0, + 356.0, + 891.0, + 356.0, + 931.0, + 294.0, + 931.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 576.0, + 891.0, + 618.0, + 891.0, + 618.0, + 931.0, + 576.0, + 931.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 778.0, + 891.0, + 952.0, + 891.0, + 952.0, + 931.0, + 778.0, + 931.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 1756.0, + 693.0, + 1756.0, + 693.0, + 1799.0, + 294.0, + 1799.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 1612.0, + 1175.0, + 1612.0, + 1175.0, + 1653.0, + 292.0, + 1653.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1262.0, + 1612.0, + 1273.0, + 1612.0, + 1273.0, + 1653.0, + 1262.0, + 1653.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 1042.0, + 465.0, + 1042.0, + 465.0, + 1082.0, + 295.0, + 1082.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 619.0, + 1042.0, + 978.0, + 1042.0, + 978.0, + 1082.0, + 619.0, + 1082.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1118.0, + 1042.0, + 1227.0, + 1042.0, + 1227.0, + 1082.0, + 1118.0, + 1082.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 1899.0, + 697.0, + 1899.0, + 697.0, + 1943.0, + 295.0, + 1943.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 1218.0, + 703.0, + 1218.0, + 703.0, + 1262.0, + 295.0, + 1262.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 797.0, + 1218.0, + 881.0, + 1218.0, + 881.0, + 1262.0, + 797.0, + 1262.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 951.0, + 1218.0, + 1002.0, + 1218.0, + 1002.0, + 1262.0, + 951.0, + 1262.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1066.0, + 1218.0, + 1129.0, + 1218.0, + 1129.0, + 1262.0, + 1066.0, + 1262.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 291.0, + 639.0, + 1170.0, + 639.0, + 1170.0, + 694.0, + 291.0, + 694.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 812.0, + 854.0, + 812.0, + 854.0, + 857.0, + 294.0, + 857.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 296.0, + 499.0, + 507.0, + 499.0, + 507.0, + 536.0, + 296.0, + 536.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 1483.0, + 508.0, + 1483.0, + 508.0, + 1520.0, + 293.0, + 1520.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 296.0, + 694.0, + 493.0, + 694.0, + 493.0, + 731.0, + 296.0, + 731.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 1409.0, + 370.0, + 1409.0, + 370.0, + 1464.0, + 293.0, + 1464.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 685.0, + 1409.0, + 736.0, + 1409.0, + 736.0, + 1464.0, + 685.0, + 1464.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1065.0, + 1409.0, + 1075.0, + 1409.0, + 1075.0, + 1464.0, + 1065.0, + 1464.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 351.0, + 291.0, + 395.0, + 291.0, + 395.0, + 349.0, + 351.0, + 349.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 603.0, + 291.0, + 655.0, + 291.0, + 655.0, + 349.0, + 603.0, + 349.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 862.0, + 291.0, + 968.0, + 291.0, + 968.0, + 349.0, + 862.0, + 349.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1035.0, + 291.0, + 1050.0, + 291.0, + 1050.0, + 349.0, + 1035.0, + 349.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 354.0, + 350.0, + 395.0, + 350.0, + 395.0, + 405.0, + 354.0, + 405.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 635.0, + 350.0, + 748.0, + 350.0, + 748.0, + 405.0, + 635.0, + 405.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 813.0, + 350.0, + 826.0, + 350.0, + 826.0, + 405.0, + 813.0, + 405.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 355.0, + 217.0, + 396.0, + 217.0, + 396.0, + 286.0, + 355.0, + 286.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 723.0, + 217.0, + 830.0, + 217.0, + 830.0, + 286.0, + 723.0, + 286.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 972.0, + 217.0, + 990.0, + 217.0, + 990.0, + 286.0, + 972.0, + 286.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 347.0, + 404.0, + 395.0, + 404.0, + 395.0, + 487.0, + 347.0, + 487.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 793.0, + 404.0, + 865.0, + 404.0, + 865.0, + 487.0, + 793.0, + 487.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1142.0, + 404.0, + 1253.0, + 404.0, + 1253.0, + 487.0, + 1142.0, + 487.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1394.0, + 404.0, + 1417.0, + 404.0, + 1417.0, + 487.0, + 1394.0, + 487.0 + ], + "score": 1.0, + "text": "" + } + ], + "page_info": { + "page_no": 11, + "width": 1700, + "height": 2200 + } + }, + { + "layout_dets": [ + { + "category_id": 1, + "poly": [ + 295, + 386, + 1411, + 386, + 1411, + 484, + 295, + 484 + ], + "score": 0.974 + }, + { + "category_id": 8, + "poly": [ + 456, + 1675, + 1242, + 1675, + 1242, + 1861, + 456, + 1861 + ], + "score": 0.974 + }, + { + "category_id": 8, + "poly": [ + 417, + 1229, + 1406, + 1229, + 1406, + 1546, + 417, + 1546 + ], + "score": 0.964 + }, + { + "category_id": 8, + "poly": [ + 574, + 860, + 1127, + 860, + 1127, + 945, + 574, + 945 + ], + "score": 0.961 + }, + { + "category_id": 8, + "poly": [ + 576, + 324, + 1123, + 324, + 1123, + 380, + 576, + 380 + ], + "score": 0.958 + }, + { + "category_id": 8, + "poly": [ + 417, + 669, + 1281, + 669, + 1281, + 773, + 417, + 773 + ], + "score": 0.957 + }, + { + "category_id": 1, + "poly": [ + 297, + 228, + 1406, + 228, + 1406, + 322, + 297, + 322 + ], + "score": 0.956 + }, + { + "category_id": 1, + "poly": [ + 297, + 953, + 1401, + 953, + 1401, + 1018, + 297, + 1018 + ], + "score": 0.951 + }, + { + "category_id": 1, + "poly": [ + 295, + 1602, + 1403, + 1602, + 1403, + 1668, + 295, + 1668 + ], + "score": 0.951 + }, + { + "category_id": 8, + "poly": [ + 581, + 1096, + 1117, + 1096, + 1117, + 1186, + 581, + 1186 + ], + "score": 0.95 + }, + { + "category_id": 1, + "poly": [ + 296, + 1915, + 1405, + 1915, + 1405, + 1992, + 296, + 1992 + ], + "score": 0.95 + }, + { + "category_id": 8, + "poly": [ + 509, + 491, + 1185, + 491, + 1185, + 584, + 509, + 584 + ], + "score": 0.949 + }, + { + "category_id": 1, + "poly": [ + 300, + 781, + 1408, + 781, + 1408, + 851, + 300, + 851 + ], + "score": 0.943 + }, + { + "category_id": 1, + "poly": [ + 297, + 1190, + 574, + 1190, + 574, + 1224, + 297, + 1224 + ], + "score": 0.929 + }, + { + "category_id": 1, + "poly": [ + 296, + 1866, + 1181, + 1866, + 1181, + 1902, + 296, + 1902 + ], + "score": 0.925 + }, + { + "category_id": 2, + "poly": [ + 298, + 73, + 817, + 73, + 817, + 106, + 298, + 106 + ], + "score": 0.923 + }, + { + "category_id": 1, + "poly": [ + 294, + 1552, + 955, + 1552, + 955, + 1592, + 294, + 1592 + ], + "score": 0.909 + }, + { + "category_id": 1, + "poly": [ + 297, + 587, + 1172, + 587, + 1172, + 623, + 297, + 623 + ], + "score": 0.907 + }, + { + "category_id": 9, + "poly": [ + 1351, + 520, + 1401, + 520, + 1401, + 552, + 1351, + 552 + ], + "score": 0.896 + }, + { + "category_id": 9, + "poly": [ + 1351, + 708, + 1400, + 708, + 1400, + 740, + 1351, + 740 + ], + "score": 0.885 + }, + { + "category_id": 1, + "poly": [ + 296, + 1037, + 1163, + 1037, + 1163, + 1088, + 296, + 1088 + ], + "score": 0.882 + }, + { + "category_id": 2, + "poly": [ + 835, + 2087, + 864, + 2087, + 864, + 2113, + 835, + 2113 + ], + "score": 0.872 + }, + { + "category_id": 2, + "poly": [ + 1374, + 2004, + 1402, + 2004, + 1402, + 2031, + 1374, + 2031 + ], + "score": 0.745 + }, + { + "category_id": 14, + "poly": [ + 454, + 1671, + 1242, + 1671, + 1242, + 1865, + 454, + 1865 + ], + "score": 0.94, + "latex": "\\begin{array} { c l } { ( Q _ { p } - Q ^ { * } ) ( s , a ) \\geq - \\gamma \\displaystyle \\left| \\displaystyle \\sum _ { i = 1 } ^ { t } \\Delta _ { i } \\right| + \\displaystyle \\sum _ { i = 1 } ^ { t } \\alpha _ { t } ^ { i } \\left[ \\gamma ( \\hat { V } _ { t _ { i } } - V ^ { * } ) ( x _ { t _ { i } + 1 } ) + b _ { i } \\right] } \\\\ { \\geq \\displaystyle \\sum _ { i = 1 } ^ { t } \\alpha _ { t } ^ { i } b _ { i } - \\gamma \\displaystyle \\left| \\displaystyle \\sum _ { i = 1 } ^ { t } \\Delta _ { i } \\right| \\geq 0 . } \\end{array}" + }, + { + "category_id": 14, + "poly": [ + 509, + 488, + 1190, + 488, + 1190, + 585, + 509, + 585 + ], + "score": 0.93, + "latex": "\\mathrm { P r } \\left[ \\left| \\sum _ { i = 1 } ^ { k } \\Delta _ { i } \\right| > \\eta \\right] \\leq 2 \\exp \\left\\{ - \\frac { \\eta ^ { 2 } } { 8 \\left( 1 - \\gamma \\right) ^ { - 2 } \\sum _ { i = 1 } ^ { k } ( \\alpha _ { k } ^ { i } ) ^ { 2 } } \\right\\} ." + }, + { + "category_id": 13, + "poly": [ + 1106, + 1913, + 1205, + 1913, + 1205, + 1953, + 1106, + 1953 + ], + "score": 0.93, + "latex": "\\hat { Q } _ { p } ( s , a )" + }, + { + "category_id": 13, + "poly": [ + 352, + 1954, + 458, + 1954, + 458, + 1991, + 352, + 1991 + ], + "score": 0.93, + "latex": "Q _ { p ^ { \\prime } } ( s , a )" + }, + { + "category_id": 13, + "poly": [ + 297, + 261, + 454, + 261, + 454, + 295, + 297, + 295 + ], + "score": 0.93, + "latex": "t _ { i } = \\tau ( s , a , i )" + }, + { + "category_id": 13, + "poly": [ + 1032, + 954, + 1183, + 954, + 1183, + 989, + 1032, + 989 + ], + "score": 0.93, + "latex": "t = N _ { p } ( s , a )" + }, + { + "category_id": 14, + "poly": [ + 572, + 853, + 1124, + 853, + 1124, + 948, + 572, + 948 + ], + "score": 0.93, + "latex": "1 - \\sum _ { s ^ { \\prime } \\in S , a ^ { \\prime } \\in A } \\sum _ { k = 1 } ^ { \\infty } \\frac { \\delta } { 2 S A ( k + 1 ) ( k + 2 ) } = 1 - \\frac { \\delta } { 2 } ." + }, + { + "category_id": 13, + "poly": [ + 1252, + 231, + 1396, + 231, + 1396, + 265, + 1252, + 265 + ], + "score": 0.93, + "latex": "t = N _ { p } ( s , a )" + }, + { + "category_id": 14, + "poly": [ + 413, + 670, + 1282, + 670, + 1282, + 775, + 413, + 775 + ], + "score": 0.93, + "latex": "\\left| \\sum _ { i = 1 } ^ { k } \\Delta _ { i } \\right| \\leq \\frac { 2 \\sqrt { 2 } } { 1 - \\gamma } \\cdot \\sqrt { \\sum _ { i = 1 } ^ { k } ( \\alpha _ { k } ^ { i } ) ^ { 2 } \\cdot \\ln \\frac { 2 ( k + 1 ) ( k + 2 ) S A } { \\delta } } \\leq \\frac { c _ { 2 } } { 1 - \\gamma } \\sqrt { \\frac { H \\iota ( k ) } { k } } ." + }, + { + "category_id": 13, + "poly": [ + 485, + 782, + 751, + 782, + 751, + 824, + 485, + 824 + ], + "score": 0.93, + "latex": "\\begin{array} { r } { \\iota ( k ) = \\ln { \\frac { ( k + 1 ) ( k + 2 ) S A } { \\delta } } } \\end{array}" + }, + { + "category_id": 13, + "poly": [ + 1107, + 1635, + 1182, + 1635, + 1182, + 1666, + 1107, + 1666 + ], + "score": 0.93, + "latex": "p ^ { \\prime } = 0" + }, + { + "category_id": 13, + "poly": [ + 297, + 417, + 463, + 417, + 463, + 450, + 297, + 450 + ], + "score": 0.92, + "latex": "\\mathbb { E } \\left[ \\Delta _ { i } | F _ { i } \\right] = 0" + }, + { + "category_id": 13, + "poly": [ + 298, + 1635, + 406, + 1635, + 406, + 1669, + 298, + 1669 + ], + "score": 0.92, + "latex": "Q _ { p } \\geq Q ^ { * }" + }, + { + "category_id": 13, + "poly": [ + 486, + 1634, + 548, + 1634, + 548, + 1668, + 486, + 1668 + ], + "score": 0.92, + "latex": "( s , a )" + }, + { + "category_id": 13, + "poly": [ + 599, + 1635, + 674, + 1635, + 674, + 1667, + 599, + 1667 + ], + "score": 0.92, + "latex": "p \\leq p ^ { \\prime }" + }, + { + "category_id": 13, + "poly": [ + 809, + 1953, + 1181, + 1953, + 1181, + 1991, + 809, + 1991 + ], + "score": 0.92, + "latex": "\\hat { Q } _ { p } ( s , a ) \\geq Q _ { p ^ { \\prime } } ( s , a ) \\geq Q ^ { * } ( s , a )" + }, + { + "category_id": 14, + "poly": [ + 574, + 321, + 1124, + 321, + 1124, + 381, + 574, + 381 + ], + "score": 0.92, + "latex": "\\Delta _ { i } = \\left( \\alpha _ { k } ^ { i } \\cdot I [ t _ { i } < \\infty ] \\cdot \\left( \\mathbb { P } V ^ { * } - \\mathbb { \\hat { P } } _ { t _ { i } } V ^ { * } \\right) ( s , a ) \\right)" + }, + { + "category_id": 13, + "poly": [ + 567, + 1954, + 642, + 1954, + 642, + 1988, + 567, + 1988 + ], + "score": 0.92, + "latex": "p ^ { \\prime } \\leq p" + }, + { + "category_id": 13, + "poly": [ + 783, + 417, + 841, + 417, + 841, + 450, + 783, + 450 + ], + "score": 0.92, + "latex": "F _ { i + 1 }" + }, + { + "category_id": 13, + "poly": [ + 427, + 985, + 517, + 985, + 517, + 1019, + 427, + 1019 + ], + "score": 0.91, + "latex": "1 - \\delta / 2" + }, + { + "category_id": 13, + "poly": [ + 664, + 1867, + 738, + 1867, + 738, + 1899, + 664, + 1899 + ], + "score": 0.91, + "latex": "p ^ { \\prime } + 1" + }, + { + "category_id": 13, + "poly": [ + 781, + 1918, + 872, + 1918, + 872, + 1952, + 781, + 1952 + ], + "score": 0.91, + "latex": "1 - \\delta / 2" + }, + { + "category_id": 13, + "poly": [ + 856, + 589, + 1158, + 589, + 1158, + 622, + 856, + 622 + ], + "score": 0.9, + "latex": "1 - \\delta / \\left[ S A ( k + 1 ) ( k + 2 ) \\right]" + }, + { + "category_id": 13, + "poly": [ + 1125, + 231, + 1196, + 231, + 1196, + 262, + 1125, + 262 + ], + "score": 0.9, + "latex": "p \\in \\mathbb N" + }, + { + "category_id": 13, + "poly": [ + 873, + 263, + 937, + 263, + 937, + 292, + 873, + 292 + ], + "score": 0.9, + "latex": "t \\geq 1" + }, + { + "category_id": 13, + "poly": [ + 1257, + 414, + 1397, + 414, + 1397, + 457, + 1257, + 457 + ], + "score": 0.9, + "latex": "\\begin{array} { r } { | \\Delta _ { i } | \\le \\frac { 2 } { 1 - \\gamma } } \\end{array}" + }, + { + "category_id": 13, + "poly": [ + 517, + 263, + 582, + 263, + 582, + 290, + 517, + 290 + ], + "score": 0.9, + "latex": "t = 0" + }, + { + "category_id": 13, + "poly": [ + 1329, + 789, + 1397, + 789, + 1397, + 817, + 1329, + 817 + ], + "score": 0.89, + "latex": "k > 0" + }, + { + "category_id": 13, + "poly": [ + 420, + 453, + 454, + 453, + 454, + 482, + 420, + 482 + ], + "score": 0.89, + "latex": "\\Delta _ { i }" + }, + { + "category_id": 13, + "poly": [ + 548, + 418, + 583, + 418, + 583, + 447, + 548, + 447 + ], + "score": 0.89, + "latex": "\\Delta _ { i }" + }, + { + "category_id": 13, + "poly": [ + 925, + 232, + 993, + 232, + 993, + 260, + 925, + 260 + ], + "score": 0.89, + "latex": "s \\in S" + }, + { + "category_id": 13, + "poly": [ + 358, + 784, + 474, + 784, + 474, + 819, + 358, + 819 + ], + "score": 0.89, + "latex": "c _ { 2 } = 4 \\sqrt { 2 }" + }, + { + "category_id": 13, + "poly": [ + 1003, + 232, + 1076, + 232, + 1076, + 260, + 1003, + 260 + ], + "score": 0.88, + "latex": "a \\in A" + }, + { + "category_id": 13, + "poly": [ + 937, + 388, + 1149, + 388, + 1149, + 419, + 937, + 419 + ], + "score": 0.88, + "latex": "( s _ { 1 } , a _ { 1 } , . . . , s _ { t _ { i } } , a _ { t _ { i } } )" + }, + { + "category_id": 14, + "poly": [ + 415, + 1228, + 1285, + 1228, + 1285, + 1418, + 415, + 1418 + ], + "score": 0.88, + "latex": "\\begin{array} { r l } & { ( Q _ { p } - Q ^ { * } ) ( s , a ) \\leq \\displaystyle \\frac { \\alpha _ { t } ^ { 0 } } { 1 - \\gamma } + \\gamma \\left| \\displaystyle \\sum _ { i = 1 } ^ { t } \\Delta _ { i } \\right| + \\displaystyle \\sum _ { i = 1 } ^ { t } \\alpha _ { t } ^ { i } \\left[ \\gamma ( \\hat { V } _ { t _ { i } } - V ^ { * } ) ( x _ { t _ { i } + 1 } ) + b _ { i } \\right] } \\\\ & { \\qquad \\leq \\displaystyle \\frac { \\alpha _ { t } ^ { 0 } } { 1 - \\gamma } + \\displaystyle \\frac { 3 c _ { 2 } } { 1 - \\gamma } \\sqrt { \\frac { H \\iota ( t ) } { t } } + \\displaystyle \\sum _ { i = 1 } ^ { t } \\gamma \\alpha _ { t } ^ { i } ( \\hat { V } ^ { t _ { i } } - V ^ { * } ) ( x _ { t _ { i } + 1 } ) } \\end{array}" + }, + { + "category_id": 14, + "poly": [ + 580, + 1093, + 1115, + 1093, + 1115, + 1187, + 580, + 1187 + ], + "score": 0.86, + "latex": "\\frac { c _ { 2 } } { 1 - \\gamma } \\sqrt { \\frac { H \\iota ( k ) } { k } } \\leq \\sum _ { i = 1 } ^ { k } \\alpha _ { k } ^ { i } b _ { i } \\leq \\frac { 2 c _ { 2 } } { 1 - \\gamma } \\sqrt { \\frac { H \\iota ( k ) } { k } } ." + }, + { + "category_id": 13, + "poly": [ + 346, + 388, + 376, + 388, + 376, + 416, + 346, + 416 + ], + "score": 0.86, + "latex": "F _ { i }" + }, + { + "category_id": 13, + "poly": [ + 407, + 1553, + 729, + 1553, + 729, + 1593, + 407, + 1593 + ], + "score": 0.85, + "latex": "\\beta _ { t } = c _ { 3 } ( 1 - \\gamma ) ^ { - 1 } \\sqrt { H \\iota ( t ) / t }" + }, + { + "category_id": 13, + "poly": [ + 996, + 417, + 1242, + 417, + 1242, + 455, + 996, + 455 + ], + "score": 0.85, + "latex": "\\textstyle 0 \\leq V ^ { \\ast } ( s , { \\bar { a } } ) \\leq { \\frac { 1 } { 1 - \\gamma } }" + }, + { + "category_id": 13, + "poly": [ + 1380, + 265, + 1398, + 265, + 1398, + 289, + 1380, + 289 + ], + "score": 0.83, + "latex": "k" + }, + { + "category_id": 13, + "poly": [ + 469, + 391, + 489, + 391, + 489, + 414, + 469, + 414 + ], + "score": 0.81, + "latex": "\\sigma" + }, + { + "category_id": 13, + "poly": [ + 1043, + 790, + 1061, + 790, + 1061, + 816, + 1043, + 816 + ], + "score": 0.81, + "latex": "k" + }, + { + "category_id": 13, + "poly": [ + 1155, + 1874, + 1171, + 1874, + 1171, + 1899, + 1155, + 1899 + ], + "score": 0.79, + "latex": "p" + }, + { + "category_id": 13, + "poly": [ + 1317, + 962, + 1334, + 962, + 1334, + 987, + 1317, + 987 + ], + "score": 0.77, + "latex": "p" + }, + { + "category_id": 13, + "poly": [ + 951, + 1922, + 1024, + 1922, + 1024, + 1951, + 951, + 1951 + ], + "score": 0.77, + "latex": "p , s , a" + }, + { + "category_id": 13, + "poly": [ + 479, + 822, + 551, + 822, + 551, + 847, + 479, + 847 + ], + "score": 0.77, + "latex": "a \\in A" + }, + { + "category_id": 13, + "poly": [ + 444, + 596, + 461, + 596, + 461, + 621, + 444, + 621 + ], + "score": 0.76, + "latex": "\\eta" + }, + { + "category_id": 13, + "poly": [ + 400, + 821, + 469, + 821, + 469, + 848, + 400, + 848 + ], + "score": 0.74, + "latex": "s \\in S" + }, + { + "category_id": 13, + "poly": [ + 740, + 1552, + 948, + 1552, + 948, + 1590, + 740, + 1590 + ], + "score": 0.73, + "latex": "c _ { 3 } = 3 c _ { 2 } = 1 2 { \\sqrt { 2 } } ." + }, + { + "category_id": 13, + "poly": [ + 801, + 237, + 819, + 237, + 819, + 258, + 801, + 258 + ], + "score": 0.73, + "latex": "a" + }, + { + "category_id": 13, + "poly": [ + 937, + 1033, + 1157, + 1033, + 1157, + 1089, + 937, + 1089 + ], + "score": 0.68, + "latex": "\\begin{array} { r } { ( b _ { k } = \\frac { c _ { 2 } } { 1 - \\gamma } \\sqrt { \\frac { H \\iota ( k ) } { k } } ) } \\end{array}" + }, + { + "category_id": 13, + "poly": [ + 708, + 238, + 725, + 238, + 725, + 262, + 708, + 262 + ], + "score": 0.6, + "latex": "p" + }, + { + "category_id": 13, + "poly": [ + 736, + 238, + 753, + 238, + 753, + 259, + 736, + 259 + ], + "score": 0.47, + "latex": "s" + }, + { + "category_id": 14, + "poly": [ + 608, + 1453, + 1121, + 1453, + 1121, + 1546, + 608, + 1546 + ], + "score": 0.38, + "latex": "\\leq \\frac { \\alpha _ { t } ^ { 0 } } { 1 - \\gamma } + \\sum _ { i = 1 } ^ { t } \\gamma \\alpha _ { t } ^ { i } ( { \\hat { V } } ^ { t _ { i } } - V ^ { * } ) ( x _ { t _ { i } + 1 } ) + \\beta _ { t } ." + }, + { + "category_id": 13, + "poly": [ + 399, + 820, + 551, + 820, + 551, + 849, + 399, + 849 + ], + "score": 0.33, + "latex": "s \\in S , a \\in A" + }, + { + "category_id": 13, + "poly": [ + 707, + 237, + 753, + 237, + 753, + 261, + 707, + 261 + ], + "score": 0.31, + "latex": "p , s" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 72.0, + 817.0, + 72.0, + 817.0, + 108.0, + 295.0, + 108.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 831.0, + 2085.0, + 868.0, + 2085.0, + 868.0, + 2124.0, + 831.0, + 2124.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1381.0, + 2009.0, + 1401.0, + 2009.0, + 1401.0, + 2029.0, + 1381.0, + 2029.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 381.0, + 345.0, + 381.0, + 345.0, + 423.0, + 292.0, + 423.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 377.0, + 381.0, + 468.0, + 381.0, + 468.0, + 423.0, + 377.0, + 423.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 490.0, + 381.0, + 936.0, + 381.0, + 936.0, + 423.0, + 490.0, + 423.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1150.0, + 381.0, + 1408.0, + 381.0, + 1408.0, + 423.0, + 1150.0, + 423.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 287.0, + 401.0, + 296.0, + 401.0, + 296.0, + 465.0, + 287.0, + 465.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 464.0, + 401.0, + 547.0, + 401.0, + 547.0, + 465.0, + 464.0, + 465.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 584.0, + 401.0, + 782.0, + 401.0, + 782.0, + 465.0, + 584.0, + 465.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 842.0, + 401.0, + 995.0, + 401.0, + 995.0, + 465.0, + 842.0, + 465.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1243.0, + 401.0, + 1256.0, + 401.0, + 1256.0, + 465.0, + 1243.0, + 465.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1398.0, + 401.0, + 1410.0, + 401.0, + 1410.0, + 465.0, + 1398.0, + 465.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 446.0, + 419.0, + 446.0, + 419.0, + 488.0, + 293.0, + 488.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 455.0, + 446.0, + 1271.0, + 446.0, + 1271.0, + 488.0, + 455.0, + 488.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 225.0, + 706.0, + 225.0, + 706.0, + 267.0, + 292.0, + 267.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 754.0, + 225.0, + 800.0, + 225.0, + 800.0, + 267.0, + 754.0, + 267.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 820.0, + 225.0, + 924.0, + 225.0, + 924.0, + 267.0, + 820.0, + 267.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 994.0, + 225.0, + 1002.0, + 225.0, + 1002.0, + 267.0, + 994.0, + 267.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1077.0, + 225.0, + 1124.0, + 225.0, + 1124.0, + 267.0, + 1077.0, + 267.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1197.0, + 225.0, + 1251.0, + 225.0, + 1251.0, + 267.0, + 1197.0, + 267.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1397.0, + 225.0, + 1408.0, + 225.0, + 1408.0, + 267.0, + 1397.0, + 267.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 291.0, + 259.0, + 296.0, + 259.0, + 296.0, + 296.0, + 291.0, + 296.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 455.0, + 259.0, + 516.0, + 259.0, + 516.0, + 296.0, + 455.0, + 296.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 583.0, + 259.0, + 872.0, + 259.0, + 872.0, + 296.0, + 583.0, + 296.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 938.0, + 259.0, + 1379.0, + 259.0, + 1379.0, + 296.0, + 938.0, + 296.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1399.0, + 259.0, + 1411.0, + 259.0, + 1411.0, + 296.0, + 1399.0, + 296.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 288.0, + 381.0, + 288.0, + 381.0, + 325.0, + 292.0, + 325.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 949.0, + 1031.0, + 949.0, + 1031.0, + 989.0, + 293.0, + 989.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1184.0, + 949.0, + 1316.0, + 949.0, + 1316.0, + 989.0, + 1184.0, + 989.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1335.0, + 949.0, + 1403.0, + 949.0, + 1403.0, + 989.0, + 1335.0, + 989.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 986.0, + 426.0, + 986.0, + 426.0, + 1019.0, + 293.0, + 1019.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 518.0, + 986.0, + 613.0, + 986.0, + 613.0, + 1019.0, + 518.0, + 1019.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 1600.0, + 1406.0, + 1600.0, + 1406.0, + 1638.0, + 293.0, + 1638.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 1632.0, + 297.0, + 1632.0, + 297.0, + 1671.0, + 294.0, + 1671.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 407.0, + 1632.0, + 485.0, + 1632.0, + 485.0, + 1671.0, + 407.0, + 1671.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 549.0, + 1632.0, + 598.0, + 1632.0, + 598.0, + 1671.0, + 549.0, + 1671.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 675.0, + 1632.0, + 1106.0, + 1632.0, + 1106.0, + 1671.0, + 675.0, + 1671.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1183.0, + 1632.0, + 1260.0, + 1632.0, + 1260.0, + 1671.0, + 1183.0, + 1671.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 1913.0, + 780.0, + 1913.0, + 780.0, + 1955.0, + 294.0, + 1955.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 873.0, + 1913.0, + 950.0, + 1913.0, + 950.0, + 1955.0, + 873.0, + 1955.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1025.0, + 1913.0, + 1105.0, + 1913.0, + 1105.0, + 1955.0, + 1025.0, + 1955.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1206.0, + 1913.0, + 1405.0, + 1913.0, + 1405.0, + 1955.0, + 1206.0, + 1955.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 1952.0, + 351.0, + 1952.0, + 351.0, + 1995.0, + 295.0, + 1995.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 459.0, + 1952.0, + 566.0, + 1952.0, + 566.0, + 1995.0, + 459.0, + 1995.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 643.0, + 1952.0, + 808.0, + 1952.0, + 808.0, + 1995.0, + 643.0, + 1995.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1182.0, + 1952.0, + 1398.0, + 1952.0, + 1398.0, + 1995.0, + 1182.0, + 1995.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 289.0, + 769.0, + 357.0, + 769.0, + 357.0, + 831.0, + 289.0, + 831.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 475.0, + 769.0, + 484.0, + 769.0, + 484.0, + 831.0, + 475.0, + 831.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 752.0, + 769.0, + 1042.0, + 769.0, + 1042.0, + 831.0, + 752.0, + 831.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1062.0, + 769.0, + 1328.0, + 769.0, + 1328.0, + 831.0, + 1062.0, + 831.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1398.0, + 769.0, + 1414.0, + 769.0, + 1414.0, + 831.0, + 1398.0, + 831.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 815.0, + 398.0, + 815.0, + 398.0, + 855.0, + 295.0, + 855.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 552.0, + 815.0, + 912.0, + 815.0, + 912.0, + 855.0, + 552.0, + 855.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 1187.0, + 576.0, + 1187.0, + 576.0, + 1229.0, + 293.0, + 1229.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 1862.0, + 663.0, + 1862.0, + 663.0, + 1905.0, + 293.0, + 1905.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 739.0, + 1862.0, + 1154.0, + 1862.0, + 1154.0, + 1905.0, + 739.0, + 1905.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1172.0, + 1862.0, + 1182.0, + 1862.0, + 1182.0, + 1905.0, + 1172.0, + 1905.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 1548.0, + 406.0, + 1548.0, + 406.0, + 1596.0, + 294.0, + 1596.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 730.0, + 1548.0, + 739.0, + 1548.0, + 739.0, + 1596.0, + 730.0, + 1596.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 949.0, + 1548.0, + 955.0, + 1548.0, + 955.0, + 1596.0, + 949.0, + 1596.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 584.0, + 443.0, + 584.0, + 443.0, + 627.0, + 295.0, + 627.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 462.0, + 584.0, + 855.0, + 584.0, + 855.0, + 627.0, + 462.0, + 627.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1159.0, + 584.0, + 1171.0, + 584.0, + 1171.0, + 627.0, + 1159.0, + 627.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 1045.0, + 936.0, + 1045.0, + 936.0, + 1083.0, + 293.0, + 1083.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1158.0, + 1029.0, + 1164.0, + 1029.0, + 1164.0, + 1075.0, + 1158.0, + 1075.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1004.0, + 1062.0, + 1056.0, + 1062.0, + 1056.0, + 1084.5, + 1004.0, + 1084.5 + ], + "score": 1.0, + "text": "" + } + ], + "page_info": { + "page_no": 12, + "width": 1700, + "height": 2200 + } + }, + { + "layout_dets": [ + { + "category_id": 8, + "poly": [ + 444, + 376, + 1252, + 376, + 1252, + 629, + 444, + 629 + ], + "score": 0.97 + }, + { + "category_id": 8, + "poly": [ + 578, + 882, + 1120, + 882, + 1120, + 1081, + 578, + 1081 + ], + "score": 0.964 + }, + { + "category_id": 8, + "poly": [ + 551, + 1350, + 1145, + 1350, + 1145, + 1592, + 551, + 1592 + ], + "score": 0.962 + }, + { + "category_id": 8, + "poly": [ + 648, + 1663, + 1048, + 1663, + 1048, + 1813, + 648, + 1813 + ], + "score": 0.962 + }, + { + "category_id": 8, + "poly": [ + 716, + 716, + 983, + 716, + 983, + 804, + 716, + 804 + ], + "score": 0.957 + }, + { + "category_id": 8, + "poly": [ + 633, + 1896, + 1064, + 1896, + 1064, + 1983, + 633, + 1983 + ], + "score": 0.954 + }, + { + "category_id": 1, + "poly": [ + 291, + 227, + 1403, + 227, + 1403, + 298, + 291, + 298 + ], + "score": 0.951 + }, + { + "category_id": 1, + "poly": [ + 297, + 1224, + 1406, + 1224, + 1406, + 1295, + 297, + 1295 + ], + "score": 0.949 + }, + { + "category_id": 1, + "poly": [ + 297, + 639, + 1403, + 639, + 1403, + 708, + 297, + 708 + ], + "score": 0.949 + }, + { + "category_id": 1, + "poly": [ + 295, + 1831, + 1400, + 1831, + 1400, + 1895, + 295, + 1895 + ], + "score": 0.939 + }, + { + "category_id": 1, + "poly": [ + 295, + 831, + 1063, + 831, + 1063, + 870, + 295, + 870 + ], + "score": 0.935 + }, + { + "category_id": 1, + "poly": [ + 296, + 329, + 870, + 329, + 870, + 364, + 296, + 364 + ], + "score": 0.927 + }, + { + "category_id": 1, + "poly": [ + 297, + 1308, + 804, + 1308, + 804, + 1340, + 297, + 1340 + ], + "score": 0.922 + }, + { + "category_id": 1, + "poly": [ + 296, + 1642, + 377, + 1642, + 377, + 1674, + 296, + 1674 + ], + "score": 0.921 + }, + { + "category_id": 2, + "poly": [ + 298, + 73, + 817, + 73, + 817, + 106, + 298, + 106 + ], + "score": 0.921 + }, + { + "category_id": 8, + "poly": [ + 704, + 1174, + 1085, + 1174, + 1085, + 1215, + 704, + 1215 + ], + "score": 0.897 + }, + { + "category_id": 9, + "poly": [ + 1351, + 739, + 1401, + 739, + 1401, + 771, + 1351, + 771 + ], + "score": 0.896 + }, + { + "category_id": 9, + "poly": [ + 1351, + 1181, + 1400, + 1181, + 1400, + 1212, + 1351, + 1212 + ], + "score": 0.896 + }, + { + "category_id": 9, + "poly": [ + 1351, + 563, + 1401, + 563, + 1401, + 595, + 1351, + 595 + ], + "score": 0.893 + }, + { + "category_id": 9, + "poly": [ + 1351, + 1499, + 1401, + 1499, + 1401, + 1531, + 1351, + 1531 + ], + "score": 0.888 + }, + { + "category_id": 9, + "poly": [ + 1351, + 1019, + 1401, + 1019, + 1401, + 1051, + 1351, + 1051 + ], + "score": 0.886 + }, + { + "category_id": 9, + "poly": [ + 1351, + 1597, + 1401, + 1597, + 1401, + 1629, + 1351, + 1629 + ], + "score": 0.885 + }, + { + "category_id": 8, + "poly": [ + 702, + 1090, + 1113, + 1090, + 1113, + 1165, + 702, + 1165 + ], + "score": 0.885 + }, + { + "category_id": 9, + "poly": [ + 1351, + 1103, + 1400, + 1103, + 1400, + 1135, + 1351, + 1135 + ], + "score": 0.879 + }, + { + "category_id": 2, + "poly": [ + 835, + 2088, + 864, + 2088, + 864, + 2113, + 835, + 2113 + ], + "score": 0.879 + }, + { + "category_id": 1, + "poly": [ + 328, + 2002, + 1096, + 2002, + 1096, + 2036, + 328, + 2036 + ], + "score": 0.731 + }, + { + "category_id": 2, + "poly": [ + 328, + 2002, + 1096, + 2002, + 1096, + 2036, + 328, + 2036 + ], + "score": 0.159 + }, + { + "category_id": 13, + "poly": [ + 457, + 262, + 532, + 262, + 532, + 295, + 457, + 295 + ], + "score": 0.95, + "latex": "( C , w )" + }, + { + "category_id": 13, + "poly": [ + 424, + 331, + 602, + 331, + 602, + 365, + 424, + 365 + ], + "score": 0.95, + "latex": "n _ { t } = N _ { t } ( s _ { t } , a _ { t } )" + }, + { + "category_id": 