{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/near-optimal-time-and-sample-complexities-for-1","title":"Near-Optimal Time and Sample Complexities for Solving Discounted Markov Decision Process with a Generative Model","arxiv_id":"1806.01492","date":"2018-06-05","proceeding":null,"authors":["Aaron Sidford","Mengdi Wang","Xian Wu","Lin F. Yang","Yinyu Ye"],"abstract":"In this paper we consider the problem of computing an $\\epsilon$-optimal policy of a discounted Markov Decision Process (DMDP) provided we can only access its transition function through a generative sampling model that given any state-action pair samples from the transition function in $O(1)$ time. Given such a DMDP with states $S$, actions $A$, discount factor $\\gamma\\in(0,1)$, and rewards in range $[0, 1]$ we provide an algorithm which computes an $\\epsilon$-optimal policy with probability $1 - \\delta$ where \\emph{both} the time spent and number of sample taken are upper bounded by \\[ O\\left[\\frac{|S||A|}{(1-\\gamma)^3 \\epsilon^2} \\log \\left(\\frac{|S||A|}{(1-\\gamma)\\delta \\epsilon} \\right) \\log\\left(\\frac{1}{(1-\\gamma)\\epsilon}\\right)\\right] ~. \\] For fixed values of $\\epsilon$, this improves upon the previous best known bounds by a factor of $(1 - \\gamma)^{-1}$ and matches the sample complexity lower bounds proved in Azar et al. (2013) up to logarithmic factors. We also extend our method to computing $\\epsilon$-optimal policies for finite-horizon MDP with a generative model and provide a nearly matching sample complexity lower bound.","url_abs":"http://arxiv.org/abs/1806.01492v2","url_pdf":"http://arxiv.org/pdf/1806.01492v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"near-optimal-time-and-sample-complexities-for-1","repo_url":"https://github.com/uclaopt/AsyncQVI","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=1806.01492","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}