logbook.json

{
  "schema_version": 1,
  "title": "Reproduction: Improved Dimension Dependence for Bandit Convex Optimization with Gradient Variations",
  "emoji": "🎯",
  "space_id": "ProCreations/repro-gradient-variation-bandit-convex-optimization",
  "paper": {"arxiv_id": "2602.04761"},
  "tags": ["icml2026-repro", "paper-X8evkEdMxb"],
  "updated_at": "2026-07-21T09:36:00+00:00",
  "root": {
    "slug": "index",
    "title": "Reproduction: Improved Dimension Dependence for Bandit Convex Optimization with Gradient Variations",
    "file": "pages/index.md",
    "children": [
      {"slug":"executive-summary","title":"Executive summary","file":"pages/executive-summary/page.md","children":[]},
      {"slug":"claim-1","title":"Claim 1: Theorem 1 establishes an Õ(d^{3/2}√V_T) regret bound for one-point bandit convex optimization with gradient variation V_T, improving the dimension dependence over Chiang et al. (2013)'s O(d^3√V_T) bound (Theorem 1, Section 3.1).","file":"pages/claim-1/page.md","children":[]},
      {"slug":"claim-2","title":"Claim 2: Theorem 2 gives an O((d/λ) log V_T) regret bound for λ-strongly convex functions, improving the prior O((d^2/λ) log V_T) bound by a factor of d (Theorem 2, Section 3.2).","file":"pages/claim-2/page.md","children":[]},
      {"slug":"claim-3","title":"Claim 3: Theorem 3 provides O(√(dW_T) + d) regret for linear functions and O(d√W_T + d) regret for convex functions in terms of the gradient variance W_T (Theorem 3, Section 3.3).","file":"pages/claim-3/page.md","children":[]},
      {"slug":"claim-4","title":"Claim 4: Theorem 4 delivers O(√(dF_T) + d) regret bounds for linear and convex functions using the small-loss quantity F_T (Theorem 4, Section 3.3).","file":"pages/claim-4/page.md","children":[]},
      {"slug":"claim-5","title":"Claim 5: Section 4 presents the first gradient-variation regret bound for one-point bandit linear optimization over hyper-rectangular domains (Section 4).","file":"pages/claim-5/page.md","children":[]},
      {"slug":"claim-6","title":"Claim 6: Table 1 summarizes the dimension-dependence improvements across gradient-variation, gradient-variance, and small-loss metrics for linear, convex, and strongly convex function classes relative to prior best-known results (Table 1).","file":"pages/claim-6/page.md","children":[]},
      {"slug":"conclusion","title":"Conclusion","file":"pages/conclusion/page.md","children":[]}
    ]
  },
  "agent_view_tokens": 5000,
  "revision": "1784626560000000000"
}