| Method | MIT-67 | FOOD-100 |
| RandomBatch | (5,218-3,936)/5,218 × 100= 24.6% | (7,263-5,365)/7,263 × 100= 26.1% |
| OnlineBatch | (6,079- 3,823)/6,079 × 100 = 37.1% | (8,333-3,685)/8,333 × 100= 55.8% |
| Active Bias | (5,738-3,032)/5,738×100=47.2% | (7,933-3,227)/7,933× 100= 59.3% |
+
+Results on Training Time: Moreover, to assess the performance gain in training time, we computed the reduction in the training time taken to reach the same error. For example, in Figure 5(b), the best test error of $2 8 . 8 \%$ achieved in 5, 218 seconds by Random Batch could be achieved only in 3, 936 seconds by Recency Bias; thus, Recency Bias improved the training time by $2 4 . 6 \%$ . Table 3 summarizes the reduction in the training time of Recency Bias over three other batch selection strategies. Notably, Recency Bias improved the training time by $2 4 . 6 \% { - 4 7 . 2 \% }$ and $2 6 . 1 \% { - 5 9 . 3 \% }$ in fine-tuning MIT-67 and FOOD-100 datasets, respectively.
+
+# 5.4 ABLATION STUDY ON SELECTION PRESSURE
+
+For an ablation study on the selection pressure, we trained DenseNet $( \mathrm { L } { = } 4 0 , \mathrm { k } { = } 1 2 )$ on two benchmark datasets using Recency Bias with four different decaying strategies: $s _ { e } : 1 0 \to 1 0$ , $s _ { e } : 1 0 0 \to 1 0 0$ , $s _ { e } : 1 0 \to 1$ , and $s _ { e } : 1 0 0 \to 1$ . The first two strategies used different initial selection pressures without decaying, but the remaining strategies exponentially decayed their initial selection pressures to 1. We used a momentum optimizer and the other experimental configurations were the same as those in Section 5.2.
+
+Figure 6 shows the convergence curves of Recency Bias using the different decaying strategies along with that of Random Batch. Generally, the two strategies without decaying (i.e., $s _ { e } : 1 0 \to 1 0$ , $s _ { e } : 1 0 0 \to 1 0 0 )$ showed much faster convergence speed in training loss compared with those with decaying (i.e., $s _ { e } : 1 0 \to 1$ , $s _ { e } : 1 0 0 \to 1 $ ). However, as mentioned earlier in Section 3.2, the two strategies without decaying exacerbated the overfitting problem because they only used the training samples classified as highly uncertain. Accordingly, their test errors were rather higher than that of Random Batch in CIFAR-100 dataset. On the other hand, the two strategies with decaying converged faster than Random Batch in both training loss and test error in all datasets because they exploited more diverse training samples by exponentially decaying the selection pressure. Thus, these observations empirically prove that decaying the selection pressure is an effective way to alleviate the overfitting problem at the later stage of training.
+
+
+0 80 10Figure 6: Ablation study on the effect of the selection pressure.
+
+# 6 CONCLUSION
+
+In this paper, we presented a novel adaptive batch selection algorithm called Recency Bias that emphasizes predictively uncertain samples for accelerating the training of neural networks. Toward this goal, the predictive uncertainty of each sample is evaluated using its recent label predictions managed by a sliding window of a fixed size. Then, uncertain samples at the moment are selected with high probability for the next mini-batch. We conducted extensive experiments on both classification and fine-tuning tasks. The results showed that Recency Bias is effective in reducing the training time as well as the best test error. It was worthwhile to note that using all historical observations to estimate the uncertainty has the side effect of slowing down the training process. Overall, a merger of uncertain samples and sliding windows greatly improves the power of adaptive batch selection.
+
+# REFERENCES
+
+Yoshua Bengio, Jérôme Louradour, Ronan Collobert, and Jason Weston. Curriculum learning. In ICML, pp. 41–48, 2009.
+
+David Chandler. Introduction to modern statistical mechanics. Oxford University Press, 1987.