14, + "poly": [ + 577, + 881, + 1119, + 881, + 1119, + 1217, + 577, + 1217 + ], + "score": 0.94, + "latex": "\\begin{array} { l } { \\displaystyle \\sum _ { t \\geq 1 } w _ { t } \\beta _ { n _ { t } } = \\sum _ { s , o } ^ { u ( s , o ) } w _ { \\tau ( s , a , i ) } \\beta _ { i } } \\\\ { \\displaystyle \\qquad \\leq \\sum _ { s , a } ( 1 - \\gamma ) ^ { - 1 } c _ { 3 } \\sum _ { i = 1 } ^ { C _ { s , a } / w } \\sqrt { \\frac { H \\iota ( i ) } { i } } w } \\\\ { \\displaystyle \\qquad \\leq 2 \\sum _ { s , a } ( 1 - \\gamma ) ^ { - 1 } c _ { 3 } \\sqrt { \\iota ( C ) H C _ { s , a } w } } \\\\ { \\displaystyle \\qquad \\leq 2 c _ { 3 } ( 1 - \\gamma ) ^ { - 1 } \\sqrt { w S A H C \\iota ( C ) } . } \\end{array}" + }, + { + "category_id": 14, + "poly": [ + 632, + 1889, + 1066, + 1889, + 1066, + 1985, + 632, + 1985 + ], + "score": 0.94, + "latex": "w _ { t ^ { \\prime } + 1 } ^ { \\prime } \\leq w \\sum _ { j = n _ { t ^ { \\prime } } } ^ { \\infty } \\alpha _ { j } ^ { n _ { t ^ { \\prime } } } = ( 1 + 1 / H ) w ." + }, + { + "category_id": 14, + "poly": [ + 439, + 374, + 1253, + 374, + 1253, + 630, + 439, + 630 + ], + "score": 0.94, + "latex": "\\begin{array} { r l } { { \\sum _ { t \\geq 1 } w _ { t } ( \\hat { Q } _ { t } - Q ^ { * } ) ( s _ { t } , a _ { t } ) } } \\\\ & { \\leq \\sum _ { t \\geq 1 } w _ { t } ( Q _ { t } - Q ^ { * } ) ( s _ { t } , a _ { t } ) } \\\\ & { \\leq \\sum _ { t \\geq 1 } w _ { t } [ \\cfrac { \\alpha _ { n _ { t } } ^ { 0 } } { 1 - \\gamma } + \\beta _ { n _ { t } } + \\gamma \\sum _ { i = 1 } ^ { n _ { t } } \\alpha _ { n _ { t } } ^ { i } ( \\hat { V } _ { \\tau ( s _ { t } , a _ { t } , i ) } - V ^ { * } ) ( s _ { \\tau ( s _ { t } , a _ { t } , i ) + 1 } ) ] } \\end{array}" + }, + { + "category_id": 14, + "poly": [ + 649, + 1662, + 1049, + 1662, + 1049, + 1810, + 649, + 1810 + ], + "score": 0.94, + "latex": "w _ { t ^ { \\prime } + 1 } ^ { \\prime } = \\left( \\sum _ { \\stackrel { t = t ^ { \\prime } + 1 } { ( s _ { t } , a _ { t } ) = ( s _ { t } ^ { \\prime } , a _ { t } ^ { \\prime } ) } } ^ { \\infty } \\alpha _ { n _ { t } } ^ { n _ { t ^ { \\prime } } } w _ { t } \\right) ." + }, + { + "category_id": 14, + "poly": [ + 713, + 713, + 984, + 713, + 984, + 806, + 713, + 806 + ], + "score": 0.93, + "latex": "\\sum _ { t \\geq 1 } w _ { t } \\frac { \\alpha _ { n _ { t } } ^ { 0 } } { 1 - \\gamma } \\leq \\frac { S A w } { 1 - \\gamma } ." + }, + { + "category_id": 14, + "poly": [ + 550, + 1348, + 1150, + 1348, + 1150, + 1593, + 550, + 1593 + ], + "score": 0.93, + "latex": "\\begin{array} { c } { { \\displaystyle \\sum _ { t \\ge 1 } w _ { t } \\sum _ { i = 1 } ^ { n _ { t } } \\alpha _ { n _ { t } } ^ { i } \\left( \\hat { V } _ { \\tau ( s _ { t } , a _ { t } , i ) } - V ^ { * } \\right) \\left( s _ { \\tau ( s _ { t } , a _ { t } , i ) + 1 } \\right) } } \\\\ { { \\displaystyle \\le \\sum _ { t ^ { \\prime } \\ge 1 } \\left( \\hat { V } _ { t ^ { \\prime } } - V ^ { * } \\right) \\left( s _ { t ^ { \\prime } + 1 } \\right) \\left( \\sum _ { t = t ^ { \\prime } + 1 } ^ { \\infty } \\alpha _ { n _ { t } } ^ { n _ { t ^ { \\prime } } } w _ { t } \\right) . } } \\end{array}" + }, + { + "category_id": 13, + "poly": [ + 606, + 834, + 874, + 834, + 874, + 869, + 606, + 869 + ], + "score": 0.93, + "latex": "u ( s , a ) = \\operatorname* { s u p } _ { t } N _ { t } ( s , a )" + }, + { + "category_id": 13, + "poly": [ + 823, + 640, + 1007, + 640, + 1007, + 679, + 823, + 679 + ], + "score": 0.93, + "latex": "\\alpha _ { n _ { t } } ^ { 0 } = \\mathbb { I } [ n _ { t } = 0 ]" + }, + { + "category_id": 13, + "poly": [ + 460, + 1834, + 520, + 1834, + 520, + 1870, + 460, + 1870 + ], + "score": 0.92, + "latex": "w _ { t + 1 } ^ { \\prime }" + }, + { + "category_id": 13, + "poly": [ + 1168, + 261, + 1330, + 261, + 1330, + 300, + 1168, + 300 + ], + "score": 0.92, + "latex": "\\textstyle \\sum _ { t \\geq 1 } w _ { t } \\leq C" + }, + { + "category_id": 13, + "poly": [ + 828, + 263, + 969, + 263, + 969, + 293, + 828, + 293 + ], + "score": 0.92, + "latex": "0 \\leq w _ { t } \\leq w" + }, + { + "category_id": 13, + "poly": [ + 975, + 231, + 1051, + 231, + 1051, + 263, + 975, + 263 + ], + "score": 0.92, + "latex": "( C , w )" + }, + { + "category_id": 13, + "poly": [ + 686, + 262, + 793, + 262, + 793, + 294, + 686, + 294 + ], + "score": 0.92, + "latex": "C , w > 0" + }, + { + "category_id": 13, + "poly": [ + 572, + 1832, + 742, + 1832, + 742, + 1871, + 572, + 1871 + ], + "score": 0.92, + "latex": "\\textstyle ( C , ( 1 + { \\frac { 1 } { H } } ) w )" + }, + { + "category_id": 13, + "poly": [ + 1312, + 230, + 1403, + 230, + 1403, + 265, + 1312, + 265 + ], + "score": 0.91, + "latex": "( w _ { t } ) _ { t \\geq 1 }" + }, + { + "category_id": 13, + "poly": [ + 379, + 1225, + 706, + 1225, + 706, + 1265, + 379, + 1265 + ], + "score": 0.91, + "latex": "\\begin{array} { r } { C _ { s , a } = \\sum _ { t \\geq 1 , ( s _ { t } , a _ { t } ) = ( s , a ) } w _ { t } } \\end{array}" + }, + { + "category_id": 13, + "poly": [ + 298, + 1260, + 377, + 1260, + 377, + 1295, + 298, + 1295 + ], + "score": 0.9, + "latex": "\\iota ( x ) / x" + }, + { + "category_id": 13, + "poly": [ + 1046, + 263, + 1110, + 263, + 1110, + 292, + 1046, + 292 + ], + "score": 0.89, + "latex": "t \\geq 1" + }, + { + "category_id": 13, + "poly": [ + 651, + 2006, + 709, + 2006, + 709, + 2035, + 651, + 2035 + ], + "score": 0.89, + "latex": "( s , a )" + }, + { + "category_id": 13, + "poly": [ + 333, + 2003, + 416, + 2003, + 416, + 2035, + 333, + 2035 + ], + "score": 0.89, + "latex": "^ 2 u ( s , a )" + }, + { + "category_id": 13, + "poly": [ + 298, + 1865, + 369, + 1865, + 369, + 1897, + 298, + 1897 + ], + "score": 0.88, + "latex": "t ^ { \\prime } \\geq 0" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 72.0, + 817.0, + 72.0, + 817.0, + 108.0, + 295.0, + 108.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 831.0, + 2085.0, + 869.0, + 2085.0, + 869.0, + 2123.0, + 831.0, + 2123.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 417.0, + 2001.0, + 650.0, + 2001.0, + 650.0, + 2038.0, + 417.0, + 2038.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 710.0, + 2001.0, + 1097.0, + 2001.0, + 1097.0, + 2038.0, + 710.0, + 2038.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 221.0, + 974.0, + 221.0, + 974.0, + 272.0, + 292.0, + 272.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1052.0, + 221.0, + 1311.0, + 221.0, + 1311.0, + 272.0, + 1052.0, + 272.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 258.0, + 456.0, + 258.0, + 456.0, + 300.0, + 293.0, + 300.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 533.0, + 258.0, + 685.0, + 258.0, + 685.0, + 300.0, + 533.0, + 300.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 794.0, + 258.0, + 827.0, + 258.0, + 827.0, + 300.0, + 794.0, + 300.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 970.0, + 258.0, + 1045.0, + 258.0, + 1045.0, + 300.0, + 970.0, + 300.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1111.0, + 258.0, + 1167.0, + 258.0, + 1167.0, + 300.0, + 1111.0, + 300.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1331.0, + 258.0, + 1342.0, + 258.0, + 1342.0, + 300.0, + 1331.0, + 300.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 289.0, + 1213.0, + 378.0, + 1213.0, + 378.0, + 1274.0, + 289.0, + 1274.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 707.0, + 1213.0, + 1409.0, + 1213.0, + 1409.0, + 1274.0, + 707.0, + 1274.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 378.0, + 1255.0, + 1251.0, + 1255.0, + 1251.0, + 1300.0, + 378.0, + 1300.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 291.0, + 635.0, + 822.0, + 635.0, + 822.0, + 684.0, + 291.0, + 684.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1008.0, + 635.0, + 1409.0, + 635.0, + 1409.0, + 684.0, + 1008.0, + 684.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 668.0, + 473.0, + 668.0, + 473.0, + 711.0, + 293.0, + 711.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 289.0, + 1825.0, + 459.0, + 1825.0, + 459.0, + 1876.0, + 289.0, + 1876.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 521.0, + 1825.0, + 571.0, + 1825.0, + 571.0, + 1876.0, + 521.0, + 1876.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 743.0, + 1825.0, + 1407.0, + 1825.0, + 1407.0, + 1876.0, + 743.0, + 1876.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 290.0, + 1857.0, + 297.0, + 1857.0, + 297.0, + 1904.0, + 290.0, + 1904.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 370.0, + 1857.0, + 385.0, + 1857.0, + 385.0, + 1904.0, + 370.0, + 1904.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 831.0, + 605.0, + 831.0, + 605.0, + 872.0, + 294.0, + 872.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 875.0, + 831.0, + 1064.0, + 831.0, + 1064.0, + 872.0, + 875.0, + 872.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 329.0, + 423.0, + 329.0, + 423.0, + 369.0, + 295.0, + 369.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 603.0, + 329.0, + 869.0, + 329.0, + 869.0, + 369.0, + 603.0, + 369.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 1305.0, + 805.0, + 1305.0, + 805.0, + 1343.0, + 294.0, + 1343.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 1638.0, + 379.0, + 1638.0, + 379.0, + 1679.0, + 294.0, + 1679.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 417.0, + 2001.0, + 650.0, + 2001.0, + 650.0, + 2038.0, + 417.0, + 2038.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 710.0, + 2001.0, + 1097.0, + 2001.0, + 1097.0, + 2038.0, + 710.0, + 2038.0 + ], + "score": 1.0, + "text": "" + } + ], + "page_info": { + "page_no": 13, + "width": 1700, + "height": 2200 + } + }, + { + "layout_dets": [ + { + "category_id": 1, + "poly": [ + 296, + 1267, + 1410, + 1267, + 1410, + 1440, + 296, + 1440 + ], + "score": 0.977 + }, + { + "category_id": 1, + "poly": [ + 301, + 750, + 1398, + 750, + 1398, + 853, + 301, + 853 + ], + "score": 0.972 + }, + { + "category_id": 8, + "poly": [ + 349, + 1454, + 1353, + 1454, + 1353, + 1714, + 349, + 1714 + ], + "score": 0.969 + }, + { + "category_id": 1, + "poly": [ + 297, + 1760, + 1406, + 1760, + 1406, + 1849, + 297, + 1849 + ], + "score": 0.967 + }, + { + "category_id": 8, + "poly": [ + 330, + 1087, + 1323, + 1087, + 1323, + 1256, + 330, + 1256 + ], + "score": 0.967 + }, + { + "category_id": 8, + "poly": [ + 410, + 871, + 1285, + 871, + 1285, + 974, + 410, + 974 + ], + "score": 0.96 + }, + { + "category_id": 8, + "poly": [ + 480, + 308, + 1219, + 308, + 1219, + 467, + 480, + 467 + ], + "score": 0.956 + }, + { + "category_id": 1, + "poly": [ + 290, + 225, + 1405, + 225, + 1405, + 297, + 290, + 297 + ], + "score": 0.942 + }, + { + "category_id": 8, + "poly": [ + 317, + 1896, + 1334, + 1896, + 1334, + 1989, + 317, + 1989 + ], + "score": 0.936 + }, + { + "category_id": 1, + "poly": [ + 297, + 1001, + 804, + 1001, + 804, + 1036, + 297, + 1036 + ], + "score": 0.931 + }, + { + "category_id": 8, + "poly": [ + 481, + 474, + 1186, + 474, + 1186, + 558, + 481, + 558 + ], + "score": 0.923 + }, + { + "category_id": 2, + "poly": [ + 297, + 73, + 817, + 73, + 817, + 106, + 297, + 106 + ], + "score": 0.92 + }, + { + "category_id": 8, + "poly": [ + 480, + 655, + 1168, + 655, + 1168, + 737, + 480, + 737 + ], + "score": 0.905 + }, + { + "category_id": 9, + "poly": [ + 1351, + 584, + 1400, + 584, + 1400, + 615, + 1351, + 615 + ], + "score": 0.883 + }, + { + "category_id": 9, + "poly": [ + 1351, + 674, + 1401, + 674, + 1401, + 706, + 1351, + 706 + ], + "score": 0.882 + }, + { + "category_id": 9, + "poly": [ + 1351, + 494, + 1401, + 494, + 1401, + 525, + 1351, + 525 + ], + "score": 0.878 + }, + { + "category_id": 9, + "poly": [ + 1350, + 402, + 1401, + 402, + 1401, + 434, + 1350, + 434 + ], + "score": 0.875 + }, + { + "category_id": 9, + "poly": [ + 1352, + 1192, + 1401, + 1192, + 1401, + 1224, + 1352, + 1224 + ], + "score": 0.869 + }, + { + "category_id": 2, + "poly": [ + 835, + 2087, + 864, + 2087, + 864, + 2113, + 835, + 2113 + ], + "score": 0.863 + }, + { + "category_id": 8, + "poly": [ + 481, + 566, + 1100, + 566, + 1100, + 646, + 481, + 646 + ], + "score": 0.853 + }, + { + "category_id": 9, + "poly": [ + 1353, + 1926, + 1400, + 1926, + 1400, + 1956, + 1353, + 1956 + ], + "score": 0.84 + }, + { + "category_id": 2, + "poly": [ + 1374, + 2004, + 1402, + 2004, + 1402, + 2032, + 1374, + 2032 + ], + "score": 0.804 + }, + { + "category_id": 14, + "poly": [ + 471, + 308, + 1219, + 308, + 1219, + 743, + 471, + 743 + ], + "score": 0.95, + "latex": "\\begin{array} { r l } & { \\quad \\underset { t \\geq 1 } { \\sum \\sigma } u _ { t + 1 } ^ { \\prime } \\left( \\hat { V } _ { t } - V ^ { * } \\right) \\left( s _ { t + 1 } \\right) } \\\\ & { = \\underset { t \\geq 1 } { \\sum \\sigma } u _ { t + 1 } ^ { \\prime } \\left( \\hat { V } _ { t + 1 } - V ^ { * } \\right) \\left( s _ { t + 1 } \\right) + \\underset { t \\geq 1 } { \\sum \\sigma } u _ { t + 1 } ^ { \\prime } \\left( \\hat { V } _ { t } - \\hat { V } _ { t + 1 } \\right) \\left( s _ { t + 1 } \\right) } \\\\ & { \\quad \\leq \\underset { t \\geq 1 } { \\sum \\sigma } u _ { t + 1 } ^ { \\prime } \\left( \\hat { V } _ { t + 1 } - V ^ { * } \\right) \\left( s _ { t + 1 } \\right) + \\underset { t \\geq 1 } { \\sum \\sigma } u _ { t + 1 } ^ { \\prime } \\left( 2 \\alpha _ { n _ { t } + 1 } \\frac { 1 } { 1 - \\gamma } \\right) } \\\\ & { \\quad \\leq \\underset { t \\geq 1 } { \\sum \\sigma } w _ { t + 1 } ^ { \\prime } \\left( \\hat { V } _ { t + 1 } - V ^ { * } \\right) \\left( s _ { t + 1 } \\right) + \\mathcal { O } \\left( \\frac { w S A H } { 1 - \\gamma } \\ln { C } \\right) } \\\\ & { \\quad \\leq \\underset { t \\geq 1 } { \\sum \\sigma } w _ { t + 1 } ^ { \\prime } \\left( \\hat { Q } _ { t + 1 } - Q ^ { * } \\right) \\left( s _ { t + 1 } , a _ { t + 1 } \\right) + \\mathcal { O } \\left( \\frac { w S A H } { 1 - \\gamma } \\ln { C } \\right) } \\end{array}" + }, + { + "category_id": 14, + "poly": [ + 349, + 1450, + 1353, + 1450, + 1353, + 1714, + 349, + 1714 + ], + "score": 0.94, + "latex": "\\begin{array} { r l } & { \\displaystyle \\sum _ { t \\geq 1 } w _ { t } ( \\hat { Q } _ { t } - Q ^ { * } ) ( s _ { t } , a _ { t } ) } \\\\ & { \\leq 2 c _ { 3 } \\frac { \\sqrt { w ^ { ( H ) } S A H C \\iota ( C ) } } { ( 1 - \\gamma ) ^ { 2 } } + \\mathcal { O } \\left( \\frac { w ^ { ( H ) } S A H } { ( 1 - \\gamma ) ^ { 2 } } \\ln C \\right) + \\gamma ^ { H } \\displaystyle \\sum _ { t \\geq 1 } w _ { t } ^ { ( H ) } \\left( \\hat { Q } _ { t } - Q ^ { * } \\right) ( s _ { t } , a _ { t } ) } \\\\ & { \\leq 2 c _ { 3 } \\frac { \\sqrt { w ^ { ( H ) } S A H C \\iota ( C ) } } { ( 1 - \\gamma ) ^ { 2 } } + \\mathcal { O } \\left( \\frac { w ^ { ( H ) } S A H } { ( 1 - \\gamma ) ^ { 2 } } \\ln C \\right) + \\gamma ^ { H } \\frac { C } { 1 - \\gamma } . } \\end{array}" + }, + { + "category_id": 13, + "poly": [ + 1009, + 1369, + 1128, + 1369, + 1128, + 1412, + 1009, + 1412 + ], + "score": 0.94, + "latex": "\\{ w _ { t } ^ { ( k ) } \\} _ { t \\ge 1 }" + }, + { + "category_id": 13, + "poly": [ + 379, + 1761, + 778, + 1761, + 778, + 1810, + 379, + 1810 + ], + "score": 0.94, + "latex": "\\begin{array} { r } { H = \\frac { \\ln 1 / ( ( 1 - \\gamma ) \\epsilon _ { 1 } ) } { \\ln 1 / \\gamma } \\leq \\frac { \\ln 1 / ( ( 1 - \\gamma ) \\epsilon _ { 1 } ) } { 1 - \\gamma } , } \\end{array}" + }, + { + "category_id": 14, + "poly": [ + 315, + 1895, + 1339, + 1895, + 1339, + 1989, + 315, + 1989 + ], + "score": 0.93, + "latex": "\\sum _ { t \\geq 1 } w _ { t } ( \\hat { Q } _ { t } - Q ^ { * } ) ( s _ { t } , a _ { t } ) \\leq \\frac { C \\epsilon _ { 1 } } { 1 - \\gamma } + \\mathcal { O } \\left( \\frac { \\sqrt { w S A C \\ell ( C ) } } { ( 1 - \\gamma ) ^ { 2 . 