{"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/gap-dependent-unsupervised-exploration-for","title":"Gap-Dependent Unsupervised Exploration for Reinforcement Learning","arxiv_id":"2108.05439","date":"2021-08-11","proceeding":null,"authors":["Jingfeng Wu","Vladimir Braverman","Lin F. Yang"],"abstract":"For the problem of task-agnostic reinforcement learning (RL), an agent first collects samples from an unknown environment without the supervision of reward signals, then is revealed with a reward and is asked to compute a corresponding near-optimal policy. Existing approaches mainly concern the worst-case scenarios, in which no structural information of the reward/transition-dynamics is utilized. Therefore the best sample upper bound is $\\propto\\widetilde{\\mathcal{O}}(1/\\epsilon^2)$, where $\\epsilon>0$ is the target accuracy of the obtained policy, and can be overly pessimistic. To tackle this issue, we provide an efficient algorithm that utilizes a gap parameter, $\\rho>0$, to reduce the amount of exploration. In particular, for an unknown finite-horizon Markov decision process, the algorithm takes only $\\widetilde{\\mathcal{O}} (1/\\epsilon \\cdot (H^3SA / \\rho + H^4 S^2 A) )$ episodes of exploration, and is able to obtain an $\\epsilon$-optimal policy for a post-revealed reward with sub-optimality gap at least $\\rho$, where $S$ is the number of states, $A$ is the number of actions, and $H$ is the length of the horizon, obtaining a nearly \\emph{quadratic saving} in terms of $\\epsilon$. We show that, information-theoretically, this bound is nearly tight for $\\rho < \\Theta(1/(HS))$ and $H>1$. We further show that $\\propto\\widetilde{\\mathcal{O}}(1)$ sample bound is possible for $H=1$ (i.e., multi-armed bandit) or with a sampling simulator, establishing a stark separation between those settings and the RL setting.","url_abs":"https://arxiv.org/abs/2108.05439v2","url_pdf":"https://arxiv.org/pdf/2108.05439v2.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":"abstracts"},"code_links":[{"paper_slug":"gap-dependent-unsupervised-exploration-for","repo_url":"https://github.com/uuujf/GapExploration","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[{"task_slug":"reinforcement-learning","task_name":"Reinforcement Learning"},{"task_slug":"reinforcement-learning-1","task_name":"Reinforcement Learning (RL)"},{"task_slug":"reinforcement-learning-2","task_name":"reinforcement-learning"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=2108.05439","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}