{"paper":{"title":"Second-Order Min-Max Optimization with Lazy Hessians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.CR","cs.LG"],"primary_cat":"math.OC","authors_text":"Chengchang Liu, Jingzhao Zhang, Lesi Chen","submitted_at":"2024-10-12T15:30:17Z","abstract_excerpt":"This paper studies second-order methods for convex-concave minimax optimization. Monteiro and Svaiter (2012) proposed a method to solve the problem with an optimal iteration complexity of $\\mathcal{O}(\\epsilon^{-3/2})$ to find an $\\epsilon$-saddle point. However, it is unclear whether the computational complexity, $\\mathcal{O}((N+ d^2) d \\epsilon^{-2/3})$, can be improved. In the above, we follow Doikov et al. (2023) and assume the complexity of obtaining a first-order oracle as $N$ and the complexity of obtaining a second-order oracle as $dN$. In this paper, we show that the computation cost "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.09568","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2410.09568/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}