5 } } + \\frac { w S A } { ( 1 - \\gamma ) ^ { 3 } } \\ln C \\ln \\frac { 1 } { ( 1 - \\gamma ) \\epsilon _ { 1 } } \\right) ." + }, + { + "category_id": 13, + "poly": [ + 803, + 1331, + 921, + 1331, + 921, + 1373, + 803, + 1373 + ], + "score": 0.93, + "latex": "\\{ w _ { t } ^ { ( k ) } \\} _ { t \\ge 1 }" + }, + { + "category_id": 13, + "poly": [ + 597, + 228, + 943, + 228, + 943, + 269, + 597, + 269 + ], + "score": 0.93, + "latex": "\\begin{array} { r } { \\sum _ { t ^ { \\prime } \\geq 1 } w _ { t ^ { \\prime } + 1 } ^ { \\prime } \\leq \\sum _ { t \\geq 1 } w _ { t } \\leq C . } \\end{array}" + }, + { + "category_id": 13, + "poly": [ + 573, + 1372, + 751, + 1372, + 751, + 1411, + 573, + 1411 + ], + "score": 0.93, + "latex": "w \\cdot \\left( 1 + 1 / H \\right) ^ { k }" + }, + { + "category_id": 13, + "poly": [ + 606, + 1330, + 724, + 1330, + 724, + 1372, + 606, + 1372 + ], + "score": 0.93, + "latex": "\\{ \\bar { w _ { t } ^ { ( 0 ) } } \\} _ { t \\ge 1 }" + }, + { + "category_id": 13, + "poly": [ + 347, + 1807, + 515, + 1807, + 515, + 1851, + 347, + 1851 + ], + "score": 0.92, + "latex": "\\gamma ^ { H } \\frac { C } { 1 - \\gamma } \\leq C \\epsilon _ { 1 }" + }, + { + "category_id": 14, + "poly": [ + 412, + 866, + 1286, + 866, + 1286, + 975, + 412, + 975 + ], + "score": 0.92, + "latex": "\\sum _ { t \\geq 1 } w _ { t + 1 } ^ { \\prime } \\alpha _ { n _ { t } + 1 } \\leq \\sum _ { s , a } \\sum _ { n = 1 } ^ { C _ { s , a } ^ { \\prime } / w ^ { \\prime } } w ^ { \\prime } \\frac { H } { n } \\leq \\sum _ { s , a } H w ^ { \\prime } \\ln ( C _ { s , a } ^ { \\prime } / w ) \\leq 2 S A H w \\ln C ." + }, + { + "category_id": 14, + "poly": [ + 326, + 1083, + 1326, + 1083, + 1326, + 1260, + 326, + 1260 + ], + "score": 0.92, + "latex": "\\begin{array} { r l } & { \\displaystyle \\sum _ { t \\geq 1 } w _ { t } ( \\hat { Q } _ { t } - Q ^ { * } ) ( s _ { t } , a _ { t } ) } \\\\ & { \\leq 2 c _ { 3 } \\frac { \\sqrt { w S A H C \\iota ( C ) } } { 1 - \\gamma } + \\mathcal { O } \\left( \\frac { w S A H } { 1 - \\gamma } \\ln C \\right) + \\gamma \\displaystyle \\sum _ { t \\geq 1 } w _ { t + 1 } ^ { \\prime } \\left( \\hat { Q } _ { t + 1 } - Q ^ { * } \\right) ( s _ { t + 1 } , a _ { t + 1 } ) . } \\end{array}" + }, + { + "category_id": 13, + "poly": [ + 951, + 1765, + 1344, + 1765, + 1344, + 1804, + 951, + 1804 + ], + "score": 0.92, + "latex": "w ^ { ( H ) } = ( 1 + 1 / H ) ^ { H } w ^ { ( 0 ) } \\leq e w ^ { ( 0 ) }" + }, + { + "category_id": 13, + "poly": [ + 1179, + 1373, + 1285, + 1373, + 1285, + 1411, + 1179, + 1411 + ], + "score": 0.91, + "latex": "( C , w ^ { ( k ) } )" + }, + { + "category_id": 13, + "poly": [ + 1315, + 782, + 1404, + 782, + 1404, + 820, + 1315, + 820 + ], + "score": 0.91, + "latex": "C _ { s , a } ^ { \\prime } =" + }, + { + "category_id": 13, + "poly": [ + 336, + 224, + 492, + 224, + 492, + 269, + 336, + 269 + ], + "score": 0.91, + "latex": "\\textstyle \\sum _ { j = 0 } ^ { i } \\alpha _ { i } ^ { j } = 1" + }, + { + "category_id": 13, + "poly": [ + 401, + 782, + 771, + 782, + 771, + 816, + 401, + 816 + ], + "score": 0.91, + "latex": "\\dot { \\alpha } _ { t } = ( H + 1 ) / ( H + t ) \\overset { \\cdot } { \\leq } H / t" + }, + { + "category_id": 13, + "poly": [ + 481, + 1373, + 534, + 1373, + 534, + 1406, + 481, + 1406 + ], + "score": 0.9, + "latex": "w ^ { ( k ) }" + }, + { + "category_id": 13, + "poly": [ + 629, + 1807, + 980, + 1807, + 980, + 1845, + 629, + 1845 + ], + "score": 0.9, + "latex": "\\ell ( C ) = \\iota ( C ) \\ln ( ( 1 - \\gamma ) ^ { - 1 } \\epsilon _ { 1 } ^ { - 1 } )" + }, + { + "category_id": 13, + "poly": [ + 297, + 816, + 537, + 816, + 537, + 857, + 297, + 857 + ], + "score": 0.85, + "latex": "\\scriptstyle \\sum _ { t \\geq 1 , ( s _ { t } , a _ { t } = s , a } w _ { t + 1 } ^ { \\prime }" + }, + { + "category_id": 13, + "poly": [ + 550, + 817, + 761, + 817, + 761, + 851, + 550, + 851 + ], + "score": 0.83, + "latex": "w ^ { \\prime } = w ( 1 + 1 / H )" + }, + { + "category_id": 13, + "poly": [ + 598, + 1411, + 626, + 1411, + 626, + 1435, + 598, + 1435 + ], + "score": 0.81, + "latex": "H" + }, + { + "category_id": 13, + "poly": [ + 337, + 1378, + 356, + 1378, + 356, + 1405, + 337, + 1405 + ], + "score": 0.81, + "latex": "k" + }, + { + "category_id": 15, + "poly": [ + 296.0, + 72.0, + 818.0, + 72.0, + 818.0, + 108.0, + 296.0, + 108.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 831.0, + 2085.0, + 868.0, + 2085.0, + 868.0, + 2124.0, + 831.0, + 2124.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1380.0, + 2009.0, + 1401.0, + 2009.0, + 1401.0, + 2030.0, + 1380.0, + 2030.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 1265.0, + 1406.0, + 1265.0, + 1406.0, + 1304.0, + 294.0, + 1304.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 1300.0, + 1406.0, + 1300.0, + 1406.0, + 1334.0, + 294.0, + 1334.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 285.0, + 1322.0, + 605.0, + 1322.0, + 605.0, + 1383.0, + 285.0, + 1383.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 725.0, + 1322.0, + 802.0, + 1322.0, + 802.0, + 1383.0, + 725.0, + 1383.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 922.0, + 1322.0, + 1413.0, + 1322.0, + 1413.0, + 1383.0, + 922.0, + 1383.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 289.0, + 1366.0, + 336.0, + 1366.0, + 336.0, + 1419.0, + 289.0, + 1419.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 357.0, + 1366.0, + 480.0, + 1366.0, + 480.0, + 1419.0, + 357.0, + 1419.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 535.0, + 1366.0, + 572.0, + 1366.0, + 572.0, + 1419.0, + 535.0, + 1419.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 752.0, + 1366.0, + 1008.0, + 1366.0, + 1008.0, + 1419.0, + 752.0, + 1419.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1129.0, + 1366.0, + 1178.0, + 1366.0, + 1178.0, + 1419.0, + 1129.0, + 1419.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1286.0, + 1366.0, + 1413.0, + 1366.0, + 1413.0, + 1419.0, + 1286.0, + 1419.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 1406.0, + 597.0, + 1406.0, + 597.0, + 1441.0, + 294.0, + 1441.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 627.0, + 1406.0, + 772.0, + 1406.0, + 772.0, + 1441.0, + 627.0, + 1441.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 297.0, + 751.0, + 1402.0, + 751.0, + 1402.0, + 786.0, + 297.0, + 786.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 291.0, + 771.0, + 400.0, + 771.0, + 400.0, + 827.0, + 291.0, + 827.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 772.0, + 771.0, + 1314.0, + 771.0, + 1314.0, + 827.0, + 772.0, + 827.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 291.0, + 813.0, + 296.0, + 813.0, + 296.0, + 861.0, + 291.0, + 861.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 538.0, + 813.0, + 549.0, + 813.0, + 549.0, + 861.0, + 538.0, + 861.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 762.0, + 813.0, + 842.0, + 813.0, + 842.0, + 861.0, + 762.0, + 861.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 285.0, + 1748.0, + 378.0, + 1748.0, + 378.0, + 1814.0, + 285.0, + 1814.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 779.0, + 1748.0, + 950.0, + 1748.0, + 950.0, + 1814.0, + 779.0, + 1814.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1345.0, + 1748.0, + 1412.0, + 1748.0, + 1412.0, + 1814.0, + 1345.0, + 1814.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 516.0, + 1804.0, + 628.0, + 1804.0, + 628.0, + 1849.0, + 516.0, + 1849.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 981.0, + 1804.0, + 1117.0, + 1804.0, + 1117.0, + 1849.0, + 981.0, + 1849.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 284.0, + 1796.0, + 442.0, + 1796.0, + 442.0, + 1856.0, + 284.0, + 1856.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 282.0, + 206.0, + 335.0, + 206.0, + 335.0, + 283.0, + 282.0, + 283.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 493.0, + 206.0, + 596.0, + 206.0, + 596.0, + 283.0, + 493.0, + 283.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 944.0, + 206.0, + 1416.0, + 206.0, + 1416.0, + 283.0, + 944.0, + 283.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 291.0, + 258.0, + 405.0, + 258.0, + 405.0, + 303.0, + 291.0, + 303.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 996.0, + 807.0, + 996.0, + 807.0, + 1043.0, + 293.0, + 1043.0 + ], + "score": 1.0, + "text": "" + } + ], + "page_info": { + "page_no": 14, + "width": 1700, + "height": 2200 + } + }, + { + "layout_dets": [ + { + "category_id": 1, + "poly": [ + 296, + 648, + 1406, + 648, + 1406, + 826, + 296, + 826 + ], + "score": 0.977 + }, + { + "category_id": 1, + "poly": [ + 298, + 293, + 1406, + 293, + 1406, + 419, + 298, + 419 + ], + "score": 0.976 + }, + { + "category_id": 1, + "poly": [ + 297, + 1176, + 1406, + 1176, + 1406, + 1274, + 297, + 1274 + ], + "score": 0.974 + }, + { + "category_id": 1, + "poly": [ + 297, + 841, + 1407, + 841, + 1407, + 993, + 297, + 993 + ], + "score": 0.974 + }, + { + "category_id": 8, + "poly": [ + 534, + 1548, + 1163, + 1548, + 1163, + 1798, + 534, + 1798 + ], + "score": 0.969 + }, + { + "category_id": 8, + "poly": [ + 582, + 1052, + 1113, + 1052, + 1113, + 1150, + 582, + 1150 + ], + "score": 0.961 + }, + { + "category_id": 1, + "poly": [ + 365, + 439, + 1404, + 439, + 1404, + 629, + 365, + 629 + ], + "score": 0.957 + }, + { + "category_id": 8, + "poly": [ + 594, + 1286, + 1101, + 1286, + 1101, + 1365, + 594, + 1365 + ], + "score": 0.956 + }, + { + "category_id": 1, + "poly": [ + 295, + 1812, + 1402, + 1812, + 1402, + 1882, + 295, + 1882 + ], + "score": 0.954 + }, + { + "category_id": 1, + "poly": [ + 294, + 1451, + 1405, + 1451, + 1405, + 1533, + 294, + 1533 + ], + "score": 0.952 + }, + { + "category_id": 1, + "poly": [ + 298, + 1373, + 1403, + 1373, + 1403, + 1438, + 298, + 1438 + ], + "score": 0.95 + }, + { + "category_id": 1, + "poly": [ + 297, + 1968, + 1403, + 1968, + 1403, + 2036, + 297, + 2036 + ], + "score": 0.929 + }, + { + "category_id": 1, + "poly": [ + 297, + 1004, + 977, + 1004, + 977, + 1038, + 297, + 1038 + ], + "score": 0.916 + }, + { + "category_id": 0, + "poly": [ + 297, + 1915, + 887, + 1915, + 887, + 1947, + 297, + 1947 + ], + "score": 0.911 + }, + { + "category_id": 2, + "poly": [ + 298, + 74, + 817, + 74, + 817, + 106, + 298, + 106 + ], + "score": 0.909 + }, + { + "category_id": 0, + "poly": [ + 300, + 226, + 822, + 226, + 822, + 262, + 300, + 262 + ], + "score": 0.901 + }, + { + "category_id": 2, + "poly": [ + 835, + 2088, + 864, + 2088, + 864, + 2113, + 835, + 2113 + ], + "score": 0.86 + }, + { + "category_id": 14, + "poly": [ + 531, + 1545, + 1167, + 1545, + 1167, + 1800, + 531, + 1800 + ], + "score": 0.94, + "latex": "\\begin{array} { r l r } { { \\operatorname { R e g r e t } ( T ) \\le T \\epsilon _ { 2 } + \\sum _ { i = 1 } ^ { M } ( | k : \\{ X _ { k } \\ge \\epsilon _ { 2 } \\cdot 2 ^ { i - 1 } \\} | ) \\epsilon _ { 2 } \\cdot 2 ^ { i } } } \\\\ & { } & \\\\ & { } & { \\le \\tilde { \\mathcal { O } } ( T \\epsilon _ { 2 } + \\sum _ { i = 1 } ^ { M } \\frac { S A \\ln 1 / \\delta } { \\epsilon _ { 2 } \\cdot 2 ^ { i - 2 } } ) } \\\\ & { } & { \\le \\tilde { \\mathcal { O } } ( \\sqrt { S A T } \\ln 1 / \\delta ) } \\end{array}" + }, + { + "category_id": 14, + "poly": [ + 594, + 1285, + 1105, + 1285, + 1105, + 1363, + 594, + 1363 + ], + "score": 0.94, + "latex": "\\mathcal { O } \\left( \\frac { S A \\ln S A \\ln 1 / \\delta } { \\epsilon _ { 2 } ^ { 2 } ( 1 - \\gamma ) ^ { 7 } } \\mathrm { p o l y l o g } \\left( \\frac { 1 } { \\epsilon _ { 1 } } , \\frac { 1 } { 1 - \\gamma } \\right) \\right)" + }, + { + "category_id": 14, + "poly": [ + 583, + 1049, + 1114, + 1049, + 1114, + 1151, + 583, + 1151 + ], + "score": 0.94, + "latex": "\\mathrm { R e g r e t } ( T ) = \\sum _ { k = 1 } ^ { T / H } \\left[ V ^ { * } ( s _ { 1 } ) - V _ { 1 } ^ { k } ( s _ { 1 } ) \\right] \\propto T ^ { 1 / 2 } ." + }, + { + "category_id": 13, + "poly": [ + 439, + 684, + 736, + 684, + 736, + 732, + 439, + 732 + ], + "score": 0.94, + "latex": "\\begin{array} { r } { \\bar { V } ^ { \\ast } ( \\bar { s } _ { s _ { 1 } , 1 } ) = \\frac { \\gamma ^ { H } } { 1 - \\gamma ^ { H } } V _ { 1 } ^ { \\ast } ( s _ { 1 } ) } \\end{array}" + }, + { + "category_id": 13, + "poly": [ + 888, + 840, + 1012, + 840, + 1012, + 883, + 888, + 883 + ], + "score": 0.94, + "latex": "\\tilde { \\mathcal O } \\big ( \\frac { 3 S A H ^ { 9 } } { \\epsilon ^ { 2 } } \\big )" + }, + { + "category_id": 13, + "poly": [ + 1008, + 954, + 1102, + 954, + 1102, + 995, + 1008, + 995 + ], + "score": 0.94, + "latex": "\\tilde { \\mathcal { O } } \\left( \\epsilon ^ { - 2 } \\right)" + }, + { + "category_id": 13, + "poly": [ + 1203, + 1451, + 1355, + 1451, + 1355, + 1490, + 1203, + 1490 + ], + "score": 0.94, + "latex": "\\epsilon = \\sqrt { S A / T }" + }, + { + "category_id": 13, + "poly": [ + 975, + 1207, + 1217, + 1207, + 1217, + 1246, + 975, + 1246 + ], + "score": 0.93, + "latex": "\\epsilon _ { 2 } > \\tilde { \\mathcal { O } } ( \\epsilon _ { 1 } / ( 1 - \\gamma ) )" + }, + { + "category_id": 13, + "poly": [ + 465, + 881, + 589, + 881, + 589, + 924, + 465, + 924 + ], + "score": 0.93, + "latex": "\\tilde { \\mathcal O } \\big ( { \\textstyle { \\frac { 3 S A H ^ { 8 } } { \\epsilon ^ { 2 } } } } \\big )" + }, + { + "category_id": 13, + "poly": [ + 1174, + 692, + 1361, + 692, + 1361, + 728, + 1174, + 728 + ], + "score": 0.93, + "latex": "\\pi _ { h } ( s ) = \\bar { \\pi } ( \\bar { s } _ { s , h } )" + }, + { + "category_id": 13, + "poly": [ + 830, + 922, + 988, + 922, + 988, + 957, + 830, + 957 + ], + "score": 0.93, + "latex": "0 \\leq t < T / H" + }, + { + "category_id": 13, + "poly": [ + 298, + 1487, + 526, + 1487, + 526, + 1527, + 298, + 1527 + ], + "score": 0.93, + "latex": "\\epsilon _ { 2 } = \\tilde { \\mathcal { O } } ( \\epsilon _ { 1 } / ( 1 - \\gamma ) )" + }, + { + "category_id": 13, + "poly": [ + 401, + 790, + 714, + 790, + 714, + 826, + 401, + 826 + ], + "score": 0.93, + "latex": "\\gamma ^ { H } = ( 1 - \\dot { 1 } / H ) ^ { \\tilde { H } } = \\mathcal { O } ( \\dot { 1 } )" + }, + { + "category_id": 13, + "poly": [ + 738, + 593, + 1068, + 593, + 1068, + 625, + 738, + 625 + ], + "score": 0.92, + "latex": "\\bar { p } ( \\bar { s } _ { s ^ { \\prime } , 1 } \\mid \\bar { s } _ { s , h } , a ) = I [ s ^ { \\prime } = s _ { 1 } ]" + }, + { + "category_id": 13, + "poly": [ + 765, + 1970, + 1263, + 1970, + 1263, + 2007, + 765, + 2007 + ], + "score": 0.91, + "latex": "\\begin{array} { r c l } { \\mathcal { M } } & { = } & { ( S , A , H , r _ { h } ( s , a ) , p _ { h } ( s ^ { \\prime } \\mathrm { ~ ~ \\chi ~ } | \\mathrm { ~ ~ \\chi ~ } s , a ) ) } \\end{array}" + }, + { + "category_id": 13, + "poly": [ + 583, + 1489, + 815, + 1489, + 815, + 1533, + 583, + 1533 + ], + "score": 0.91, + "latex": "\\begin{array} { r } { M = \\lceil \\log _ { 2 } \\frac { 1 } { \\epsilon _ { 2 } ( 1 - \\gamma ) } \\rceil } \\end{array}" + }, + { + "category_id": 13, + "poly": [ + 528, + 593, + 687, + 593, + 687, + 625, + 528, + 625 + ], + "score": 0.91, + "latex": "\\bar { r } ( \\bar { s } _ { s , h } , a ) = 0" + }, + { + "category_id": 13, + "poly": [ + 1241, + 958, + 1332, + 958, + 