{
  "schema_version": 1,
  "title": "Reproduction: The Optimal Sample Complexity of Linear Contracts",
  "emoji": "📜",
  "space_id": "snaykey/repro-linear-contracts",
  "paper": {
    "openreview_id": "ry5HitnXzc"
  },
  "tags": [
    "icml2026-repro",
    "paper-ry5HitnXzc"
  ],
  "updated_at": "2026-07-31T06:44:08+00:00",
  "root": {
    "slug": "index",
    "title": "Reproduction: The Optimal Sample Complexity of Linear Contracts",
    "file": "pages/index.md",
    "children": [
      {
        "slug": "claim-1-thm1-1-uniform-convergence",
        "title": "Theorem 1.1 establishes uniform convergence: for sample size s ≥ 3456 ln(4/δ)/ε², with probability at least 1−δ, the empirical and expected utility of every linear contract differ by at most ε (Theorem 1.1).",
        "file": "pages/claim-1-thm1-1-uniform-convergence/page.md",
        "children": []
      },
      {
        "slug": "claim-2-cor1-2-eum-sample-complexity",
        "title": "Corollary 1.2 shows the Empirical Utility Maximization algorithm achieves an ε-approximation of the optimal linear contract using s ≥ 6912 ln(4/δ)/ε² samples and O(1/ε) oracle queries (Corollary 1.2).",
        "file": "pages/claim-2-cor1-2-eum-sample-complexity/page.md",
        "children": []
      },
      {
        "slug": "claim-3-rate-optimal-independent-of-n-and-m",
        "title": "The O(ln(1/δ)/ε²) sample complexity matches the lower bound of Dütting et al. (2025) up to constant factors, and is independent of the action space size n and the number of outcomes m (Theorem 1.1).",
        "file": "pages/claim-3-rate-optimal-independent-of-n-and-m/page.md",
        "children": []
      },
      {
        "slug": "claim-4-lemma2-1-reward-monotone",
        "title": "Lemma 2.1 shows the expected reward of a linear contract is non-decreasing in the contract parameter α, a structural property exploited to build fine-grained covering arguments where general pseudo-dimension bounds fail (Lemma 2.1).",
        "file": "pages/claim-4-lemma2-1-reward-monotone/page.md",
        "children": []
      },
      {
        "slug": "claim-5-lemma2-2-l2-cover",
        "title": "Lemma 2.2 constructs an L2 cover of the reward function class of size O(1/ν²), obtained by discretizing empirical rewards into ν-intervals, taking pullbacks to parameter space, and combining with grid discretization of the outcome axis (Lemma 2.2).",
        "file": "pages/claim-5-lemma2-2-l2-cover/page.md",
        "children": []
      },
      {
        "slug": "executive-summary",
        "title": "Executive summary",
        "file": "pages/executive-summary/page.md",
        "children": []
      },
      {
        "slug": "conclusion",
        "title": "Conclusion",
        "file": "pages/conclusion/page.md",
        "children": []
      }
    ]
  }
}