| { |
| "schema_version": 1, |
| "title": "Reproduction: Certificate-Guided Pruning for Stochastic Lipschitz Optimization", |
| "emoji": "\ud83c\udfaf", |
| "space_id": "ProCreations/repro-certificate-guided-pruning-for-stochastic-lipschitz-optimization", |
| "paper": { |
| "arxiv_id": "2601.20231" |
| }, |
| "tags": [ |
| "icml2026-repro", |
| "paper-9CqZoRWpoc" |
| ], |
| "claims": [ |
| "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).", |
| "Under a margin condition with near-optimality dimension \u03b1 (Assumption 2.3), the Shrinkage Theorem bounds the active set volume as Vol(A_t) \u2264 C\u00b7(2(\u03b2_t + L\u03b7_t) + \u03b3_t)^(d\u2212\u03b1) (Theorem 4.6).", |
| "CGP achieves \u03b5-optimality with probability at least 1\u2212\u03b4 using T = \u00d5(L^d \u03b5^{-(2+\u03b1)} log(1/\u03b4)) samples, improving on the worst-case \u00d5(\u03b5^{-(2+d)}) rate whenever \u03b1 < d (Theorem 4.8).", |
| "A matching lower bound shows any algorithm requires \u03a9(\u03b5^{-(2+\u03b1)}) samples under the same margin condition, establishing CGP's minimax sample-complexity optimality (Theorem 4.9).", |
| "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).", |
| "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)." |
| ], |
| "updated_at": "2026-07-26T10:08:00+00:00", |
| "root": { |
| "slug": "index", |
| "title": "Reproduction: Certificate-Guided Pruning for Stochastic Lipschitz Optimization", |
| "file": "pages/index.md", |
| "children": [ |
| { |
| "slug": "executive-summary", |
| "title": "Executive summary", |
| "file": "pages/executive-summary/page.md", |
| "children": [] |
| }, |
| { |
| "slug": "claim-0-judge-first-scorecard", |
| "title": "Claim 0: Judge-first scorecard \u2014 six direct verdicts", |
| "file": "pages/claim-0-judge-first-scorecard/page.md", |
| "children": [] |
| }, |
| { |
| "slug": "claim-1-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", |
| "title": "Claim 1: 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).", |
| "file": "pages/claim-1-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/page.md", |
| "children": [] |
| }, |
| { |
| "slug": "claim-2-under-a-margin-condition-with-near-optimality-dimension-assumption-2-3-the-shrinkage-theorem-bounds-the-active-set-volume-as-vol-a-t-c-2-t-l-t-t-d-theorem-4-6", |
| "title": "Claim 2: Under a margin condition with near-optimality dimension \u03b1 (Assumption 2.3), the Shrinkage Theorem bounds the active set volume as Vol(A_t) \u2264 C\u00b7(2(\u03b2_t + L\u03b7_t) + \u03b3_t)^(d\u2212\u03b1) (Theorem 4.6).", |
| "file": "pages/claim-2-under-a-margin-condition-with-near-optimality-dimension-assumption-2-3-the-shrinkage-theorem-bounds-the-active-set-volume-as-vol-a-t-c-2-t-l-t-t-d-theorem-4-6/page.md", |
| "children": [] |
| }, |
| { |
| "slug": "claim-3-cgp-achieves-optimality-with-probability-at-least-1-using-t-l-d-2-log-1-samples-improving-on-the-worst-case-2-d-rate-whenever-d-theorem-4-8", |
| "title": "Claim 3: CGP achieves \u03b5-optimality with probability at least 1\u2212\u03b4 using T = \u00d5(L^d \u03b5^{-(2+\u03b1)} log(1/\u03b4)) samples, improving on the worst-case \u00d5(\u03b5^{-(2+d)}) rate whenever \u03b1 < d (Theorem 4.8).", |
| "file": "pages/claim-3-cgp-achieves-optimality-with-probability-at-least-1-using-t-l-d-2-log-1-samples-improving-on-the-worst-case-2-d-rate-whenever-d-theorem-4-8/page.md", |
| "children": [] |
| }, |
| { |
| "slug": "claim-4-a-matching-lower-bound-shows-any-algorithm-requires-2-samples-under-the-same-margin-condition-establishing-cgp-s-minimax-sample-complexity-optimality-theorem-4-9", |
| "title": "Claim 4: A matching lower bound shows any algorithm requires \u03a9(\u03b5^{-(2+\u03b1)}) samples under the same margin condition, establishing CGP's minimax sample-complexity optimality (Theorem 4.9).", |
| "file": "pages/claim-4-a-matching-lower-bound-shows-any-algorithm-requires-2-samples-under-the-same-margin-condition-establishing-cgp-s-minimax-sample-complexity-optimality-theorem-4-9/page.md", |
| "children": [] |
| }, |
| { |
| "slug": "claim-5-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", |
| "title": "Claim 5: 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).", |
| "file": "pages/claim-5-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/page.md", |
| "children": [] |
| }, |
| { |
| "slug": "claim-6-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", |
| "title": "Claim 6: 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).", |
| "file": "pages/claim-6-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/page.md", |
| "children": [] |
| }, |
| { |
| "slug": "conclusion", |
| "title": "Conclusion", |
| "file": "pages/conclusion/page.md", |
| "children": [] |
| } |
| ] |
| }, |
| "agent_view_tokens": 9000, |
| "revision": "1785060480000000000" |
| } |
|
|
