{"paper":{"title":"Stochastic subGradient Methods with Linear Convergence for Polyhedral Convex Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.LG","authors_text":"Qihang Lin, Tianbao Yang","submitted_at":"2015-10-06T06:17:56Z","abstract_excerpt":"In this paper, we show that simple {Stochastic} subGradient Decent methods with multiple Restarting, named {\\bf RSGD}, can achieve a \\textit{linear convergence rate} for a class of non-smooth and non-strongly convex optimization problems where the epigraph of the objective function is a polyhedron, to which we refer as {\\bf polyhedral convex optimization}. Its applications in machine learning include $\\ell_1$ constrained or regularized piecewise linear loss minimization and submodular function minimization. To the best of our knowledge, this is the first result on the linear convergence rate o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.01444","kind":"arxiv","version":5},"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"}