| { | |
| "schema_version": 2, | |
| "title": "Reproduction: Provably Data-driven Lagrangian Relaxation for Mixed Integer Linear Programming", | |
| "emoji": "🎯", | |
| "space_id": "amkkk/repro-provably-data-driven-lagrangian-relaxation-for-mixed-integer-linear-programming", | |
| "paper": { | |
| "arxiv_id": "2605.19052" | |
| }, | |
| "tags": [ | |
| "icml2026-repro", | |
| "paper-OwLuqetJuB" | |
| ], | |
| "updated_at": "2026-07-23T01:10:12+00:00", | |
| "root": { | |
| "slug": "index", | |
| "title": "Reproduction: Provably Data-driven Lagrangian Relaxation for Mixed Integer Linear Programming", | |
| "file": "pages/index.md", | |
| "children": [ | |
| { | |
| "slug": "executive-summary", | |
| "title": "Executive summary", | |
| "file": "pages/executive-summary/page.md", | |
| "children": [] | |
| }, | |
| { | |
| "slug": "claim-1-for-learned-lagrangian-relaxation-multipliers-over-s-coupling-constraints-and-n-training-samples-the-expected-excess-risk-of-the-erm-solution-is-upper-bounded-by-o-s-1-5-n-theorem-5-5", | |
| "title": "Claim 1: For learned Lagrangian Relaxation multipliers over s coupling constraints and N training samples, the expected excess risk of the ERM solution is upper bounded by O(s^1.5/√N) (Theorem 5.5).", | |
| "file": "pages/claim-1-for-learned-lagrangian-relaxation-multipliers-over-s-coupling-constraints-and-n-training-samples-the-expected-excess-risk-of-the-erm-solution-is-upper-bounded-by-o-s-1-5-n-theorem-5-5/page.md", | |
| "children": [] | |
| }, | |
| { | |
| "slug": "claim-2-a-minimax-lower-bound-of-s-n-is-proven-showing-linear-dependence-on-the-number-of-coupled-constraints-s-is-unavoidable-for-any-learning-algorithm-theorem-5-6", | |
| "title": "Claim 2: A minimax lower bound of Ω(s/√N) is proven, showing linear dependence on the number of coupled constraints s is unavoidable for any learning algorithm (Theorem 5.6).", | |
| "file": "pages/claim-2-a-minimax-lower-bound-of-s-n-is-proven-showing-linear-dependence-on-the-number-of-coupled-constraints-s-is-unavoidable-for-any-learning-algorithm-theorem-5-6/page.md", | |
| "children": [] | |
| }, | |
| { | |
| "slug": "claim-3-stochastic-gradient-ascent-with-iterate-averaging-is-shown-to-achieve-the-matching-o-s-n-rate-closing-the-o-s-gap-between-the-erm-upper-bound-and-the-minimax-lower-bound-and-establishing-minimax-optimality-theorem-5-12", | |
| "title": "Claim 3: Stochastic Gradient Ascent with iterate averaging is shown to achieve the matching O(s/√N) rate, closing the O(√s) gap between the ERM upper bound and the minimax lower bound and establishing minimax optimality (Theorem 5.12).", | |
| "file": "pages/claim-3-stochastic-gradient-ascent-with-iterate-averaging-is-shown-to-achieve-the-matching-o-s-n-rate-closing-the-o-s-gap-between-the-erm-upper-bound-and-the-minimax-lower-bound-and-establishing-minimax-optimality-theorem-5-12/page.md", | |
| "children": [] | |
| }, | |
| { | |
| "slug": "claim-4-the-framework-is-extended-to-learning-to-warm-start-sub-gradient-ascent-for-large-scale-mixed-integer-linear-programming-with-an-o-s-n-risk-upper-bound-theorem-6-1-and-matching-s-n-minimax-lower-bound-theorem-6-2", | |
| "title": "Claim 4: The framework is extended to learning-to-warm-start sub-gradient ascent for large-scale Mixed Integer Linear Programming, with an O(s/N) risk upper bound (Theorem 6.1) and matching Ω(s/N) minimax lower bound (Theorem 6.2).", | |
| "file": "pages/claim-4-the-framework-is-extended-to-learning-to-warm-start-sub-gradient-ascent-for-large-scale-mixed-integer-linear-programming-with-an-o-s-n-risk-upper-bound-theorem-6-1-and-matching-s-n-minimax-lower-bound-theorem-6-2/page.md", | |
| "children": [] | |
| }, | |
| { | |
| "slug": "claim-5-the-covering-number-of-the-dual-multiplier-class-u-is-bounded-as-log-n-u-n-s-log-1-2b-max-s-used-to-derive-the-rademacher-complexity-bound-r-n-u-o-s-1-5-n-lemma-5-3-lemma-5-4", | |
| "title": "Claim 5: The covering number of the dual multiplier class U is bounded as log N(δ,U,‖·‖₂,N) ≤ s·log(1+2Bπ_max s/δ), used to derive the Rademacher complexity bound R_N(U)=O(s^1.5/√N) (Lemma 5.3, Lemma 5.4).", | |
| "file": "pages/claim-5-the-covering-number-of-the-dual-multiplier-class-u-is-bounded-as-log-n-u-n-s-log-1-2b-max-s-used-to-derive-the-rademacher-complexity-bound-r-n-u-o-s-1-5-n-lemma-5-3-lemma-5-4/page.md", | |
| "children": [] | |
| }, | |
| { | |
| "slug": "claim-6-the-dual-function-u-p-is-shown-to-be-concave-in-with-subgradient-norm-bounded-by-2b-s-under-bounded-constraint-violation-assumptions-on-the-milp-instance-proposition-5-1-section-4", | |
| "title": "Claim 6: The dual function u(π,P) is shown to be concave in π with subgradient norm bounded by 2B√s under bounded constraint-violation assumptions on the MILP instance (Proposition 5.1, Section 4).", | |
| "file": "pages/claim-6-the-dual-function-u-p-is-shown-to-be-concave-in-with-subgradient-norm-bounded-by-2b-s-under-bounded-constraint-violation-assumptions-on-the-milp-instance-proposition-5-1-section-4/page.md", | |
| "children": [] | |
| }, | |
| { | |
| "slug": "conclusion", | |
| "title": "Conclusion", | |
| "file": "pages/conclusion/page.md", | |
| "children": [] | |
| } | |
| ] | |
| }, | |
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