{"paper":{"title":"Stochastic Multi-armed Bandits in Constant Space","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG","stat.ML"],"primary_cat":"cs.DS","authors_text":"David Liau, Eric Price, Ger Yang, Zhao Song","submitted_at":"2017-12-25T05:04:35Z","abstract_excerpt":"We consider the stochastic bandit problem in the sublinear space setting, where one cannot record the win-loss record for all $K$ arms. We give an algorithm using $O(1)$ words of space with regret \\[\n  \\sum_{i=1}^{K}\\frac{1}{\\Delta_i}\\log \\frac{\\Delta_i}{\\Delta}\\log T \\] where $\\Delta_i$ is the gap between the best arm and arm $i$ and $\\Delta$ is the gap between the best and the second-best arms. If the rewards are bounded away from $0$ and $1$, this is within an $O(\\log 1/\\Delta)$ factor of the optimum regret possible without space constraints."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.09007","kind":"arxiv","version":2},"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"}