+
+Haw-Shiuan Chang, Erik Learned-Miller, and Andrew McCallum. Active Bias: Training more accurate neural networks by emphasizing high variance samples. In NeurIPS, pp. 1002–1012, 2017.
+
+Brian Chen and Gregory W Wornell. Quantization index modulation: A class of provably good methods for digital watermarking and information embedding. IEEE Trans. on Information Theory, 47(4):1423–1443, 2001.
+
+Jia Deng, Wei Dong, Richard Socher, Li-Jia Li, Kai Li, and Li Fei-Fei. Imagenet: A large-scale hierarchical image database. In CVPR, pp. 248–255, 2009.
+
+Yang Fan, Fei Tian, Tao Qin, and Tie-Yan Liu. Neural data filter for bootstrapping stochastic gradient descent. In ICLR, 2017.
+
+Bo Han, Quanming Yao, Xingrui Yu, Gang Niu, Miao Xu, Weihua Hu, Ivor Tsang, and Masashi Sugiyama. Co-teaching: Robust training of deep neural networks with extremely noisy labels. In NeurIPS, pp. 8527–8537, 2018.
+
+KJ Joseph, Krishnakant Singh, Vineeth N Balasubramanian, et al. Submodular batch selection for training deep neural networks. In IJCAI, pp. 2677–3683, 2019.
+
+Angelos Katharopoulos and François Fleuret. Not all samples are created equal: Deep learning with importance sampling. In ICML, pp. 2525–2534, 2018.
+
+Y. Kawano and K. Yanai. Food image recognition with deep convolutional features. In UbiComp, 2014.
+
+Alex Krizhevsky, Ilya Sutskever, and Geoffrey E Hinton. ImageNet classification with deep convolutional neural networks. In NeurIPS, pp. 1097–1105, 2012.
+
+Alex Krizhevsky, Vinod Nair, and Geoffrey Hinton. CIFAR-10 and CIFAR-100 datasets, 2014. https://www.cs.toronto.edu/\~kriz/cifar.html.
+
+M Pawan Kumar, Benjamin Packer, and Daphne Koller. Self-paced learning for latent variable models. In NeurIPS, pp. 1189–1197, 2010.
+
+Yann LeCun. The MNIST database of handwritten digits, 1998. http://yann.lecun.com/ exdb/mnist.
+
+Ilya Loshchilov and Frank Hutter. Online batch selection for faster training of neural networks. In ICLR, 2016.
+
+Ariadna Quattoni and Antonio Torralba. Recognizing indoor scenes. In CVPR, pp. 413–420, 2009.
+
+Mrinmaya Sachan and Eric Xing. Easy questions first? A case study on curriculum learning for question answering. In ACL, pp. 453–463, 2016.
+
+Abhinav Shrivastava, Abhinav Gupta, and Ross Girshick. Training region-based object detectors with online hard example mining. In CVPR, pp. 761–769, 2016.
+
+Hwanjun Song, Minseok Kim, and Jae-Gil Lee. SELFIE: Refurbishing unclean samples for robust deep learning. In ICML, pp. 5907–5915, 2019.
+
+Luis Torgo. Data mining with R: learning with case studies. Chapman and Hall/CRC, 2011.
+
+Yulia Tsvetkov, Manaal Faruqui, Wang Ling, Brian MacWhinney, and Chris Dyer. Learning the curriculum with bayesian optimization for task-specific word representation learning. In ACL, pp. 130–139, 2016.
+
+Shengjie Wang, Wenruo Bai, Chandrashekhar Lavania, and Jeff Bilmes. Fixing mini-batch sequences with hierarchical robust partitioning. In AISTATS, pp. 3352–3361, 2019.
+
+Bernard Widrow, Istvan Kollar, and Ming-Chang Liu. Statistical theory of quantization. IEEE Transactions on instrumentation and measurement, 45(2):353–361, 1996.
+
+Tianyi Zhou and Jeff Bilmes. Minimax curriculum learning: Machine teaching with desirable difficulties and scheduled diversity. In ICLR, 2018.
