{"paper":{"title":"Beyond Minimax Rates in Group Distributionally Robust Optimization via a Novel Notion of Sparsity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI","math.OC"],"primary_cat":"cs.LG","authors_text":"Crist\\'obal Guzm\\'an, Nishant A. Mehta, Quan Nguyen","submitted_at":"2024-10-01T13:45:55Z","abstract_excerpt":"The minimax sample complexity of group distributionally robust optimization (GDRO) has been determined up to a $\\log(K)$ factor, where $K$ is the number of groups. In this work, we venture beyond the minimax perspective via a novel notion of sparsity that we dub $(\\lambda, \\beta)$-sparsity. In short, this condition means that at any parameter $\\theta$, there is a set of at most $\\beta$ groups whose risks at $\\theta$ all are at least $\\lambda$ larger than the risks of the other groups. To find an $\\epsilon$-optimal $\\theta$, we show via a novel algorithm and analysis that the $\\epsilon$-depende"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.00690","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/2410.00690/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"}