{"paper":{"title":"Online convex optimization for cumulative constraints","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Andrew Lamperski, Jianjun Yuan","submitted_at":"2018-02-19T00:06:47Z","abstract_excerpt":"We propose the algorithms for online convex optimization which lead to cumulative squared constraint violations of the form $\\sum\\limits_{t=1}^T\\big([g(x_t)]_+\\big)^2=O(T^{1-\\beta})$, where $\\beta\\in(0,1)$. \nPrevious literature has focused on long-term constraints of the form $\\sum\\limits_{t=1}^Tg(x_t)$. There, strictly feasible solutions can cancel out the effects of violated constraints. In contrast, the new form heavily penalizes large constraint violations and cancellation effects cannot occur.\n  Furthermore, useful bounds on the single step constraint violation $[g(x_t)]_+$ are derived.\n "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.06472","kind":"arxiv","version":4},"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"}