{
  "schema_version": 1,
  "title": "Reproduction: Minimizing Upper Confidence Bounds - A Data-Driven Framework for Stochastic Programming",
  "emoji": "📉",
  "space_id": "snaykey/repro-ucb-minimization",
  "paper": {
    "openreview_id": "eXLcL70GXO"
  },
  "tags": [
    "icml2026-repro",
    "paper-eXLcL70GXO"
  ],
  "updated_at": "2026-07-31T00:00:00Z",
  "root": {
    "slug": "index",
    "title": "Reproduction: Minimizing Upper Confidence Bounds - A Data-Driven Framework for Stochastic Programming",
    "file": "pages/index.md",
    "children": [
      {
        "slug": "executive-summary",
        "title": "Executive summary",
        "file": "pages/executive-summary/page.md",
        "children": []
      },
      {
        "slug": "claim-1-definition-apub",
        "title": "The Average Percentile Upper Bound (APUB) is defined as U^apub[μ|P̂_n] := (1/α)∫₀^α U^efron[μ|P̂_n] dτ, integrating Efron's percentile upper bound over confidence level τ from 0 to α (Definition 2.2, Section 2)",
        "file": "pages/claim-1-definition-apub/page.md",
        "children": []
      },
      {
        "slug": "claim-2-theorem-2-7-consistency",
        "title": "Theorem 2.7 proves APUB converges almost surely to the true population mean as sample size n approaches infinity, for every confidence level in (0,1] (Theorem 2.7)",
        "file": "pages/claim-2-theorem-2-7-consistency/page.md",
        "children": []
      },
      {
        "slug": "claim-3-theorem-3-3-asymptotic-correctness",
        "title": "Theorem 3.3 shows the APUB-embedded stochastic optimization model achieves first-order asymptotic correctness, with coverage probability exceeding the nominal confidence level up to an O(N^{-1/2}) term (Theorem 3.3)",
        "file": "pages/claim-3-theorem-3-3-asymptotic-correctness/page.md",
        "children": []
      },
      {
        "slug": "claim-4-theorem-3-5-optimization-consistency",
        "title": "Theorem 3.5 establishes that both the optimal values and optimal solution sets of the APUB-based optimization problem converge almost surely to their true counterparts as sample size increases (Theorem 3.5)",
        "file": "pages/claim-4-theorem-3-5-optimization-consistency/page.md",
        "children": []
      },
      {
        "slug": "claim-5-figure-1-gamma-coverage",
        "title": "On a Gamma(2,1) numerical example with nominal level α=0.05 and sample sizes ranging from 80 to 10,000, APUB's coverage probability approaches the 0.95 nominal level faster than Efron's percentile bound and standard large-sample approximations (Figure 1, Example 2.5)",
        "file": "pages/claim-5-figure-1-gamma-coverage/page.md",
        "children": []
      },
      {
        "slug": "claim-6-section-5-newsvendor-productmix",
        "title": "The framework is validated on two-stage product mix and multi-product newsvendor problems, showing APUB balances robustness and practicality compared to Sample Average Approximation (SAA) and Distributionally Robust Optimization (DRO) (Section 5)",
        "file": "pages/claim-6-section-5-newsvendor-productmix/page.md",
        "children": []
      },
      {
        "slug": "conclusion",
        "title": "Conclusion",
        "file": "pages/conclusion/page.md",
        "children": []
      }
    ]
  }
}