1332, + 990, + 1241, + 990 + ], + "score": 0.91, + "latex": "S , A , H" + }, + { + "category_id": 13, + "poly": [ + 692, + 761, + 776, + 761, + 776, + 796, + 692, + 796 + ], + "score": 0.91, + "latex": "( \\epsilon / \\gamma ^ { H } )" + }, + { + "category_id": 13, + "poly": [ + 831, + 650, + 869, + 650, + 869, + 687, + 831, + 687 + ], + "score": 0.91, + "latex": "V _ { h } ^ { k }" + }, + { + "category_id": 13, + "poly": [ + 443, + 1453, + 717, + 1453, + 717, + 1489, + 443, + 1489 + ], + "score": 0.91, + "latex": "X _ { k } = V ^ { \\ast } ( s _ { 1 } ) - V _ { 1 } ^ { k } ( s _ { 1 } )" + }, + { + "category_id": 13, + "poly": [ + 898, + 559, + 1296, + 559, + 1296, + 593, + 898, + 593 + ], + "score": 0.91, + "latex": "\\bar { p } ( \\bar { s } _ { s ^ { \\prime } , h + 1 } \\mid \\bar { s } _ { s , h } , a ) = p _ { h } ( s ^ { \\prime } \\mid s , h )" + }, + { + "category_id": 13, + "poly": [ + 511, + 559, + 844, + 559, + 844, + 593, + 511, + 593 + ], + "score": 0.91, + "latex": "\\bar { r } ( \\bar { s } _ { s , h } , a ) = \\gamma ^ { H - h + 1 } r _ { h } ( s , a )" + }, + { + "category_id": 13, + "poly": [ + 868, + 326, + 1293, + 326, + 1293, + 359, + 868, + 359 + ], + "score": 0.91, + "latex": "\\mathcal { M } = ( S , A , H , r _ { h } ( s _ { \\perp } a ) , p _ { h } ( s ^ { \\prime } \\mid s , a ) )" + }, + { + "category_id": 13, + "poly": [ + 296, + 2000, + 616, + 2000, + 616, + 2036, + 296, + 2036 + ], + "score": 0.9, + "latex": "( \\bar { S } , \\bar { A } , \\gamma , \\bar { r } ( \\bar { s } , \\bar { a } ) , \\bar { p } ( \\bar { s } ^ { \\prime } \\mid \\bar { s } , \\bar { a } ) )" + }, + { + "category_id": 13, + "poly": [ + 471, + 1847, + 730, + 1847, + 730, + 1879, + 471, + 1879 + ], + "score": 0.9, + "latex": "( H , \\log T , \\log S , \\log A )" + }, + { + "category_id": 13, + "poly": [ + 709, + 921, + 785, + 921, + 785, + 952, + 709, + 952 + ], + "score": 0.9, + "latex": "\\pi ^ { t H + 1 }" + }, + { + "category_id": 13, + "poly": [ + 341, + 650, + 370, + 650, + 370, + 683, + 341, + 683 + ], + "score": 0.88, + "latex": "\\bar { V } _ { t }" + }, + { + "category_id": 13, + "poly": [ + 393, + 849, + 462, + 849, + 462, + 877, + 393, + 877 + ], + "score": 0.88, + "latex": "\\epsilon > 0" + }, + { + "category_id": 13, + "poly": [ + 397, + 592, + 478, + 592, + 478, + 620, + 397, + 620 + ], + "score": 0.88, + "latex": "h = H" + }, + { + "category_id": 13, + "poly": [ + 684, + 530, + 731, + 530, + 731, + 559, + 684, + 559 + ], + "score": 0.88, + "latex": "\\bar { s } _ { s , h }" + }, + { + "category_id": 13, + "poly": [ + 1012, + 359, + 1402, + 359, + 1402, + 390, + 1012, + 390 + ], + "score": 0.88, + "latex": "\\mathcal { M } = ( S , A , \\gamma , \\bar { r } ( \\bar { s } , \\bar { a } ) , \\bar { p } ( \\bar { s } ^ { \\prime } \\mid \\bar { s } , \\bar { a } ) )" + }, + { + "category_id": 13, + "poly": [ + 982, + 1814, + 1218, + 1814, + 1218, + 1850, + 982, + 1850 + ], + "score": 0.87, + "latex": "( 1 / ( 1 - \\gamma ) , \\log { 1 / \\epsilon _ { 1 } } )" + }, + { + "category_id": 13, + "poly": [ + 644, + 650, + 679, + 650, + 679, + 681, + 644, + 681 + ], + "score": 0.87, + "latex": "\\bar { \\mathcal { M } }" + }, + { + "category_id": 13, + "poly": [ + 833, + 730, + 869, + 730, + 869, + 761, + 833, + 761 + ], + "score": 0.86, + "latex": "\\bar { \\mathcal { M } }" + }, + { + "category_id": 13, + "poly": [ + 697, + 1811, + 723, + 1811, + 723, + 1843, + 697, + 1843 + ], + "score": 0.85, + "latex": "\\tilde { \\mathcal { O } }" + }, + { + "category_id": 13, + "poly": [ + 616, + 1411, + 641, + 1411, + 641, + 1435, + 616, + 1435 + ], + "score": 0.85, + "latex": "\\epsilon _ { 1 }" + }, + { + "category_id": 13, + "poly": [ + 425, + 730, + 460, + 730, + 460, + 760, + 425, + 760 + ], + "score": 0.85, + "latex": "\\bar { \\mathcal { M } }" + }, + { + "category_id": 13, + "poly": [ + 298, + 1247, + 324, + 1247, + 324, + 1273, + 298, + 1273 + ], + "score": 0.85, + "latex": "\\epsilon _ { 2 }" + }, + { + "category_id": 13, + "poly": [ + 809, + 844, + 841, + 844, + 841, + 876, + 809, + 876 + ], + "score": 0.85, + "latex": "\\bar { M }" + }, + { + "category_id": 13, + "poly": [ + 1345, + 853, + 1373, + 853, + 1373, + 878, + 1345, + 878 + ], + "score": 0.85, + "latex": "s _ { 1 }" + }, + { + "category_id": 13, + "poly": [ + 1244, + 1379, + 1270, + 1379, + 1270, + 1404, + 1244, + 1404 + ], + "score": 0.84, + "latex": "\\epsilon _ { 1 }" + }, + { + "category_id": 13, + "poly": [ + 1341, + 597, + 1369, + 597, + 1369, + 622, + 1341, + 622 + ], + "score": 0.84, + "latex": "s _ { 1 }" + }, + { + "category_id": 13, + "poly": [ + 397, + 560, + 420, + 560, + 420, + 588, + 397, + 588 + ], + "score": 0.84, + "latex": "s ^ { \\prime }" + }, + { + "category_id": 13, + "poly": [ + 892, + 1457, + 910, + 1457, + 910, + 1483, + 892, + 1483 + ], + "score": 0.83, + "latex": "k" + }, + { + "category_id": 13, + "poly": [ + 838, + 1007, + 866, + 1007, + 866, + 1033, + 838, + 1033 + ], + "score": 0.83, + "latex": "K" + }, + { + "category_id": 13, + "poly": [ + 1001, + 764, + 1037, + 764, + 1037, + 791, + 1001, + 791 + ], + "score": 0.83, + "latex": "\\mathcal { M }" + }, + { + "category_id": 13, + "poly": [ + 617, + 528, + 636, + 528, + 636, + 555, + 617, + 555 + ], + "score": 0.83, + "latex": "h" + }, + { + "category_id": 13, + "poly": [ + 1109, + 654, + 1145, + 654, + 1145, + 681, + 1109, + 681 + ], + "score": 0.82, + "latex": "\\mathcal { M }" + }, + { + "category_id": 13, + "poly": [ + 427, + 761, + 462, + 761, + 462, + 790, + 427, + 790 + ], + "score": 0.82, + "latex": "\\bar { \\mathcal { M } }" + }, + { + "category_id": 13, + "poly": [ + 1132, + 1457, + 1155, + 1457, + 1155, + 1483, + 1132, + 1483 + ], + "score": 0.81, + "latex": "T" + }, + { + "category_id": 13, + "poly": [ + 1317, + 1968, + 1403, + 1968, + 1403, + 2005, + 1317, + 2005 + ], + "score": 0.8, + "latex": "\\begin{array} { r l } { \\bar { \\mathcal { M } } } & { { } = } \\end{array}" + }, + { + "category_id": 13, + "poly": [ + 298, + 1217, + 323, + 1217, + 323, + 1242, + 298, + 1242 + ], + "score": 0.79, + "latex": "\\epsilon _ { 1 }" + }, + { + "category_id": 13, + "poly": [ + 1373, + 327, + 1401, + 327, + 1401, + 354, + 1373, + 354 + ], + "score": 0.79, + "latex": "H" + }, + { + "category_id": 13, + "poly": [ + 372, + 766, + 393, + 766, + 393, + 790, + 372, + 790 + ], + "score": 0.79, + "latex": "\\bar { \\pi }" + }, + { + "category_id": 13, + "poly": [ + 747, + 733, + 782, + 733, + 782, + 760, + 747, + 760 + ], + "score": 0.78, + "latex": "\\mathcal { M }" + }, + { + "category_id": 13, + "poly": [ + 372, + 735, + 393, + 735, + 393, + 761, + 372, + 761 + ], + "score": 0.78, + "latex": "\\bar { \\pi }" + }, + { + "category_id": 13, + "poly": [ + 1268, + 654, + 1286, + 654, + 1286, + 680, + 1268, + 680 + ], + "score": 0.78, + "latex": "k" + }, + { + "category_id": 13, + "poly": [ + 477, + 1374, + 535, + 1374, + 535, + 1403, + 477, + 1403 + ], + "score": 0.77, + "latex": "1 - \\delta" + }, + { + "category_id": 13, + "poly": [ + 1220, + 534, + 1238, + 534, + 1238, + 554, + 1220, + 554 + ], + "score": 0.77, + "latex": "a" + }, + { + "category_id": 13, + "poly": [ + 766, + 655, + 781, + 655, + 781, + 680, + 766, + 680 + ], + "score": 0.76, + "latex": "t" + }, + { + "category_id": 13, + "poly": [ + 1349, + 654, + 1368, + 654, + 1368, + 680, + 1349, + 680 + ], + "score": 0.76, + "latex": "h" + }, + { + "category_id": 13, + "poly": [ + 517, + 534, + 533, + 534, + 533, + 554, + 517, + 554 + ], + "score": 0.76, + "latex": "s" + }, + { + "category_id": 13, + "poly": [ + 948, + 767, + 969, + 767, + 969, + 790, + 948, + 790 + ], + "score": 0.75, + "latex": "\\pi" + }, + { + "category_id": 13, + "poly": [ + 806, + 887, + 850, + 887, + 850, + 921, + 806, + 921 + ], + "score": 0.72, + "latex": "1 / 3" + }, + { + "category_id": 13, + "poly": [ + 477, + 1816, + 539, + 1816, + 539, + 1844, + 477, + 1844 + ], + "score": 0.71, + "latex": "1 - \\delta" + }, + { + "category_id": 13, + "poly": [ + 396, + 483, + 575, + 483, + 575, + 520, + 396, + 520 + ], + "score": 0.71, + "latex": "\\gamma = ( 1 - 1 / H )" + }, + { + "category_id": 13, + "poly": [ + 1031, + 894, + 1045, + 894, + 1045, + 915, + 1031, + 915 + ], + "score": 0.71, + "latex": "\\epsilon" + }, + { + "category_id": 13, + "poly": [ + 1294, + 739, + 1308, + 739, + 1308, + 760, + 1294, + 760 + ], + "score": 0.68, + "latex": "\\epsilon" + }, + { + "category_id": 13, + "poly": [ + 371, + 965, + 384, + 965, + 384, + 986, + 371, + 986 + ], + "score": 0.65, + "latex": "\\epsilon" + }, + { + "category_id": 13, + "poly": [ + 1271, + 922, + 1316, + 922, + 1316, + 957, + 1271, + 957 + ], + "score": 0.44, + "latex": "2 / 3" + }, + { + "category_id": 14, + "poly": [ + 392, + 440, + 626, + 440, + 626, + 477, + 392, + 477 + ], + "score": 0.42, + "latex": "\\bar { S } = S \\times H , \\bar { A } = A ;" + }, + { + "category_id": 14, + "poly": [ + 366, + 438, + 630, + 438, + 630, + 522, + 366, + 522 + ], + "score": 0.37, + "latex": "\\begin{array} { l } { { \\bullet \\ { \\bar { S } } = S \\times H , { \\bar { A } } = A ; } } \\\\ { { \\bullet \\ \\gamma = ( 1 - 1 / H ) ; } } \\end{array}" + }, + { + "category_id": 13, + "poly": [ + 395, + 440, + 625, + 440, + 625, + 477, + 395, + 477 + ], + "score": 0.3, + "latex": "\\bar { S } = S \\times H , \\bar { A } = A ;" + }, + { + "category_id": 15, + "poly": [ + 297.0, + 1915.0, + 887.0, + 1915.0, + 887.0, + 1950.0, + 297.0, + 1950.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 72.0, + 817.0, + 72.0, + 817.0, + 109.0, + 295.0, + 109.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 224.0, + 827.0, + 224.0, + 827.0, + 266.0, + 294.0, + 266.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 831.0, + 2085.0, + 869.0, + 2085.0, + 869.0, + 2124.0, + 831.0, + 2124.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 649.0, + 340.0, + 649.0, + 340.0, + 687.0, + 294.0, + 687.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 371.0, + 649.0, + 643.0, + 649.0, + 643.0, + 687.0, + 371.0, + 687.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 680.0, + 649.0, + 765.0, + 649.0, + 765.0, + 687.0, + 680.0, + 687.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 782.0, + 649.0, + 830.0, + 649.0, + 830.0, + 687.0, + 782.0, + 687.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 870.0, + 649.0, + 1108.0, + 649.0, + 1108.0, + 687.0, + 870.0, + 687.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1146.0, + 649.0, + 1267.0, + 649.0, + 1267.0, + 687.0, + 1146.0, + 687.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1287.0, + 649.0, + 1348.0, + 649.0, + 1348.0, + 687.0, + 1287.0, + 687.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1369.0, + 649.0, + 1407.0, + 649.0, + 1407.0, + 687.0, + 1369.0, + 687.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 290.0, + 682.0, + 438.0, + 682.0, + 438.0, + 737.0, + 290.0, + 737.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 737.0, + 682.0, + 1173.0, + 682.0, + 1173.0, + 737.0, + 737.0, + 737.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1362.0, + 682.0, + 1409.0, + 682.0, + 1409.0, + 737.0, + 1362.0, + 737.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 730.0, + 371.0, + 730.0, + 371.0, + 767.0, + 294.0, + 767.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 394.0, + 730.0, + 424.0, + 730.0, + 424.0, + 767.0, + 394.0, + 767.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 461.0, + 730.0, + 746.0, + 730.0, + 746.0, + 767.0, + 461.0, + 767.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 783.0, + 730.0, + 832.0, + 730.0, + 832.0, + 767.0, + 783.0, + 767.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 870.0, + 730.0, + 1293.0, + 730.0, + 1293.0, + 767.0, + 870.0, + 767.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1309.0, + 730.0, + 1406.0, + 730.0, + 1406.0, + 767.0, + 1309.0, + 767.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 759.0, + 371.0, + 759.0, + 371.0, + 798.0, + 294.0, + 798.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 394.0, + 759.0, + 426.0, + 759.0, + 426.0, + 798.0, + 394.0, + 798.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 463.0, + 759.0, + 691.0, + 759.0, + 691.0, + 798.0, + 463.0, + 798.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 777.0, + 759.0, + 947.0, + 759.0, + 947.0, + 798.0, + 777.0, + 798.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 970.0, + 759.0, + 1000.0, + 759.0, + 1000.0, + 798.0, + 970.0, + 798.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1038.0, + 759.0, + 1407.0, + 759.0, + 1407.0, + 798.0, + 1038.0, + 798.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 788.0, + 400.0, + 788.0, + 400.0, + 829.0, + 294.0, + 829.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 715.0, + 788.0, + 871.0, + 788.0, + 871.0, + 829.0, + 715.0, + 829.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 294.0, + 1404.0, + 294.0, + 1404.0, + 328.0, + 292.0, + 328.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 324.0, + 867.0, + 324.0, + 867.0, + 361.0, + 295.0, + 361.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1294.0, + 324.0, + 1372.0, + 324.0, + 1372.0, + 361.0, + 1294.0, + 361.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 355.0, + 1011.0, + 355.0, + 1011.0, + 391.0, + 292.0, + 391.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1403.0, + 355.0, + 1406.0, + 355.0, + 1406.0, + 391.0, + 1403.0, + 391.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 291.0, + 384.0, + 450.0, + 384.0, + 450.0, + 422.0, + 291.0, + 422.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 1173.0, + 1404.0, + 1173.0, + 1404.0, + 1215.0, + 292.0, + 1215.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 1209.0, + 297.0, + 1209.0, + 297.0, + 1247.0, + 294.0, + 1247.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 324.0, + 1209.0, + 974.0, + 1209.0, + 974.0, + 1247.0, + 324.0, + 1247.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1218.0, + 1209.0, + 1406.0, + 1209.0, + 1406.0, + 1247.0, + 1218.0, + 1247.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 1241.0, + 297.0, + 1241.0, + 297.0, + 1278.0, + 294.0, + 1278.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 325.0, + 1241.0, + 684.0, + 1241.0, + 684.0, + 1278.0, + 325.0, + 1278.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 289.0, + 833.0, + 392.0, + 833.0, + 392.0, + 931.0, + 289.0, + 931.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 590.0, + 833.0, + 805.0, + 833.0, + 805.0, + 931.0, + 590.0, + 931.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 851.0, + 833.0, + 887.0, + 833.0, + 887.0, + 931.0, + 851.0, + 931.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1013.0, + 833.0, + 1030.0, + 833.0, + 1030.0, + 931.0, + 1013.0, + 931.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1046.0, + 833.0, + 1344.0, + 833.0, + 1344.0, + 931.0, + 1046.0, + 931.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1374.0, + 833.0, + 1410.0, + 833.0, + 1410.0, + 931.0, + 1374.0, + 931.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 914.0, + 708.0, + 914.0, + 708.0, + 963.0, + 292.0, + 963.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 786.0, + 914.0, + 829.0, + 914.0, + 829.0, + 963.0, + 786.0, + 963.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 989.0, + 914.0, + 1270.0, + 914.0, + 1270.0, + 963.0, + 989.0, + 963.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1317.0, + 914.0, + 1408.0, + 914.0, + 1408.0, + 963.0, + 1317.0, + 963.