+
+# A HYPERPARAMETER SELECTION
+
+Recency Bias receives the two hyperparameters: $( i )$ the initial selection pressure $s _ { e _ { 0 } }$ that determines the sampling probability gap between the most and the least uncertain samples and $( i i )$ the window size $q$ that determines how many recent label predictions are involved in predicting the uncertainty. To decide the best hyperparameters, we trained ResNet $( \mathrm { L } { = } 5 0 )$ ) on CIFAR-10 and CIFAR-100 with a momentum optimizer. For hyperparameters selection, the two hyperparameters were chosen in a grid $s _ { e _ { 0 } } \in \{ 1 , 1 0 , \mathsf { \bar { 1 0 0 } } , 1 0 0 0 \}$ and $\mathsf { \bar { q } } \in \{ 5 , 1 0 , 1 5 \}$ .
+
+
+Figure 7: Grid search on CIFAR-10 and CIFAR-100 datasets using ResNet.
+
+Figure 7 shows the test errors of Recency Bias obtained by the grid search on the two datasets. Regarding the initial selection pressure $s _ { e _ { 0 } }$ , the lowest test error was typically achieved when the $s _ { e _ { 0 } }$ value was 100. As for the window size $q$ , the test error was almost always the lowest when the $q$ value was 10. Similar trends were observed for the other combinations of a neural network and an optimizer. Therefore, in all experiments, we set $s _ { e _ { 0 } }$ to be 100 and $q$ to be 10.
+
+# B EXPERIMENT USING TINY-IMAGENET DATASET
+
+For a larger-scale experiment, we repeated the image classification task on Tiny-ImageNet (200 classes), a subset of ImageNet (Krizhevsky et al., 2012), with 100, 000 training and $1 0 , 0 0 0$ validation images. Because no test set exists, we used the validation set as the test data. For Tiny-ImageNet dataset, we trained the network for 80, 000 iterations and used an initial learning rate of 0.1, which was divided by 10 at $5 0 \%$ and $7 5 \%$ of the total number of training iterations. The remaining experimental configurations were the same as those in Section 5.2.
+
+
+1 20 40 60 80 10Figure 8: Convergence curves of four batch selection strategies using DenseNet with momentum.
+
+Table 4: The best test errors $( \% )$ of four batch selection strategies using DenseNet.
+
+| Method | MIT-67 | FOOD-100 |
| RandomBatch | (5,218-3,936)/5,218 × 100= 24.6% | (7,263-5,365)/7,263 × 100= 26.1% |
| OnlineBatch | (6,079- 3,823)/6,079 × 100 = 37.1% | (8,333-3,685)/8,333 × 100= 55.8% |
| Active Bias | (5,738-3,032)/5,738×100=47.2% | (7,933-3,227)/7,933× 100= 59.3% |
",
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+ "text": "5.4 ABLATION STUDY ON SELECTION PRESSURE ",
+ "text_level": 1,
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+ "page_idx": 7
+ },
+ {
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+ "text": "For an ablation study on the selection pressure, we trained DenseNet $( \\mathrm { L } { = } 4 0 , \\mathrm { k } { = } 1 2 )$ on two benchmark datasets using Recency Bias with four different decaying strategies: $s _ { e } : 1 0 \\to 1 0$ , $s _ { e } : 1 0 0 \\to 1 0 0$ , $s _ { e } : 1 0 \\to 1$ , and $s _ { e } : 1 0 0 \\to 1$ . The first two strategies used different initial selection pressures without decaying, but the remaining strategies exponentially decayed their initial selection pressures to 1. We used a momentum optimizer and the other experimental configurations were the same as those in Section 5.2. ",
