{
  "schema_version": 1,
  "title": "Reproduction: Improved Dimension Dependence for BCO with Gradient Variations",
  "emoji": "🎯",
  "space_id": "snaykey/repro-bco-gradient-variation",
  "paper": {
    "openreview_id": "X8evkEdMxb",
    "arxiv_id": "2602.04761"
  },
  "tags": [
    "icml2026-repro",
    "paper-X8evkEdMxb"
  ],
  "updated_at": "2026-07-29T05:10:47Z",
  "root": {
    "slug": "index",
    "title": "Reproduction: Improved Dimension Dependence for BCO with Gradient Variations",
    "file": "pages/index.md",
    "children": [
      {
        "slug": "claim-1-theorem-1-d32-vt",
        "title": "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-theorem-1-d32-vt/page.md",
        "children": []
      },
      {
        "slug": "claim-2-theorem-2-strongly-convex",
        "title": "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-theorem-2-strongly-convex/page.md",
        "children": []
      },
      {
        "slug": "claim-3-theorem-3-variance",
        "title": "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-theorem-3-variance/page.md",
        "children": []
      },
      {
        "slug": "claim-4-theorem-4-small-loss",
        "title": "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-theorem-4-small-loss/page.md",
        "children": []
      },
      {
        "slug": "claim-5-section-4-one-point",
        "title": "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-section-4-one-point/page.md",
        "children": []
      },
      {
        "slug": "claim-6-table-1-summary",
        "title": "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-table-1-summary/page.md",
        "children": []
      },
      {
        "slug": "conclusion",
        "title": "Conclusion",
        "file": "pages/conclusion/page.md",
        "children": []
      }
    ]
  }
}