Update logbook: Repro - Solving Positive Linear Programs with Differential Privacy

logbook.json

@@ -10,7 +10,7 @@
     "icml2026-repro",
     "paper-zlSioMUQ2Y"
   ],
-  "updated_at": "2026-07-17T10:30:33+00:00",
+  "updated_at": "2026-07-17T10:33:43+00:00",
   "root": {
     "slug": "index",
     "title": "Repro - Solving Positive Linear Programs with Differential Privacy",
@@ -66,6 +66,6 @@
       }
     ]
   },
-  "agent_view_tokens": 18629,
-  "revision": "1784284233550636000"
+  "agent_view_tokens": 19027,
+  "revision": "1784284423334061000"
 }

pages/claim-5-mwu-variants-for-mixed-packing-covering-algorithms-3-4/page.md

@@ -147,3 +147,24 @@ Both algorithms of Section 5 exist, are implementable from the pseudocode, have
 **🎯 Trackio dashboard** `private-positive-lp-repro`
 
 trackio-local-dashboard://private-positive-lp-repro
+
+
+---
+<!-- trackio-cell
+{"type": "markdown", "id": "cell_d74e1939dd55", "created_at": "2026-07-17T10:33:40+00:00", "title": "Algorithm 3: alpha = 0.5 completes the sweep"}
+-->
+## Algorithm 3 — final row (alpha = 0.5), completing the sweep
+
+The `alpha = 0.5` configuration finished: **T = 140,623 iterations at full length, uncapped** (~23 min on the L4). It is the hardest of the three — the smallest approximation factor, hence the largest `T` and the loosest `s`.
+
+| alpha | T (full) | s | **s/n** | scale-EM error | Lemma 21 smax/smin | **violations @ private** | time |
+|---|---|---|---|---|---|---|---|
+| 0.8 | 34,331 | 3.31e5 | 0.083 ✓ | 0.41% of n ✓ | 0.4142 ≤ 1.8 ✓ | **0 / 4,000,000** | 261s |
+| 0.7 | 51,247 | 6.20e5 | 0.155 ✓ | 0.51% of n ✓ | 0.4081 ≤ 1.7 ✓ | **0 / 4,000,000** | 409s |
+| **0.5** | **140,623** | 3.01e6 | **0.752** ✓ | **0.88%** of n ✓ | **0.5368 ≤ 1.5** ✓ | **0 / 4,000,000** | 1371s |
+
+`[PASS] Theorem 11.1 guarantee in all 3 configurations`
+
+At `alpha = 0.5` the theorem permits **3,007,000** of the 4,000,000 constraints to be violated and the algorithm violates **zero**. Lemma 21's ratio bound tightens as `alpha` shrinks (1.8 → 1.7 → 1.5) and the measured ratio tracks it with room to spare (0.41 → 0.41 → 0.54).
+
+Raw results: [txus/private-positive-lp-repro](https://huggingface.co/datasets/txus/private-positive-lp-repro) (`gpu_mixed_n4000000.json`).