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+ "text": "Figure 6 shows the convergence curves of Recency Bias using the different decaying strategies along with that of Random Batch. Generally, the two strategies without decaying (i.e., $s _ { e } : 1 0 \\to 1 0$ , $s _ { e } : 1 0 0 \\to 1 0 0 )$ showed much faster convergence speed in training loss compared with those with decaying (i.e., $s _ { e } : 1 0 \\to 1$ , $s _ { e } : 1 0 0 \\to 1 $ ). However, as mentioned earlier in Section 3.2, the two strategies without decaying exacerbated the overfitting problem because they only used the training samples classified as highly uncertain. Accordingly, their test errors were rather higher than that of Random Batch in CIFAR-100 dataset. On the other hand, the two strategies with decaying converged faster than Random Batch in both training loss and test error in all datasets because they exploited more diverse training samples by exponentially decaying the selection pressure. Thus, these observations empirically prove that decaying the selection pressure is an effective way to alleviate the overfitting problem at the later stage of training. ",
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+ "0 80 10Figure 6: Ablation study on the effect of the selection pressure. "
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+ "text": "In this paper, we presented a novel adaptive batch selection algorithm called Recency Bias that emphasizes predictively uncertain samples for accelerating the training of neural networks. Toward this goal, the predictive uncertainty of each sample is evaluated using its recent label predictions managed by a sliding window of a fixed size. Then, uncertain samples at the moment are selected with high probability for the next mini-batch. We conducted extensive experiments on both classification and fine-tuning tasks. The results showed that Recency Bias is effective in reducing the training time as well as the best test error. It was worthwhile to note that using all historical observations to estimate the uncertainty has the side effect of slowing down the training process. Overall, a merger of uncertain samples and sliding windows greatly improves the power of adaptive batch selection. ",
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+ {
+ "type": "text",
+ "text": "REFERENCES ",
+ "text_level": 1,
+ "bbox": [
+ 174,
+ 744,
+ 285,
+ 760
+ ],
+ "page_idx": 8
+ },
+ {
+ "type": "text",
+ "text": "Yoshua Bengio, Jérôme Louradour, Ronan Collobert, and Jason Weston. Curriculum learning. In ICML, pp. 41–48, 2009. ",
+ "bbox": [
+ 176,
+ 767,
+ 825,
+ 795
+ ],
+ "page_idx": 8
+ },
+ {
+ "type": "text",
+ "text": "David Chandler. Introduction to modern statistical mechanics. Oxford University Press, 1987. ",
+ "bbox": [
+ 173,
+ 805,
+ 794,
+ 820
+ ],
+ "page_idx": 8
+ },
+ {
+ "type": "text",
+ "text": "Haw-Shiuan Chang, Erik Learned-Miller, and Andrew McCallum. Active Bias: Training more accurate neural networks by emphasizing high variance samples. In NeurIPS, pp. 1002–1012, 2017. ",
+ "bbox": [
+ 174,
+ 829,
+ 823,
+ 871
+ ],
+ "page_idx": 8
+ },
+ {
+ "type": "text",
+ "text": "Brian Chen and Gregory W Wornell. Quantization index modulation: A class of provably good methods for digital watermarking and information embedding. IEEE Trans. on Information Theory, 47(4):1423–1443, 2001. ",
+ "bbox": [
+ 176,
+ 882,
+ 825,
+ 922
+ ],
+ "page_idx": 8
+ },
+ {
+ "type": "text",
+ "text": "Jia Deng, Wei Dong, Richard Socher, Li-Jia Li, Kai Li, and Li Fei-Fei. Imagenet: A large-scale hierarchical image database. In CVPR, pp. 248–255, 2009. ",
+ "bbox": [
+ 171,
+ 103,
+ 823,
+ 133
+ ],
+ "page_idx": 9
+ },
+ {
+ "type": "text",
+ "text": "Yang Fan, Fei Tian, Tao Qin, and Tie-Yan Liu. Neural data filter for bootstrapping stochastic gradient descent. In ICLR, 2017. ",
