{"paper":{"title":"Sharp Gap-Dependent Variance-Aware Regret Bounds for Tabular MDPs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Maryam Fazel, Runlong Zhou, Shulun Chen, Simon S. Du, Zihan Zhang","submitted_at":"2025-06-06T20:33:57Z","abstract_excerpt":"We consider the gap-dependent regret bounds for episodic MDPs. We show that the Monotonic Value Propagation (MVP) algorithm achieves a variance-aware gap-dependent regret bound of $$\\tilde{O}\\left(\\left(\\sum_{\\Delta_h(s,a)>0} \\frac{H^2 \\log K \\land \\mathtt{Var}_{\\max}^{\\text{c}}}{\\Delta_h(s,a)} +\\sum_{\\Delta_h(s,a)=0}\\frac{ H^2 \\land \\mathtt{Var}_{\\max}^{\\text{c}}}{\\Delta_{\\mathrm{min}}} + SAH^4 (S \\lor H) \\right) \\log K\\right),$$ where $H$ is the planning horizon, $S$ is the number of states, $A$ is the number of actions, and $K$ is the number of episodes. Here, $\\Delta_h(s,a) =V_h^* (a) - Q_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.06521","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.06521/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"}