{"paper":{"title":"Understanding Memory-Regret Trade-Off for Streaming Stochastic Multi-Armed Bandits","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DS","stat.ML"],"primary_cat":"cs.LG","authors_text":"Chihao Zhang, Yuchen He, Zichun Ye","submitted_at":"2024-05-30T06:56:48Z","abstract_excerpt":"We study the stochastic multi-armed bandit problem in the $P$-pass streaming model. In this problem, the $n$ arms are present in a stream and at most $m<n$ arms and their statistics can be stored in the memory. We give a complete characterization of the optimal regret in terms of $m, n$ and $P$. Specifically, we design an algorithm with $\\tilde O\\left((n-m)^{1+\\frac{2^{P}-2}{2^{P+1}-1}} n^{\\frac{2-2^{P+1}}{2^{P+1}-1}} T^{\\frac{2^P}{2^{P+1}-1}}\\right)$ regret and complement it with an $\\tilde \\Omega\\left((n-m)^{1+\\frac{2^{P}-2}{2^{P+1}-1}} n^{\\frac{2-2^{P+1}}{2^{P+1}-1}} T^{\\frac{2^P}{2^{P+1}-1"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.19752","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2405.19752/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}