+ "bbox": [
+ 173,
+ 140,
+ 823,
+ 170
+ ],
+ "page_idx": 9
+ },
+ {
+ "type": "text",
+ "text": "Bo Han, Quanming Yao, Xingrui Yu, Gang Niu, Miao Xu, Weihua Hu, Ivor Tsang, and Masashi Sugiyama. Co-teaching: Robust training of deep neural networks with extremely noisy labels. In NeurIPS, pp. 8527–8537, 2018. ",
+ "bbox": [
+ 178,
+ 178,
+ 823,
+ 222
+ ],
+ "page_idx": 9
+ },
+ {
+ "type": "text",
+ "text": "KJ Joseph, Krishnakant Singh, Vineeth N Balasubramanian, et al. Submodular batch selection for training deep neural networks. In IJCAI, pp. 2677–3683, 2019. ",
+ "bbox": [
+ 173,
+ 231,
+ 825,
+ 260
+ ],
+ "page_idx": 9
+ },
+ {
+ "type": "text",
+ "text": "Angelos Katharopoulos and François Fleuret. Not all samples are created equal: Deep learning with importance sampling. In ICML, pp. 2525–2534, 2018. ",
+ "bbox": [
+ 171,
+ 267,
+ 823,
+ 297
+ ],
+ "page_idx": 9
+ },
+ {
+ "type": "text",
+ "text": "Y. Kawano and K. Yanai. Food image recognition with deep convolutional features. In UbiComp, 2014. ",
+ "bbox": [
+ 173,
+ 305,
+ 825,
+ 335
+ ],
+ "page_idx": 9
+ },
+ {
+ "type": "text",
+ "text": "Alex Krizhevsky, Ilya Sutskever, and Geoffrey E Hinton. ImageNet classification with deep convolutional neural networks. In NeurIPS, pp. 1097–1105, 2012. ",
+ "bbox": [
+ 173,
+ 343,
+ 823,
+ 373
+ ],
+ "page_idx": 9
+ },
+ {
+ "type": "text",
+ "text": "Alex Krizhevsky, Vinod Nair, and Geoffrey Hinton. CIFAR-10 and CIFAR-100 datasets, 2014. https://www.cs.toronto.edu/\\~kriz/cifar.html. ",
+ "bbox": [
+ 174,
+ 381,
+ 823,
+ 411
+ ],
+ "page_idx": 9
+ },
+ {
+ "type": "text",
+ "text": "M Pawan Kumar, Benjamin Packer, and Daphne Koller. Self-paced learning for latent variable models. In NeurIPS, pp. 1189–1197, 2010. ",
+ "bbox": [
+ 174,
+ 419,
+ 821,
+ 449
+ ],
+ "page_idx": 9
+ },
+ {
+ "type": "text",
+ "text": "Yann LeCun. The MNIST database of handwritten digits, 1998. http://yann.lecun.com/ exdb/mnist. ",
+ "bbox": [
+ 174,
+ 457,
+ 821,
+ 486
+ ],
+ "page_idx": 9
+ },
+ {
+ "type": "text",
+ "text": "Ilya Loshchilov and Frank Hutter. Online batch selection for faster training of neural networks. In ICLR, 2016. ",
+ "bbox": [
+ 174,
+ 494,
+ 820,
+ 523
+ ],
+ "page_idx": 9
+ },
+ {
+ "type": "text",
+ "text": "Ariadna Quattoni and Antonio Torralba. Recognizing indoor scenes. In CVPR, pp. 413–420, 2009. ",
+ "bbox": [
+ 171,
+ 531,
+ 820,
+ 549
+ ],
+ "page_idx": 9
+ },
+ {
+ "type": "text",
+ "text": "Mrinmaya Sachan and Eric Xing. Easy questions first? A case study on curriculum learning for question answering. In ACL, pp. 453–463, 2016. ",
+ "bbox": [
+ 174,
+ 556,
+ 820,
+ 585
+ ],
+ "page_idx": 9
+ },
+ {
+ "type": "text",
+ "text": "Abhinav Shrivastava, Abhinav Gupta, and Ross Girshick. Training region-based object detectors with online hard example mining. In CVPR, pp. 761–769, 2016. ",
+ "bbox": [
+ 173,
+ 593,
+ 821,
+ 623
+ ],
+ "page_idx": 9
+ },
+ {
+ "type": "text",
+ "text": "Hwanjun Song, Minseok Kim, and Jae-Gil Lee. SELFIE: Refurbishing unclean samples for robust deep learning. In ICML, pp. 5907–5915, 2019. ",
+ "bbox": [
+ 174,
+ 631,
+ 823,
+ 661
+ ],
+ "page_idx": 9
+ },
+ {
+ "type": "text",
+ "text": "Luis Torgo. Data mining with R: learning with case studies. Chapman and Hall/CRC, 2011. ",
+ "bbox": [
+ 169,
+ 669,
+ 779,
+ 685
+ ],
+ "page_idx": 9
+ },
+ {
+ "type": "text",
+ "text": "Yulia Tsvetkov, Manaal Faruqui, Wang Ling, Brian MacWhinney, and Chris Dyer. Learning the curriculum with bayesian optimization for task-specific word representation learning. In ACL, pp. 130–139, 2016. ",
+ "bbox": [
