{"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/loop-estimator-for-discounted-values-in","title":"Loop Estimator for Discounted Values in Markov Reward Processes","arxiv_id":"2002.06299","date":"2020-02-15","proceeding":null,"authors":["Falcon Z. Dai","Matthew R. Walter"],"abstract":"At the working heart of policy iteration algorithms commonly used and studied in the discounted setting of reinforcement learning, the policy evaluation step estimates the value of states with samples from a Markov reward process induced by following a Markov policy in a Markov decision process. We propose a simple and efficient estimator called loop estimator that exploits the regenerative structure of Markov reward processes without explicitly estimating a full model. Our method enjoys a space complexity of $O(1)$ when estimating the value of a single positive recurrent state $s$ unlike TD with $O(S)$ or model-based methods with $O\\left(S^2\\right)$. Moreover, the regenerative structure enables us to show, without relying on the generative model approach, that the estimator has an instance-dependent convergence rate of $\\widetilde{O}\\left(\\sqrt{\\tau_s/T}\\right)$ over steps $T$ on a single sample path, where $\\tau_s$ is the maximal expected hitting time to state $s$. In preliminary numerical experiments, the loop estimator outperforms model-free methods, such as TD(k), and is competitive with the model-based estimator.","url_abs":"https://arxiv.org/abs/2002.06299v3","url_pdf":"https://arxiv.org/pdf/2002.06299v3.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":"loop-estimator-for-discounted-values-in","repo_url":"https://github.com/falcondai/loop-estimator","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"reinforcement-learning","task_name":"Reinforcement Learning"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=2002.06299","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}