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 954.0, + 370.0, + 954.0, + 370.0, + 998.0, + 292.0, + 998.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 385.0, + 954.0, + 1007.0, + 954.0, + 1007.0, + 998.0, + 385.0, + 998.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1103.0, + 954.0, + 1240.0, + 954.0, + 1240.0, + 998.0, + 1103.0, + 998.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1333.0, + 954.0, + 1409.0, + 954.0, + 1409.0, + 998.0, + 1333.0, + 998.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 631.0, + 436.0, + 636.0, + 436.0, + 636.0, + 479.0, + 631.0, + 479.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 366.0, + 523.0, + 516.0, + 523.0, + 516.0, + 560.0, + 366.0, + 560.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 534.0, + 523.0, + 616.0, + 523.0, + 616.0, + 560.0, + 534.0, + 560.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 637.0, + 523.0, + 683.0, + 523.0, + 683.0, + 560.0, + 637.0, + 560.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 732.0, + 523.0, + 1219.0, + 523.0, + 1219.0, + 560.0, + 732.0, + 560.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1239.0, + 523.0, + 1405.0, + 523.0, + 1405.0, + 560.0, + 1239.0, + 560.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 390.0, + 550.0, + 396.0, + 550.0, + 396.0, + 601.0, + 390.0, + 601.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 421.0, + 550.0, + 510.0, + 550.0, + 510.0, + 601.0, + 421.0, + 601.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 845.0, + 550.0, + 897.0, + 550.0, + 897.0, + 601.0, + 845.0, + 601.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1297.0, + 550.0, + 1409.0, + 550.0, + 1409.0, + 601.0, + 1297.0, + 601.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 392.0, + 587.0, + 396.0, + 587.0, + 396.0, + 629.0, + 392.0, + 629.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 479.0, + 587.0, + 527.0, + 587.0, + 527.0, + 629.0, + 479.0, + 629.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 688.0, + 587.0, + 737.0, + 587.0, + 737.0, + 629.0, + 688.0, + 629.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1069.0, + 587.0, + 1340.0, + 587.0, + 1340.0, + 629.0, + 1069.0, + 629.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1370.0, + 587.0, + 1383.0, + 587.0, + 1383.0, + 629.0, + 1370.0, + 629.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 1808.0, + 476.0, + 1808.0, + 476.0, + 1852.0, + 293.0, + 1852.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 540.0, + 1808.0, + 696.0, + 1808.0, + 696.0, + 1852.0, + 540.0, + 1852.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 724.0, + 1808.0, + 981.0, + 1808.0, + 981.0, + 1852.0, + 724.0, + 1852.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1219.0, + 1808.0, + 1405.0, + 1808.0, + 1405.0, + 1852.0, + 1219.0, + 1852.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 1843.0, + 470.0, + 1843.0, + 470.0, + 1883.0, + 294.0, + 1883.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 731.0, + 1843.0, + 742.0, + 1843.0, + 742.0, + 1883.0, + 731.0, + 1883.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 1449.0, + 442.0, + 1449.0, + 442.0, + 1493.0, + 294.0, + 1493.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 718.0, + 1449.0, + 891.0, + 1449.0, + 891.0, + 1493.0, + 718.0, + 1493.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 911.0, + 1449.0, + 1131.0, + 1449.0, + 1131.0, + 1493.0, + 911.0, + 1493.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1156.0, + 1449.0, + 1202.0, + 1449.0, + 1202.0, + 1493.0, + 1156.0, + 1493.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1356.0, + 1449.0, + 1405.0, + 1449.0, + 1405.0, + 1493.0, + 1356.0, + 1493.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 1485.0, + 297.0, + 1485.0, + 297.0, + 1539.0, + 292.0, + 1539.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 527.0, + 1485.0, + 582.0, + 1485.0, + 582.0, + 1539.0, + 527.0, + 1539.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 816.0, + 1485.0, + 1001.0, + 1485.0, + 1001.0, + 1539.0, + 816.0, + 1539.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 1371.0, + 476.0, + 1371.0, + 476.0, + 1411.0, + 293.0, + 1411.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 536.0, + 1371.0, + 1243.0, + 1371.0, + 1243.0, + 1411.0, + 536.0, + 1411.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1271.0, + 1371.0, + 1405.0, + 1371.0, + 1405.0, + 1411.0, + 1271.0, + 1411.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 1401.0, + 615.0, + 1401.0, + 615.0, + 1443.0, + 295.0, + 1443.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 642.0, + 1401.0, + 654.0, + 1401.0, + 654.0, + 1443.0, + 642.0, + 1443.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 1965.0, + 764.0, + 1965.0, + 764.0, + 2010.0, + 292.0, + 2010.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1264.0, + 1965.0, + 1316.0, + 1965.0, + 1316.0, + 2010.0, + 1264.0, + 2010.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1404.0, + 1965.0, + 1408.0, + 1965.0, + 1408.0, + 2010.0, + 1404.0, + 2010.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 1998.0, + 295.0, + 1998.0, + 295.0, + 2039.0, + 292.0, + 2039.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 617.0, + 1998.0, + 775.0, + 1998.0, + 775.0, + 2039.0, + 617.0, + 2039.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 997.0, + 837.0, + 997.0, + 837.0, + 1045.0, + 294.0, + 1045.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 867.0, + 997.0, + 980.0, + 997.0, + 980.0, + 1045.0, + 867.0, + 1045.0 + ], + "score": 1.0, + "text": "" + } + ], + "page_info": { + "page_no": 15, + "width": 1700, + "height": 2200 + } + }, + { + "layout_dets": [ + { + "category_id": 1, + "poly": [ + 298, + 1939, + 1404, + 1939, + 1404, + 2037, + 298, + 2037 + ], + "score": 0.972 + }, + { + "category_id": 1, + "poly": [ + 302, + 433, + 1409, + 433, + 1409, + 530, + 302, + 530 + ], + "score": 0.965 + }, + { + "category_id": 3, + "poly": [ + 677, + 1555, + 1022, + 1555, + 1022, + 1825, + 677, + 1825 + ], + "score": 0.96 + }, + { + "category_id": 1, + "poly": [ + 298, + 694, + 1405, + 694, + 1405, + 789, + 298, + 789 + ], + "score": 0.951 + }, + { + "category_id": 8, + "poly": [ + 295, + 542, + 1482, + 542, + 1482, + 682, + 295, + 682 + ], + "score": 0.951 + }, + { + "category_id": 8, + "poly": [ + 687, + 846, + 1011, + 846, + 1011, + 892, + 687, + 892 + ], + "score": 0.945 + }, + { + "category_id": 8, + "poly": [ + 521, + 1126, + 1178, + 1126, + 1178, + 1196, + 521, + 1196 + ], + "score": 0.94 + }, + { + "category_id": 1, + "poly": [ + 297, + 1210, + 852, + 1210, + 852, + 1248, + 297, + 1248 + ], + "score": 0.936 + }, + { + "category_id": 8, + "poly": [ + 494, + 939, + 1205, + 939, + 1205, + 984, + 494, + 984 + ], + "score": 0.935 + }, + { + "category_id": 1, + "poly": [ + 296, + 1397, + 1407, + 1397, + 1407, + 1516, + 296, + 1516 + ], + "score": 0.926 + }, + { + "category_id": 1, + "poly": [ + 366, + 226, + 1412, + 226, + 1412, + 413, + 366, + 413 + ], + "score": 0.921 + }, + { + "category_id": 1, + "poly": [ + 297, + 799, + 897, + 799, + 897, + 833, + 297, + 833 + ], + "score": 0.92 + }, + { + "category_id": 1, + "poly": [ + 297, + 900, + 457, + 900, + 457, + 931, + 297, + 931 + ], + "score": 0.918 + }, + { + "category_id": 2, + "poly": [ + 298, + 74, + 817, + 74, + 817, + 106, + 298, + 106 + ], + "score": 0.914 + }, + { + "category_id": 1, + "poly": [ + 296, + 994, + 368, + 994, + 368, + 1024, + 296, + 1024 + ], + "score": 0.903 + }, + { + "category_id": 1, + "poly": [ + 298, + 1085, + 509, + 1085, + 509, + 1117, + 298, + 1117 + ], + "score": 0.897 + }, + { + "category_id": 2, + "poly": [ + 835, + 2087, + 863, + 2087, + 863, + 2113, + 835, + 2113 + ], + "score": 0.867 + }, + { + "category_id": 4, + "poly": [ + 292, + 1854, + 1406, + 1854, + 1406, + 1918, + 292, + 1918 + ], + "score": 0.833 + }, + { + "category_id": 0, + "poly": [ + 297, + 1286, + 1035, + 1286, + 1035, + 1326, + 297, + 1326 + ], + "score": 0.827 + }, + { + "category_id": 1, + "poly": [ + 302, + 1356, + 1268, + 1356, + 1268, + 1392, + 302, + 1392 + ], + "score": 0.773 + }, + { + "category_id": 8, + "poly": [ + 291, + 1032, + 1401, + 1032, + 1401, + 1077, + 291, + 1077 + ], + "score": 0.74 + }, + { + "category_id": 1, + "poly": [ + 291, + 1032, + 1401, + 1032, + 1401, + 1077, + 291, + 1077 + ], + "score": 0.135 + }, + { + "category_id": 1, + "poly": [ + 292, + 1854, + 1406, + 1854, + 1406, + 1918, + 292, + 1918 + ], + "score": 0.117 + }, + { + "category_id": 13, + "poly": [ + 1093, + 1428, + 1227, + 1428, + 1227, + 1483, + 1093, + 1483 + ], + "score": 0.94, + "latex": "\\Omega \\left( \\frac { \\epsilon ^ { - 3 } } { \\ln ( 1 / \\delta ) } \\right)" + }, + { + "category_id": 13, + "poly": [ + 578, + 739, + 875, + 739, + 875, + 790, + 578, + 790 + ], + "score": 0.94, + "latex": "\\begin{array} { r } { \\bar { V } ^ { \\ast } ( \\bar { s } _ { s _ { 1 } , 1 } ) = \\frac { \\gamma ^ { H } } { 1 - \\gamma ^ { H } } V ^ { \\ast } ( s _ { 1 } ) } \\end{array}" + }, + { + "category_id": 13, + "poly": [ + 823, + 694, + 1123, + 694, + 1123, + 742, + 823, + 742 + ], + "score": 0.94, + "latex": "\\begin{array} { r } { \\bar { V } ^ { \\bar { \\pi } } ( \\bar { s } _ { s _ { 1 } , 1 } ) = \\frac { \\gamma ^ { H } } { 1 - \\gamma ^ { H } } V ^ { \\pi } ( s _ { 1 } ) } \\end{array}" + }, + { + "category_id": 14, + "poly": [ + 521, + 1123, + 1175, + 1123, + 1175, + 1199, + 521, + 1199 + ], + "score": 0.93, + "latex": "{ V ^ { \\pi } } ^ { t } ( s _ { 1 } ) \\ge \\frac { 1 - \\gamma ^ { H } } { \\gamma ^ { H } } \\bar { V } ^ { * } ( \\bar { s } _ { s 1 , 1 } ) - \\epsilon / \\gamma ^ { H } = V ^ { * } ( s _ { 1 } ) - \\epsilon / \\gamma ^ { H } ," + }, + { + "category_id": 13, + "poly": [ + 1102, + 2004, + 1229, + 2004, + 1229, + 2036, + 1102, + 2036 + ], + "score": 0.92, + "latex": "R ( c , \\cdot ) = 0" + }, + { + "category_id": 13, + "poly": [ + 298, + 1973, + 391, + 1973, + 391, + 2005, + 298, + 2005 + ], + "score": 0.92, + "latex": "\\{ a , b , c \\}" + }, + { + "category_id": 13, + "poly": [ + 488, + 1939, + 632, + 1939, + 632, + 1976, + 488, + 1976 + ], + "score": 0.92, + "latex": "0 < \\epsilon < \\frac { 1 } { 1 0 }" + }, + { + "category_id": 13, + "poly": [ + 904, + 436, + 1167, + 436, + 1167, + 470, + 904, + 470 + ], + "score": 0.92, + "latex": "\\{ ( s _ { 1 } , a _ { 1 } ) , ( s _ { 2 } , a _ { 2 } ) , \\cdot \\cdot \\cdot \\}" + }, + { + "category_id": 13, + "poly": [ + 436, + 379, + 595, + 379, + 595, + 410, + 436, + 410 + ], + "score": 0.92, + "latex": "\\bar { r } ( \\bar { s } _ { s , h } , a ) = 0" + }, + { + "category_id": 13, + "poly": [ + 859, + 345, + 1204, + 345, + 1204, + 380, + 859, + 380 + ], + "score": 0.91, + "latex": "\\bar { p } ( \\bar { s } _ { s ^ { \\prime } , h + 1 } \\mid \\bar { s } _ { s , h } , a ) = p _ { h } ( s , h )" + }, + { + "category_id": 13, + "poly": [ + 590, + 1210, + 674, + 1210, + 674, + 1247, + 590, + 1247 + ], + "score": 0.91, + "latex": "( \\epsilon / \\gamma ^ { H } )" + }, + { + "category_id": 13, + "poly": [ + 297, + 1478, + 463, + 1478, + 463, + 1516, + 297, + 1516 + ], + "score": 0.91, + "latex": "\\ln ( 1 / \\delta ) < \\epsilon ^ { - 2 }" + }, + { + "category_id": 14, + "poly": [ + 685, + 844, + 1012, + 844, + 1012, + 890, + 685, + 890 + ], + "score": 0.91, + "latex": "\\begin{array} { r } { \\bar { V } ^ { \\bar { \\pi } ^ { t } } ( \\bar { s } _ { s _ { 1 } , 1 } ) \\geq \\bar { V } ^ { * } ( \\bar { s } _ { s _ { 1 } , 1 } ) - \\epsilon . } \\end{array}" + }, + { + "category_id": 13, + "poly": [ + 595, + 1973, + 727, + 1973, + 727, + 2005, + 595, + 2005 + ], + "score": 0.91, + "latex": "\\overset { \\vartriangle } { \\mathcal { A } } = \\{ \\ v { x } , \\ v { y } \\}" + }, + { + "category_id": 13, + "poly": [ + 350, + 2003, + 508, + 2003, + 508, + 2036, + 350, + 2036 + ], + "score": 0.91, + "latex": "P ( b | a , x ) = 1" + }, + { + "category_id": 13, + "poly": [ + 1226, + 472, + 1362, + 472, + 1362, + 500, + 1226, + 500 + ], + "score": 0.9, + "latex": "s _ { t H + 1 } = s _ { 1 }" + }, + { + "category_id": 14, + "poly": [ + 310, + 540, + 1428, + 540, + 1428, + 683, + 310, + 683 + ], + "score": 0.9, + "latex": "\\begin{array} { r l } & { \\bar { \\gamma } ^ { \\pi ^ { t } } ( \\bar { s } _ { s _ { 1 } , 1 } ) = \\mathbb { E } \\left[ \\bar { r } ( \\bar { s } _ { s _ { 1 } , 1 } , \\bar { a } _ { 1 } ) + \\gamma \\bar { r } ( \\bar { s } _ { s _ { 2 } , 2 } , \\bar { a } _ { 2 } ) + \\cdot \\cdot \\cdot + \\gamma ^ { H - 1 } \\bar { r } ( \\bar { s } _ { s _ { H - 1 } , H - 1 } , \\bar { a } _ { H - 1 } ) + \\gamma ^ { H } \\bar { V } ^ { \\pi _ { t + H - 1 } } ( \\bar { s } _ { s _ { H + 1 } , 1 } ) \\right] } \\\\ & { \\phantom { \\frac { 1 } { 1 } } = \\gamma ^ { H } \\mathbb { E } \\left[ r _ { 1 } ( s _ { 1 } , a _ { 1 } ) + r _ { 2 } ( s _ { 2 } , a _ { 2 } ) + \\cdot \\cdot \\cdot + r _ { H - 1 } ( s _ { H - 1 } , a _ { H - 1 } ) + \\bar { V } ^ { \\pi _ { t + H } } ( \\bar { s } _ { s _ { H + 1 } , 1 } ) \\right] } \\\\ & { \\phantom { \\frac { 1 } { 1 } } = \\gamma ^ { H } V ^ { \\pi ^ { t } } ( s _ { 1 } ) + \\gamma ^ { H } \\bar { V } ^ { \\pi + H } ( \\bar { s } _ { s _ { 1 } , 1 } ) . } \\end{array}" + }, + { + "category_id": 13, + "poly": [ + 474, + 344, + 805, + 344, + 805, + 378, + 474, + 378 + ], + "score": 0.9, + "latex": "\\bar { r } ( \\bar { s } _ { s , h } , a ) = \\gamma ^ { H - h + 1 } r _ { h } ( s , a )" + }, + { + "category_id": 13, + "poly": [ + 1314, + 346, + 1397, + 346, + 1397, + 375, + 1314, + 375 + ], + "score": 0.89, + "latex": "h = H" + }, + { + "category_id": 13, + "poly": [ + 333, + 499, + 395, + 499, + 395, + 528, + 333, + 528 + ], + "score": 0.89, + "latex": "t \\geq 0" + }, + { + "category_id": 13, + "poly": [ + 646, + 378, + 978, + 378, + 978, + 410, + 646, + 410 + ], + "score": 0.89, + "latex": "\\bar { p } ( \\bar { s } _ { s ^ { \\prime } , 1 } \\mid \\bar { s } _ { s , h } , a ) = I [ s ^ { \\prime } = s _ { 1 } ]" + }, + { + "category_id": 13, + "poly": [ + 674, + 316, + 721, + 316, + 721, + 345, + 674, + 345 + ], + "score": 0.88, + "latex": "\\bar { s } _ { s , h }" + }, + { + "category_id": 13, + "poly": [ + 519, + 2004, + 804, + 2004, + 804, + 2036, + 519, + 2036 + ], + "score": 0.88, + "latex": "P ( a | b , \\cdot ) = P ( a | c , \\cdot ) = 1" + }, + { + "category_id": 13, + "poly": [ + 497, + 1213, + 527, + 1213, + 527, + 1241, + 497, + 1241 + ], + "score": 0.88, + "latex": "\\pi ^ { t }" + }, + { + "category_id": 14, + "poly": [ + 494, + 936, + 1200, + 936, + 1200, + 983, + 494, + 983 + ], + "score": 0.88, + "latex": "\\gamma ^ { H } V ^ { \\pi ^ { t } } ( s _ { 1 } ) + \\gamma ^ { H } \\bar { V } ^ { \\pi _ { t + H } } ( \\bar { s } _ { s _ { 1 } , 1 } ) = \\bar { V } ^ { \\bar { \\pi } } ( \\bar { s } _ { s _ { 1 } , 1 } ) \\geq \\bar { V } ^ { * } ( \\bar { s } _ { s _ { 1 } , 1 } ) - \\epsilon ," + }, + { + "category_id": 13, + "poly": [ + 807, + 497, + 836, + 497, + 836, + 525, + 807, + 525 + ], + "score": 0.87, + "latex": "\\bar { \\pi } ^ { t }" + }, + { + "category_id": 13, + "poly": [ + 472, + 436, + 791, + 436, + 791, + 470, + 472, + 470 + ], + "score": 0.87, + "latex": "\\left\\{ { \\left( { \\bar { s } } _ { s _ { 1 } , 1 } , { \\bar { a } } _ { 1 } \\right) } , { \\left( { \\bar { s } } _ { s _ { 2 } , 2 } , { \\bar { a } } _ { 2 } \\right) } , \\cdot \\cdot \\cdot \\right\\}" + }, + { + "category_id": 13, + "poly": [ + 988, + 474, + 1016, + 