{"paper":{"title":"Tight Sample Complexity Bounds for Entropic Best Policy Identification","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"A new stopping rule closes the exponential gap and matches the lower bound for entropic best-policy identification.","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Amer Essakine, Claire Vernade","submitted_at":"2026-05-13T16:02:26Z","abstract_excerpt":"We study best-policy identification for finite-horizon risk-sensitive reinforcement learning under the entropic risk measure. Recent work established a constant gap in the exponential horizon dependence between lower and upper bounds on the number of samples required to identify an approximately optimal policy. Precisely, known lower bounds scale in $\\Omega(e^{|\\beta| H})$ where $H$ is the horizon of the MDP, while the state-of-the-art upper bound achieves at best $O(e^{2|\\beta| H})$ (arXiv:2506.00286v2) using a generative model. We show that this extra exponential factor can be traced to over"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We show that this extra exponential factor can be traced to overly loose concentration control for exponential utilities. [...] we propose a new stopping rule that exploits further this tightness to obtain a sample complexity that matches the lower bound.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The smoothness properties of the exponential utility suffice to derive sharper concentration bounds that are tight enough for the new stopping rule to match the lower bound.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"New concentration bounds and stopping rule close the exponential gap to match the lower bound for entropic best policy identification.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A new stopping rule closes the exponential gap and matches the lower bound for entropic best-policy identification.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"0bfc4575045b0452dd66ae86453e41ec9d39252ef27d5bfb4ee3cd6de482f088"},"source":{"id":"2605.13717","kind":"arxiv","version":1},"verdict":{"id":"a4de2269-15d5-48aa-8269-9fd9bfbd11c6","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T20:10:14.826127Z","strongest_claim":"We show that this extra exponential factor can be traced to overly loose concentration control for exponential utilities. [...] we propose a new stopping rule that exploits further this tightness to obtain a sample complexity that matches the lower bound.","one_line_summary":"New concentration bounds and stopping rule close the exponential gap to match the lower bound for entropic best policy identification.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The smoothness properties of the exponential utility suffice to derive sharper concentration bounds that are tight enough for the new stopping rule to match the lower bound.","pith_extraction_headline":"A new stopping rule closes the exponential gap and matches the lower bound for entropic best-policy identification."},"references":{"count":29,"sample":[{"doi":"","year":2012,"title":"Proceedings of the 29th International Conference on Machine Learning (ICML-12) , series =","work_id":"ad6ca1b2-68e6-4d58-8124-75e24003aaf4","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"arXiv preprint arXiv:2506.00286 , year =","work_id":"715e52da-416c-402d-88cb-a7b195df8fb1","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Computational Economics , year =","work_id":"17929e36-771c-437e-8198-b02330fa0da0","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2017,"title":"Journal of Intelligent","work_id":"faabab27-c1a4-4527-8344-6d74ecc10ac6","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Beyond Average Return in Markov Decision Processes , url =","work_id":"e397c916-0e06-471f-9cc8-d929de9e5bc8","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":29,"snapshot_sha256":"4519f968eb6213ab2b774adb2f22f307167ea555ca1ca88b748fdf3773e9c3c5","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"}