+ 176,
+ 693,
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+ 736
+ ],
+ "page_idx": 9
+ },
+ {
+ "type": "text",
+ "text": "Shengjie Wang, Wenruo Bai, Chandrashekhar Lavania, and Jeff Bilmes. Fixing mini-batch sequences with hierarchical robust partitioning. In AISTATS, pp. 3352–3361, 2019. ",
+ "bbox": [
+ 173,
+ 744,
+ 823,
+ 775
+ ],
+ "page_idx": 9
+ },
+ {
+ "type": "text",
+ "text": "Bernard Widrow, Istvan Kollar, and Ming-Chang Liu. Statistical theory of quantization. IEEE Transactions on instrumentation and measurement, 45(2):353–361, 1996. ",
+ "bbox": [
+ 176,
+ 781,
+ 823,
+ 813
+ ],
+ "page_idx": 9
+ },
+ {
+ "type": "text",
+ "text": "Tianyi Zhou and Jeff Bilmes. Minimax curriculum learning: Machine teaching with desirable difficulties and scheduled diversity. In ICLR, 2018. ",
+ "bbox": [
+ 174,
+ 820,
+ 823,
+ 849
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+ "page_idx": 9
+ },
+ {
+ "type": "text",
+ "text": "A HYPERPARAMETER SELECTION ",
+ "text_level": 1,
+ "bbox": [
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+ "page_idx": 10
+ },
+ {
+ "type": "text",
+ "text": "Recency Bias receives the two hyperparameters: $( i )$ the initial selection pressure $s _ { e _ { 0 } }$ that determines the sampling probability gap between the most and the least uncertain samples and $( i i )$ the window size $q$ that determines how many recent label predictions are involved in predicting the uncertainty. To decide the best hyperparameters, we trained ResNet $( \\mathrm { L } { = } 5 0 )$ ) on CIFAR-10 and CIFAR-100 with a momentum optimizer. For hyperparameters selection, the two hyperparameters were chosen in a grid $s _ { e _ { 0 } } \\in \\{ 1 , 1 0 , \\mathsf { \\bar { 1 0 0 } } , 1 0 0 0 \\}$ and $\\mathsf { \\bar { q } } \\in \\{ 5 , 1 0 , 1 5 \\}$ . ",
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+ "image_caption": [
+ "Figure 7: Grid search on CIFAR-10 and CIFAR-100 datasets using ResNet. "
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+ "image_footnote": [],
+ "bbox": [
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+ {
+ "type": "text",
+ "text": "Figure 7 shows the test errors of Recency Bias obtained by the grid search on the two datasets. Regarding the initial selection pressure $s _ { e _ { 0 } }$ , the lowest test error was typically achieved when the $s _ { e _ { 0 } }$ value was 100. As for the window size $q$ , the test error was almost always the lowest when the $q$ value was 10. Similar trends were observed for the other combinations of a neural network and an optimizer. Therefore, in all experiments, we set $s _ { e _ { 0 } }$ to be 100 and $q$ to be 10. ",
+ "bbox": [
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+ "page_idx": 10
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+ {
+ "type": "text",
+ "text": "B EXPERIMENT USING TINY-IMAGENET DATASET ",
+ "text_level": 1,
+ "bbox": [
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+ "page_idx": 10
+ },
+ {
+ "type": "text",
+ "text": "For a larger-scale experiment, we repeated the image classification task on Tiny-ImageNet (200 classes), a subset of ImageNet (Krizhevsky et al., 2012), with 100, 000 training and $1 0 , 0 0 0$ validation images. Because no test set exists, we used the validation set as the test data. For Tiny-ImageNet dataset, we trained the network for 80, 000 iterations and used an initial learning rate of 0.1, which was divided by 10 at $5 0 \\%$ and $7 5 \\%$ of the total number of training iterations. The remaining experimental configurations were the same as those in Section 5.2. ",