474, + 1016, + 498, + 988, + 498 + ], + "score": 0.87, + "latex": "s _ { 1 }" + }, + { + "category_id": 13, + "poly": [ + 870, + 497, + 899, + 497, + 899, + 525, + 870, + 525 + ], + "score": 0.87, + "latex": "\\pi ^ { t }" + }, + { + "category_id": 14, + "poly": [ + 310, + 1032, + 1402, + 1032, + 1402, + 1076, + 310, + 1076 + ], + "score": 0.86, + "latex": "^ { H } V ^ { \\pi ^ { \\varepsilon } } ( s _ { 1 } ) \\geq ( 1 - \\gamma ^ { H } ) \\bar { V } ^ { * } ( \\bar { s } _ { s _ { 1 } , 1 } ) + \\gamma ^ { H } ( \\bar { V } ^ { * } ( \\bar { s } _ { s _ { 1 } , 1 } ) - \\bar { V } ^ { \\pi _ { t + H } } ( \\bar { s } _ { s _ { 1 } , 1 } ) ) - \\epsilon \\geq ( 1 - \\gamma ^ { H } ) \\bar { V } ^ { * } ( \\bar { s } _ { s _ { 1 } , 1 } ) - \\epsilon ." + }, + { + "category_id": 13, + "poly": [ + 1346, + 1944, + 1404, + 1944, + 1404, + 1972, + 1346, + 1972 + ], + "score": 0.86, + "latex": "{ \\boldsymbol { s } } =" + }, + { + "category_id": 13, + "poly": [ + 1374, + 314, + 1396, + 314, + 1396, + 340, + 1374, + 340 + ], + "score": 0.85, + "latex": "s ^ { \\prime }" + }, + { + "category_id": 13, + "poly": [ + 822, + 434, + 858, + 434, + 858, + 466, + 822, + 466 + ], + "score": 0.85, + "latex": "\\bar { \\mathcal { M } }" + }, + { + "category_id": 13, + "poly": [ + 298, + 751, + 329, + 751, + 329, + 777, + 298, + 777 + ], + "score": 0.85, + "latex": "\\bar { \\pi } ^ { * }" + }, + { + "category_id": 13, + "poly": [ + 1250, + 383, + 1277, + 383, + 1277, + 407, + 1250, + 407 + ], + "score": 0.84, + "latex": "s _ { 1 }" + }, + { + "category_id": 13, + "poly": [ + 596, + 470, + 630, + 470, + 630, + 494, + 596, + 494 + ], + "score": 0.84, + "latex": "\\mathcal { M }" + }, + { + "category_id": 13, + "poly": [ + 439, + 469, + 474, + 469, + 474, + 494, + 439, + 494 + ], + "score": 0.83, + "latex": "\\mathcal { M }" + }, + { + "category_id": 13, + "poly": [ + 395, + 226, + 624, + 226, + 624, + 262, + 395, + 262 + ], + "score": 0.81, + "latex": "\\bar { S } = S \\times H , \\bar { A } = A" + }, + { + "category_id": 13, + "poly": [ + 604, + 707, + 623, + 707, + 623, + 730, + 604, + 730 + ], + "score": 0.8, + "latex": "\\bar { \\pi }" + }, + { + "category_id": 13, + "poly": [ + 457, + 804, + 476, + 804, + 476, + 828, + 457, + 828 + ], + "score": 0.79, + "latex": "\\bar { \\pi }" + }, + { + "category_id": 13, + "poly": [ + 984, + 1399, + 1006, + 1399, + 1006, + 1426, + 984, + 1426 + ], + "score": 0.78, + "latex": "S" + }, + { + "category_id": 13, + "poly": [ + 610, + 314, + 629, + 314, + 629, + 341, + 610, + 341 + ], + "score": 0.78, + "latex": "h" + }, + { + "category_id": 13, + "poly": [ + 513, + 320, + 529, + 320, + 529, + 340, + 513, + 340 + ], + "score": 0.76, + "latex": "s" + }, + { + "category_id": 13, + "poly": [ + 1194, + 320, + 1212, + 320, + 1212, + 340, + 1194, + 340 + ], + "score": 0.75, + "latex": "a" + }, + { + "category_id": 13, + "poly": [ + 752, + 804, + 766, + 804, + 766, + 828, + 752, + 828 + ], + "score": 0.74, + "latex": "t" + }, + { + "category_id": 13, + "poly": [ + 396, + 270, + 575, + 270, + 575, + 305, + 396, + 305 + ], + "score": 0.73, + "latex": "\\gamma = ( 1 - 1 / H )" + }, + { + "category_id": 13, + "poly": [ + 1028, + 1973, + 1250, + 1973, + 1250, + 2005, + 1028, + 2005 + ], + "score": 0.73, + "latex": "P ( b | a , y ) = 1 - 1 0 \\epsilon" + }, + { + "category_id": 13, + "poly": [ + 506, + 807, + 520, + 807, + 520, + 828, + 506, + 828 + ], + "score": 0.73, + "latex": "\\epsilon" + }, + { + "category_id": 13, + "poly": [ + 1066, + 1400, + 1089, + 1400, + 1089, + 1426, + 1066, + 1426 + ], + "score": 0.71, + "latex": "A" + }, + { + "category_id": 13, + "poly": [ + 473, + 1440, + 496, + 1440, + 496, + 1470, + 473, + 1470 + ], + "score": 0.71, + "latex": "Q" + }, + { + "category_id": 13, + "poly": [ + 296, + 1437, + 360, + 1437, + 360, + 1469, + 296, + 1469 + ], + "score": 0.71, + "latex": "1 - \\delta" + }, + { + "category_id": 13, + "poly": [ + 1265, + 1973, + 1405, + 1973, + 1405, + 2006, + 1265, + 2006 + ], + "score": 0.61, + "latex": "P ( c | a , y ) =" + }, + { + "category_id": 13, + "poly": [ + 971, + 1598, + 985, + 1598, + 985, + 1621, + 971, + 1621 + ], + "score": 0.44, + "latex": "b" + }, + { + "category_id": 13, + "poly": [ + 788, + 1563, + 837, + 1563, + 837, + 1586, + 788, + 1586 + ], + "score": 0.27, + "latex": "x , y" + }, + { + "category_id": 15, + "poly": [ + 780.0, + 1553.0, + 787.0, + 1553.0, + 787.0, + 1591.0, + 780.0, + 1591.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 838.0, + 1553.0, + 847.0, + 1553.0, + 847.0, + 1591.0, + 838.0, + 1591.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 966.0, + 1592.0, + 970.0, + 1592.0, + 970.0, + 1624.0, + 966.0, + 1624.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 986.0, + 1592.0, + 994.0, + 1592.0, + 994.0, + 1624.0, + 986.0, + 1624.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 795.0, + 1627.0, + 826.0, + 1627.0, + 826.0, + 1656.0, + 795.0, + 1656.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 847.0, + 1645.0, + 970.0, + 1645.0, + 970.0, + 1670.0, + 847.0, + 1670.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 702.0, + 1677.0, + 736.0, + 1677.0, + 736.0, + 1709.0, + 702.0, + 1709.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 835.0, + 1684.0, + 842.0, + 1684.0, + 842.0, + 1694.0, + 835.0, + 1694.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 794.0, + 1689.0, + 825.0, + 1689.0, + 825.0, + 1724.0, + 794.0, + 1724.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 891.0, + 1756.0, + 942.0, + 1756.0, + 942.0, + 1775.0, + 891.0, + 1775.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 966.0, + 1756.0, + 995.0, + 1756.0, + 995.0, + 1784.0, + 966.0, + 1784.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 887.0, + 1757.0, + 895.0, + 1757.0, + 895.0, + 1765.0, + 887.0, + 1765.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 784.0, + 1789.0, + 849.0, + 1789.0, + 849.0, + 1833.0, + 784.0, + 1833.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 871.0, + 1740.5, + 876.0, + 1740.5, + 876.0, + 1745.5, + 871.0, + 1745.5 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 72.0, + 817.0, + 72.0, + 817.0, + 109.0, + 295.0, + 109.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 831.0, + 2085.0, + 868.0, + 2085.0, + 868.0, + 2125.0, + 831.0, + 2125.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 1854.0, + 1408.0, + 1854.0, + 1408.0, + 1890.0, + 295.0, + 1890.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 1886.0, + 570.0, + 1886.0, + 570.0, + 1922.0, + 294.0, + 1922.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 1281.0, + 1038.0, + 1281.0, + 1038.0, + 1335.0, + 292.0, + 1335.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 1936.0, + 487.0, + 1936.0, + 487.0, + 1982.0, + 292.0, + 1982.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 633.0, + 1936.0, + 1345.0, + 1936.0, + 1345.0, + 1982.0, + 633.0, + 1982.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1405.0, + 1936.0, + 1408.0, + 1936.0, + 1408.0, + 1982.0, + 1405.0, + 1982.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 392.0, + 1971.0, + 594.0, + 1971.0, + 594.0, + 2009.0, + 392.0, + 2009.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 728.0, + 1971.0, + 1027.0, + 1971.0, + 1027.0, + 2009.0, + 728.0, + 2009.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1251.0, + 1971.0, + 1264.0, + 1971.0, + 1264.0, + 2009.0, + 1251.0, + 2009.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 2000.0, + 349.0, + 2000.0, + 349.0, + 2038.0, + 293.0, + 2038.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 509.0, + 2000.0, + 518.0, + 2000.0, + 518.0, + 2038.0, + 509.0, + 2038.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 805.0, + 2000.0, + 1101.0, + 2000.0, + 1101.0, + 2038.0, + 805.0, + 2038.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1230.0, + 2000.0, + 1240.0, + 2000.0, + 1240.0, + 2038.0, + 1230.0, + 2038.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 432.0, + 471.0, + 432.0, + 471.0, + 474.0, + 293.0, + 474.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 792.0, + 432.0, + 821.0, + 432.0, + 821.0, + 474.0, + 792.0, + 474.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 859.0, + 432.0, + 903.0, + 432.0, + 903.0, + 474.0, + 859.0, + 474.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1168.0, + 432.0, + 1406.0, + 432.0, + 1406.0, + 474.0, + 1168.0, + 474.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 464.0, + 438.0, + 464.0, + 438.0, + 502.0, + 295.0, + 502.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 475.0, + 464.0, + 595.0, + 464.0, + 595.0, + 502.0, + 475.0, + 502.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 631.0, + 464.0, + 987.0, + 464.0, + 987.0, + 502.0, + 631.0, + 502.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1017.0, + 464.0, + 1225.0, + 464.0, + 1225.0, + 502.0, + 1017.0, + 502.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1363.0, + 464.0, + 1405.0, + 464.0, + 1405.0, + 502.0, + 1363.0, + 502.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 296.0, + 498.0, + 332.0, + 498.0, + 332.0, + 532.0, + 296.0, + 532.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 396.0, + 498.0, + 806.0, + 498.0, + 806.0, + 532.0, + 396.0, + 532.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 837.0, + 498.0, + 869.0, + 498.0, + 869.0, + 532.0, + 837.0, + 532.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 900.0, + 498.0, + 1336.0, + 498.0, + 1336.0, + 532.0, + 900.0, + 532.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 280.0, + 682.0, + 603.0, + 682.0, + 603.0, + 751.0, + 280.0, + 751.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 624.0, + 682.0, + 822.0, + 682.0, + 822.0, + 751.0, + 624.0, + 751.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1124.0, + 682.0, + 1417.0, + 682.0, + 1417.0, + 751.0, + 1124.0, + 751.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 287.0, + 740.0, + 297.0, + 740.0, + 297.0, + 796.0, + 287.0, + 796.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 330.0, + 740.0, + 577.0, + 740.0, + 577.0, + 796.0, + 330.0, + 796.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 876.0, + 740.0, + 893.0, + 740.0, + 893.0, + 796.0, + 876.0, + 796.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 731.0, + 737.0, + 783.0, + 737.0, + 783.0, + 769.0, + 731.0, + 769.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 1203.0, + 496.0, + 1203.0, + 496.0, + 1254.0, + 292.0, + 1254.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 528.0, + 1203.0, + 589.0, + 1203.0, + 589.0, + 1254.0, + 528.0, + 1254.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 675.0, + 1203.0, + 853.0, + 1203.0, + 853.0, + 1254.0, + 675.0, + 1254.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 1392.0, + 983.0, + 1392.0, + 983.0, + 1435.0, + 294.0, + 1435.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1007.0, + 1392.0, + 1065.0, + 1392.0, + 1065.0, + 1435.0, + 1007.0, + 1435.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1090.0, + 1392.0, + 1404.0, + 1392.0, + 1404.0, + 1435.0, + 1090.0, + 1435.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 291.0, + 1432.0, + 295.0, + 1432.0, + 295.0, + 1478.0, + 291.0, + 1478.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 361.0, + 1432.0, + 472.0, + 1432.0, + 472.0, + 1478.0, + 361.0, + 1478.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 497.0, + 1432.0, + 1092.0, + 1432.0, + 1092.0, + 1478.0, + 497.0, + 1478.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1230.0, + 1436.0, + 1405.0, + 1436.0, + 1405.0, + 1473.0, + 1230.0, + 1473.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 1477.0, + 296.0, + 1477.0, + 296.0, + 1512.0, + 292.0, + 1512.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 464.0, + 1477.0, + 472.0, + 1477.0, + 472.0, + 1512.0, + 464.0, + 1512.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1145.0, + 1426.5, + 1201.0, + 1426.5, + 1201.0, + 1456.5, + 1145.0, + 1456.5 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 365.0, + 222.0, + 394.0, + 222.0, + 394.0, + 265.0, + 365.0, + 265.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 625.0, + 222.0, + 636.0, + 222.0, + 636.0, + 265.0, + 625.0, + 265.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 365.0, + 270.0, + 395.0, + 270.0, + 395.0, + 305.0, + 365.0, + 305.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 576.0, + 270.0, + 588.0, + 270.0, + 588.0, + 305.0, + 576.0, + 305.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 366.0, + 309.0, + 512.0, + 309.0, + 512.0, + 348.0, + 366.0, + 348.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 530.0, + 309.0, + 609.0, + 309.0, + 609.0, + 348.0, + 530.0, + 348.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 630.0, + 309.0, + 673.0, + 309.0, + 673.0, + 348.0, + 630.0, + 348.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 722.0, + 309.0, + 1193.0, + 309.0, + 1193.0, + 348.0, + 722.0, + 348.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1213.0, + 309.0, + 1373.0, + 309.0, + 1373.0, + 348.0, + 1213.0, + 348.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1397.0, + 309.0, + 1409.0, + 309.0, + 1409.0, + 348.0, + 1397.0, + 348.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 390.0, + 339.0, + 473.0, + 339.0, + 473.0, + 385.0, + 390.0, + 385.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 806.0, + 339.0, + 858.0, + 339.0, + 858.0, + 385.0, + 806.0, + 385.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1205.0, + 339.0, + 1313.0, + 339.0, + 1313.0, + 385.0, + 1205.0, + 385.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1398.0, + 339.0, + 1415.0, + 339.0, + 1415.0, + 385.0, + 1398.0, + 385.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 391.0, + 373.0, + 435.0, + 373.0, + 435.0, + 414.0, + 391.0, + 414.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 596.0, + 373.0, + 645.0, + 373.0, + 645.0, + 414.0, + 596.0, + 414.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 979.0, + 373.0, + 1249.0, + 373.0, + 1249.0, + 414.0, + 979.0, + 414.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1278.0, + 373.0, + 1291.0, + 373.0, + 1291.0, + 414.0, + 1278.0, + 414.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 296.0, + 797.0, + 456.0, + 797.0, + 456.0, + 837.0, + 296.0, + 837.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 477.0, + 797.0, + 505.0, + 797.0, + 505.0, + 837.0, + 477.0, + 837.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 521.0, + 797.0, + 751.0, + 797.0, + 751.0, + 837.0, + 521.0, + 837.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 767.0, + 797.0, + 896.0, + 797.0, + 896.0, + 837.0, + 767.0, + 837.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 896.0, + 461.0, + 896.0, + 461.0, + 934.0, + 293.0, + 934.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 991.0, + 371.0, + 991.0, + 371.0, + 1030.0, + 294.0, + 1030.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 1081.0, + 511.0, + 1081.0, + 511.0, + 1120.0, + 294.0, + 1120.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 1349.0, + 1267.0, + 1349.0, + 1267.0, + 1401.0, + 292.0, + 1401.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 1026.0, + 309.0, + 1026.0, + 309.0, + 1083.0, + 292.0, + 1083.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1403.0, + 1026.0, + 1408.0, + 1026.0, + 1408.0, + 1083.0, + 1403.0, + 1083.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 1854.0, + 1408.0, + 1854.0, + 1408.0, + 1890.0, + 295.0, + 1890.