{"paper":{"title":"Conditional Gradient Method for Stochastic Submodular Maximization: Closing the Gap","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"math.OC","authors_text":"Amin Karbasi, Aryan Mokhtari, Hamed Hassani","submitted_at":"2017-11-05T20:56:44Z","abstract_excerpt":"In this paper, we study the problem of \\textit{constrained} and \\textit{stochastic} continuous submodular maximization. Even though the objective function is not concave (nor convex) and is defined in terms of an expectation, we develop a variant of the conditional gradient method, called \\alg, which achieves a \\textit{tight} approximation guarantee. More precisely, for a monotone and continuous DR-submodular function and subject to a \\textit{general} convex body constraint, we prove that \\alg achieves a $[(1-1/e)\\text{OPT} -\\eps]$ guarantee (in expectation) with $\\mathcal{O}{(1/\\eps^3)}$ stoc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.01660","kind":"arxiv","version":1},"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"}