{"paper":{"title":"Online Continuous DR-Submodular Maximization with Long-Term Budget Constraints","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.ML"],"primary_cat":"math.OC","authors_text":"Maryam Fazel, Omid Sadeghi","submitted_at":"2019-06-30T04:01:32Z","abstract_excerpt":"In this paper, we study a class of online optimization problems with long-term budget constraints where the objective functions are not necessarily concave (nor convex) but they instead satisfy the Diminishing Returns (DR) property. Specifically, a sequence of monotone DR-submodular objective functions $\\{f_t(x)\\}_{t=1}^T$ and monotone linear budget functions $\\{\\langle p_t,x \\rangle \\}_{t=1}^T$ arrive over time and assuming a total targeted budget $B_T$, the goal is to choose points $x_t$ at each time $t\\in\\{1,\\dots,T\\}$, without knowing $f_t$ and $p_t$ on that step, to achieve sub-linear reg"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.00316","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"}