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 1886.0, + 570.0, + 1886.0, + 570.0, + 1922.0, + 294.0, + 1922.0 + ], + "score": 1.0, + "text": "" + } + ], + "page_info": { + "page_no": 16, + "width": 1700, + "height": 2200 + } + }, + { + "layout_dets": [ + { + "category_id": 1, + "poly": [ + 297, + 226, + 1405, + 226, + 1405, + 470, + 297, + 470 + ], + "score": 0.981 + }, + { + "category_id": 1, + "poly": [ + 296, + 603, + 1405, + 603, + 1405, + 763, + 296, + 763 + ], + "score": 0.979 + }, + { + "category_id": 1, + "poly": [ + 298, + 485, + 1406, + 485, + 1406, + 593, + 298, + 593 + ], + "score": 0.972 + }, + { + "category_id": 8, + "poly": [ + 715, + 778, + 983, + 778, + 983, + 854, + 715, + 854 + ], + "score": 0.956 + }, + { + "category_id": 1, + "poly": [ + 295, + 867, + 1058, + 867, + 1058, + 907, + 295, + 907 + ], + "score": 0.929 + }, + { + "category_id": 2, + "poly": [ + 299, + 75, + 816, + 75, + 816, + 105, + 299, + 105 + ], + "score": 0.906 + }, + { + "category_id": 2, + "poly": [ + 836, + 2088, + 864, + 2088, + 864, + 2112, + 836, + 2112 + ], + "score": 0.843 + }, + { + "category_id": 2, + "poly": [ + 1374, + 871, + 1403, + 871, + 1403, + 900, + 1374, + 900 + ], + "score": 0.822 + }, + { + "category_id": 13, + "poly": [ + 627, + 335, + 714, + 335, + 714, + 372, + 627, + 372 + ], + "score": 0.95, + "latex": "\\hat { Q } ( a , y )" + }, + { + "category_id": 14, + "poly": [ + 714, + 776, + 984, + 776, + 984, + 854, + 714, + 854 + ], + "score": 0.94, + "latex": "t _ { 0 } = \\Omega \\left( { \\frac { 1 } { \\epsilon ^ { 3 } \\left( \\ln { 1 / \\delta } \\right) } } \\right) ." + }, + { + "category_id": 13, + "poly": [ + 1243, + 483, + 1331, + 483, + 1331, + 522, + 1243, + 522 + ], + "score": 0.94, + "latex": "\\hat { Q } ( a , y )" + }, + { + "category_id": 13, + "poly": [ + 610, + 696, + 697, + 696, + 697, + 733, + 610, + 733 + ], + "score": 0.94, + "latex": "\\hat { Q } ( a , y )" + }, + { + "category_id": 13, + "poly": [ + 1260, + 300, + 1349, + 300, + 1349, + 338, + 1260, + 338 + ], + "score": 0.93, + "latex": "\\hat { Q } ( a , x )" + }, + { + "category_id": 13, + "poly": [ + 663, + 430, + 749, + 430, + 749, + 469, + 663, + 469 + ], + "score": 0.93, + "latex": "\\hat { Q } ( a , y )" + }, + { + "category_id": 13, + "poly": [ + 752, + 866, + 1051, + 866, + 1051, + 908, + 752, + 908 + ], + "score": 0.93, + "latex": "\\begin{array} { r } { C = 3 \\ln \\frac { 1 } { \\delta } + 1 < \\frac { 4 } { \\epsilon ^ { 2 } } < m } \\end{array}" + }, + { + "category_id": 13, + "poly": [ + 803, + 555, + 942, + 555, + 942, + 594, + 803, + 594 + ], + "score": 0.93, + "latex": "\\begin{array} { r } { m = \\Omega \\left( \\frac { 1 } { \\epsilon ^ { 2 } } \\right) } \\end{array}" + }, + { + "category_id": 13, + "poly": [ + 722, + 483, + 796, + 483, + 796, + 522, + 722, + 522 + ], + "score": 0.93, + "latex": "\\hat { Q } ( \\cdot , \\cdot )" + }, + { + "category_id": 13, + "poly": [ + 990, + 487, + 1104, + 487, + 1104, + 522, + 990, + 522 + ], + "score": 0.92, + "latex": "1 / ( 1 - \\gamma )" + }, + { + "category_id": 13, + "poly": [ + 573, + 633, + 752, + 633, + 752, + 670, + 573, + 670 + ], + "score": 0.92, + "latex": "\\begin{array} { r } { C ^ { ' } = 3 \\ln \\frac { 1 } { \\delta } + 1 } \\end{array}" + }, + { + "category_id": 13, + "poly": [ + 1327, + 227, + 1401, + 227, + 1401, + 267, + 1327, + 267 + ], + "score": 0.92, + "latex": "\\begin{array} { r } { \\gamma > \\frac { 1 } { 2 } } \\end{array}" + }, + { + "category_id": 13, + "poly": [ + 369, + 868, + 535, + 868, + 535, + 904, + 369, + 904 + ], + "score": 0.92, + "latex": "\\ln ( 1 / \\delta ) < \\epsilon ^ { - 2 }" + }, + { + "category_id": 13, + "poly": [ + 298, + 371, + 645, + 371, + 645, + 404, + 298, + 404 + ], + "score": 0.91, + "latex": "Q ( a , x ) - Q ( a , y ) = 1 0 \\epsilon \\gamma > \\epsilon" + }, + { + "category_id": 13, + "poly": [ + 298, + 335, + 384, + 335, + 384, + 372, + 298, + 372 + ], + "score": 0.91, + "latex": "\\hat { Q } ( a , y )" + }, + { + "category_id": 13, + "poly": [ + 297, + 634, + 483, + 634, + 483, + 668, + 297, + 668 + ], + "score": 0.91, + "latex": "t _ { 0 } = m / ( 1 0 \\epsilon C )" + }, + { + "category_id": 13, + "poly": [ + 1012, + 636, + 1101, + 636, + 1101, + 665, + 1012, + 665 + ], + "score": 0.91, + "latex": "C \\leq m" + }, + { + "category_id": 13, + "poly": [ + 1073, + 524, + 1194, + 524, + 1194, + 558, + 1073, + 558 + ], + "score": 0.9, + "latex": "1 / ( 1 - \\gamma ) )" + }, + { + "category_id": 13, + "poly": [ + 1243, + 636, + 1282, + 636, + 1282, + 666, + 1243, + 666 + ], + "score": 0.89, + "latex": "2 t _ { 0 }" + }, + { + "category_id": 13, + "poly": [ + 1053, + 701, + 1092, + 701, + 1092, + 731, + 1053, + 731 + ], + "score": 0.89, + "latex": "2 t _ { 0 }" + }, + { + "category_id": 13, + "poly": [ + 563, + 520, + 641, + 520, + 641, + 558, + 563, + 558 + ], + "score": 0.88, + "latex": "\\hat { Q } ( c , \\cdot )" + }, + { + "category_id": 13, + "poly": [ + 1035, + 667, + 1099, + 667, + 1099, + 695, + 1035, + 695 + ], + "score": 0.87, + "latex": "1 - \\delta" + }, + { + "category_id": 13, + "poly": [ + 426, + 731, + 490, + 731, + 490, + 760, + 426, + 760 + ], + "score": 0.87, + "latex": "1 - \\delta" + }, + { + "category_id": 13, + "poly": [ + 486, + 668, + 512, + 668, + 512, + 696, + 486, + 696 + ], + "score": 0.87, + "latex": "t _ { 0 }" + }, + { + "category_id": 13, + "poly": [ + 1201, + 264, + 1227, + 264, + 1227, + 302, + 1201, + 302 + ], + "score": 0.86, + "latex": "\\hat { Q }" + }, + { + "category_id": 13, + "poly": [ + 716, + 270, + 743, + 270, + 743, + 302, + 716, + 302 + ], + "score": 0.84, + "latex": "Q" + }, + { + "category_id": 13, + "poly": [ + 1187, + 344, + 1207, + 344, + 1207, + 372, + 1187, + 372 + ], + "score": 0.79, + "latex": "y" + }, + { + "category_id": 13, + "poly": [ + 925, + 376, + 944, + 376, + 944, + 402, + 925, + 402 + ], + "score": 0.76, + "latex": "y" + }, + { + "category_id": 13, + "poly": [ + 1032, + 310, + 1052, + 310, + 1052, + 337, + 1032, + 337 + ], + "score": 0.76, + "latex": "y" + }, + { + "category_id": 13, + "poly": [ + 678, + 563, + 694, + 563, + 694, + 585, + 678, + 585 + ], + "score": 0.74, + "latex": "c" + }, + { + "category_id": 13, + "poly": [ + 722, + 612, + 739, + 612, + 739, + 632, + 722, + 632 + ], + "score": 0.74, + "latex": "a" + }, + { + "category_id": 13, + "poly": [ + 1169, + 671, + 1185, + 671, + 1185, + 693, + 1169, + 693 + ], + "score": 0.73, + "latex": "c" + }, + { + "category_id": 13, + "poly": [ + 362, + 441, + 380, + 441, + 380, + 463, + 362, + 463 + ], + "score": 0.73, + "latex": "a" + }, + { + "category_id": 13, + "poly": [ + 353, + 705, + 382, + 705, + 382, + 729, + 353, + 729 + ], + "score": 0.73, + "latex": "m" + }, + { + "category_id": 13, + "poly": [ + 1139, + 237, + 1157, + 237, + 1157, + 259, + 1139, + 259 + ], + "score": 0.72, + "latex": "a" + }, + { + "category_id": 13, + "poly": [ + 1300, + 346, + 1318, + 346, + 1318, + 367, + 1300, + 367 + ], + "score": 0.71, + "latex": "a" + }, + { + "category_id": 13, + "poly": [ + 1033, + 376, + 1051, + 376, + 1051, + 398, + 1033, + 398 + ], + "score": 0.66, + "latex": "a" + }, + { + "category_id": 13, + "poly": [ + 298, + 672, + 316, + 672, + 316, + 693, + 298, + 693 + ], + "score": 0.64, + "latex": "a" + }, + { + "category_id": 13, + "poly": [ + 960, + 606, + 1003, + 606, + 1003, + 633, + 960, + 633 + ], + "score": 0.61, + "latex": "1 0 \\epsilon" + }, + { + "category_id": 13, + "poly": [ + 298, + 408, + 312, + 408, + 312, + 428, + 298, + 428 + ], + "score": 0.59, + "latex": "\\epsilon" + }, + { + "category_id": 13, + "poly": [ + 1323, + 611, + 1339, + 611, + 1339, + 632, + 1323, + 632 + ], + "score": 0.57, + "latex": "c" + }, + { + "category_id": 13, + "poly": [ + 767, + 635, + 784, + 635, + 784, + 662, + 767, + 662 + ], + "score": 0.55, + "latex": "\\delta" + }, + { + "category_id": 13, + "poly": [ + 539, + 276, + 555, + 276, + 555, + 297, + 539, + 297 + ], + "score": 0.49, + "latex": "\\epsilon" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 73.0, + 817.0, + 73.0, + 817.0, + 108.0, + 295.0, + 108.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 831.0, + 2084.0, + 868.0, + 2084.0, + 868.0, + 2122.0, + 831.0, + 2122.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1378.0, + 875.0, + 1403.0, + 875.0, + 1403.0, + 901.0, + 1378.0, + 901.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 226.0, + 1138.0, + 226.0, + 1138.0, + 270.0, + 292.0, + 270.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1158.0, + 226.0, + 1326.0, + 226.0, + 1326.0, + 270.0, + 1158.0, + 270.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1402.0, + 226.0, + 1406.0, + 226.0, + 1406.0, + 270.0, + 1402.0, + 270.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 269.0, + 538.0, + 269.0, + 538.0, + 303.0, + 294.0, + 303.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 556.0, + 269.0, + 715.0, + 269.0, + 715.0, + 303.0, + 556.0, + 303.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 744.0, + 269.0, + 1200.0, + 269.0, + 1200.0, + 303.0, + 744.0, + 303.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1228.0, + 269.0, + 1405.0, + 269.0, + 1405.0, + 303.0, + 1228.0, + 303.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 291.0, + 300.0, + 1031.0, + 300.0, + 1031.0, + 340.0, + 291.0, + 340.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1053.0, + 300.0, + 1259.0, + 300.0, + 1259.0, + 340.0, + 1053.0, + 340.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1350.0, + 300.0, + 1406.0, + 300.0, + 1406.0, + 340.0, + 1350.0, + 340.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 335.0, + 297.0, + 335.0, + 297.0, + 377.0, + 294.0, + 377.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 385.0, + 335.0, + 626.0, + 335.0, + 626.0, + 377.0, + 385.0, + 377.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 715.0, + 335.0, + 1186.0, + 335.0, + 1186.0, + 377.0, + 715.0, + 377.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1208.0, + 335.0, + 1299.0, + 335.0, + 1299.0, + 377.0, + 1208.0, + 377.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1319.0, + 335.0, + 1406.0, + 335.0, + 1406.0, + 377.0, + 1319.0, + 377.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 368.0, + 297.0, + 368.0, + 297.0, + 407.0, + 294.0, + 407.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 646.0, + 368.0, + 924.0, + 368.0, + 924.0, + 407.0, + 646.0, + 407.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 945.0, + 368.0, + 1032.0, + 368.0, + 1032.0, + 407.0, + 945.0, + 407.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1052.0, + 368.0, + 1407.0, + 368.0, + 1407.0, + 407.0, + 1052.0, + 407.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 313.0, + 402.0, + 1405.0, + 402.0, + 1405.0, + 435.0, + 313.0, + 435.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 433.0, + 361.0, + 433.0, + 361.0, + 472.0, + 292.0, + 472.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 381.0, + 433.0, + 662.0, + 433.0, + 662.0, + 472.0, + 381.0, + 472.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 750.0, + 433.0, + 762.0, + 433.0, + 762.0, + 472.0, + 750.0, + 472.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 604.0, + 721.0, + 604.0, + 721.0, + 638.0, + 295.0, + 638.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 740.0, + 604.0, + 959.0, + 604.0, + 959.0, + 638.0, + 740.0, + 638.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1004.0, + 604.0, + 1322.0, + 604.0, + 1322.0, + 638.0, + 1004.0, + 638.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1340.0, + 604.0, + 1405.0, + 604.0, + 1405.0, + 638.0, + 1340.0, + 638.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 632.0, + 296.0, + 632.0, + 296.0, + 674.0, + 293.0, + 674.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 484.0, + 632.0, + 572.0, + 632.0, + 572.0, + 674.0, + 484.0, + 674.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 753.0, + 632.0, + 766.0, + 632.0, + 766.0, + 674.0, + 753.0, + 674.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 785.0, + 632.0, + 1011.0, + 632.0, + 1011.0, + 674.0, + 785.0, + 674.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1102.0, + 632.0, + 1242.0, + 632.0, + 1242.0, + 674.0, + 1102.0, + 674.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1283.0, + 632.0, + 1408.0, + 632.0, + 1408.0, + 674.0, + 1283.0, + 674.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 665.0, + 297.0, + 665.0, + 297.0, + 699.0, + 294.0, + 699.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 317.0, + 665.0, + 485.0, + 665.0, + 485.0, + 699.0, + 317.0, + 699.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 513.0, + 665.0, + 1034.0, + 665.0, + 1034.0, + 699.0, + 513.0, + 699.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1100.0, + 665.0, + 1168.0, + 665.0, + 1168.0, + 699.0, + 1100.0, + 699.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1186.0, + 665.0, + 1405.0, + 665.0, + 1405.0, + 699.0, + 1186.0, + 699.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 698.0, + 352.0, + 698.0, + 352.0, + 736.0, + 295.0, + 736.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 383.0, + 698.0, + 609.0, + 698.0, + 609.0, + 736.0, + 383.0, + 736.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 698.0, + 698.0, + 1052.0, + 698.0, + 1052.0, + 736.0, + 698.0, + 736.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1093.0, + 698.0, + 1405.0, + 698.0, + 1405.0, + 736.0, + 1093.0, + 736.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 294.0, + 730.0, + 425.0, + 730.0, + 425.0, + 767.0, + 294.0, + 767.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 491.0, + 730.0, + 992.0, + 730.0, + 992.0, + 767.0, + 491.0, + 767.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 482.0, + 721.0, + 482.0, + 721.0, + 526.0, + 292.0, + 526.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 797.0, + 482.0, + 989.0, + 482.0, + 989.0, + 526.0, + 797.0, + 526.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1105.0, + 482.0, + 1242.0, + 482.0, + 1242.0, + 526.0, + 1105.0, + 526.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1332.0, + 482.0, + 1406.0, + 482.0, + 1406.0, + 526.0, + 1332.0, + 526.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 293.0, + 519.0, + 562.0, + 519.0, + 562.0, + 561.0, + 293.0, + 561.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 642.0, + 519.0, + 1072.0, + 519.0, + 1072.0, + 561.0, + 642.0, + 561.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1195.0, + 519.0, + 1404.0, + 519.0, + 1404.0, + 561.0, + 1195.0, + 561.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 295.0, + 555.0, + 677.0, + 555.0, + 677.0, + 595.0, + 295.0, + 595.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 695.0, + 555.0, + 802.0, + 555.0, + 802.0, + 595.0, + 695.0, + 595.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 943.0, + 555.0, + 1023.0, + 555.0, + 1023.0, + 595.0, + 943.0, + 595.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 292.0, + 857.0, + 368.0, + 857.0, + 368.0, + 913.0, + 292.0, + 913.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 536.0, + 857.0, + 751.0, + 857.0, + 751.0, + 913.0, + 536.0, + 913.0 + ], + "score": 1.0, + "text": "" + }, + { + "category_id": 15, + "poly": [ + 1052.0, + 857.0, + 1064.0, + 857.0, + 1064.0, + 913.0, + 1052.0, + 913.0 + ], + "score": 1.0, + "text": "" + } + ], + "page_info": { + "page_no": 17, + "width": 1700, + "height": 2200 + } + } +] \ No newline at end of file