{"paper":{"title":"On Randomized Fictitious Play for Approximating Saddle Points Over Convex Sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.GT","authors_text":"Fahimeh Ramezani, Kazuhisa Makino, Khaled Elbassioni, Kurt Mehlhorn","submitted_at":"2013-01-22T19:27:17Z","abstract_excerpt":"Given two bounded convex sets $X\\subseteq\\RR^m$ and $Y\\subseteq\\RR^n,$ specified by membership oracles, and a continuous convex-concave function $F:X\\times Y\\to\\RR$, we consider the problem of computing an $\\eps$-approximate saddle point, that is, a pair $(x^*,y^*)\\in X\\times Y$ such that $\\sup_{y\\in Y} F(x^*,y)\\le \\inf_{x\\in\n  X}F(x,y^*)+\\eps.$ Grigoriadis and Khachiyan (1995) gave a simple randomized variant of fictitious play for computing an $\\eps$-approximate saddle point for matrix games, that is, when $F$ is bilinear and the sets $X$ and $Y$ are simplices. In this paper, we extend their"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.5290","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}