logbook.json

{
  "schema_version": "1.0",
  "title": "Reproduction: Certificate-Guided Pruning for Stochastic Lipschitz Optimization",
  "emoji": "📏",
  "space_id": "snaykey/repro-graph-alignment",
  "paper": {
    "arxiv_id": "2601.20231",
    "openreview_id": "9CqZoRWpoc"
  },
  "tags": [
    "icml2026-repro",
    "paper-9CqZoRWpoc"
  ],
  "updated_at": "2026-07-29T00:00:00+00:00",
  "root": {
    "slug": "index",
    "title": "Reproduction: Certificate-Guided Pruning for Stochastic Lipschitz Optimization",
    "children": [
      {
        "slug": "executive-summary",
        "title": "Executive summary",
        "children": []
      },
      {
        "slug": "claim-1-certificates",
        "title": "Certificate-Guided Pruning (CGP) maintains an explicit active set A_t of candidate optima using confidence-adjusted Lipschitz envelopes, certifying with high probability that any point outside A_t is suboptimal (Section 3, Algorithm 1).",
        "children": []
      },
      {
        "slug": "claim-2-shrinkage",
        "title": "Under a margin condition with near-optimality dimension α (Assumption 2.3), the Shrinkage Theorem bounds the active set volume as Vol(A_t) ≤ C·(2(β_t + Lη_t) + γ_t)^(d−α) (Theorem 4.6).",
        "children": []
      },
      {
        "slug": "claim-3-sample-complexity",
        "title": "CGP achieves ε-optimality with probability at least 1−δ using T = Õ(L^d ε^{-(2+α)} log(1/δ)) samples, improving on the worst-case Õ(ε^{-(2+d)}) rate whenever α < d (Theorem 4.8).",
        "children": []
      },
      {
        "slug": "claim-4-lower-bound",
        "title": "A matching lower bound shows any algorithm requires Ω(ε^{-(2+α)}) samples under the same margin condition, establishing CGP's minimax sample-complexity optimality (Theorem 4.9).",
        "children": []
      },
      {
        "slug": "claim-5-adaptive-l",
        "title": "CGP-Adaptive learns the Lipschitz constant L online via a doubling scheme, adding only an O(log T) multiplicative overhead to the sample complexity (Theorem 5.1, Section 5).",
        "children": []
      },
      {
        "slug": "claim-6-cgp-tr",
        "title": "CGP-TR, a trust-region variant, scales to dimension d > 50 via certified restarts that provably never falsely eliminate the region containing the true optimizer x* (Theorem 6.1, Section 6).",
        "children": []
      },
      {
        "slug": "conclusion",
        "title": "Conclusion",
        "children": []
      }
    ]
  },
  "revision": 1
}