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+ "img_path": "images/a0eb70a7d351e780640a2e722bd4687c2db5edac63d5d35b4a532322ce1bc99e.jpg",
+ "image_caption": [
+ "1 20 40 60 80 10Figure 8: Convergence curves of four batch selection strategies using DenseNet with momentum. "
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| RandomBatch | (5,218-3,936)/5,218 × 100= 24.6% | (7,263-5,365)/7,263 × 100= 26.1% |
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| 3: | for ith time-step of the agent do > Sampling Data |
| 4: 5: | Initialize parameter-sequence noise distribution. μ = μo,∑ = o² I for jth CEM Update do CEM Planning |
| 6: | Sample parameter noise sequences {ωi} from N(μ,Σ). |
| 7: | for Every candidate ωi do |
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| 8: | fort=itoi+T,St+1 = f(St+1lSt,at = Tθ+ωt(St)) |
| 9: | Evaluate expected reward of this candidate. |
| 10: | end for |
| 11: | Fit distribution of the elite candidates as μ',∑'. |
| 12: | Update noise distribution μ= (1-α)μ + αμ',∑= (1-α)Σ+αΣ' |
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| 14: | Execute the first action from the optimal candidate action sequence. |
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| 18: end while | Update 0 using data-set D |
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| 3: | for ith time-step of the agent do > Sampling Data |
| 4: 5: | Initialize parameter-sequence noise distribution. μ = μo,∑ = o² I for jth CEM Update do CEM Planning |
| 6: | Sample parameter noise sequences {ωi} from N(μ,Σ). |
| 7: | for Every candidate ωi do |
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| 8: | fort=itoi+T,St+1 = f(St+1lSt,at = Tθ+ωt(St)) |
| 9: | Evaluate expected reward of this candidate. |
| 10: | end for |
| 11: | Fit distribution of the elite candidates as μ',∑'. |
| 12: | Update noise distribution μ= (1-α)μ + αμ',∑= (1-α)Σ+αΣ' |
| 13: | end for |
| 14: | Execute the first action from the optimal candidate action sequence. |
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| 3: | for ith time-step of the agent do > Sampling Data |
| 4: 5: | Initialize parameter-sequence noise distribution. μ = μo,∑ = o² I for jth CEM Update do CEM Planning |
| 6: | Sample parameter noise sequences {ωi} from N(μ,Σ). |
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| 8: | fort=itoi+T,St+1 = f(St+1lSt,at = Tθ+ωt(St)) |
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| 15: | end for |
| 16: | Update using data-set D |
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| 18: end while | Update 0 using data-set D |
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+ "html": "| 1: Initialize policy network parameters 0, dynamics network parameters Φ, data-set D 2: while Training iterations not Finished do |
| 3: | for ith time-step of the agent do > Sampling Data |
| 4: 5: | Initialize parameter-sequence noise distribution. μ = μo,∑ = o² I for jth CEM Update do CEM Planning |
| 6: | Sample parameter noise sequences {ωi} from N(μ,Σ). |
| 7: | for Every candidate ωi do |
| Trajectory Predicting |
| 8: | fort=itoi+T,St+1 = f(St+1lSt,at = Tθ+ωt(St)) |
| 9: | Evaluate expected reward of this candidate. |
| 10: | end for |
| 11: | Fit distribution of the elite candidates as μ',∑'. |
| 12: | Update noise distribution μ= (1-α)μ + αμ',∑= (1-α)Σ+αΣ' |
| 13: | end for |
| 14: | Execute the first action from the optimal candidate action sequence. |
| 15: | end for |
| 16: | Update using data-set D |
| 17: | |
| 18: end while | Update 0 using data-set D |
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