{"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/hamilton-jacobi-deep-q-learning-for","title":"Hamilton-Jacobi Deep Q-Learning for Deterministic Continuous-Time Systems with Lipschitz Continuous Controls","arxiv_id":"2010.14087","date":"2020-10-27","proceeding":null,"authors":["Jeongho Kim","Jaeuk Shin","Insoon Yang"],"abstract":"In this paper, we propose Q-learning algorithms for continuous-time deterministic optimal control problems with Lipschitz continuous controls. Our method is based on a new class of Hamilton-Jacobi-Bellman (HJB) equations derived from applying the dynamic programming principle to continuous-time Q-functions. A novel semi-discrete version of the HJB equation is proposed to design a Q-learning algorithm that uses data collected in discrete time without discretizing or approximating the system dynamics. We identify the condition under which the Q-function estimated by this algorithm converges to the optimal Q-function. For practical implementation, we propose the Hamilton-Jacobi DQN, which extends the idea of deep Q-networks (DQN) to our continuous control setting. This approach does not require actor networks or numerical solutions to optimization problems for greedy actions since the HJB equation provides a simple characterization of optimal controls via ordinary differential equations. We empirically demonstrate the performance of our method through benchmark tasks and high-dimensional linear-quadratic problems.","url_abs":"https://arxiv.org/abs/2010.14087v1","url_pdf":"https://arxiv.org/pdf/2010.14087v1.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":"hamilton-jacobi-deep-q-learning-for","repo_url":"https://github.com/HJDQN/HJQ","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"continuous-control","task_name":"Continuous Control"},{"task_slug":"q-learning","task_name":"Q-Learning"},{"task_slug":"continuous-control","task_name":"continuous-control"}],"methods":[{"method_slug":"convolution","method_name":"Convolution"},{"method_slug":"dqn","method_name":"DQN"},{"method_slug":"dense-connections","method_name":"Dense Connections"},{"method_slug":"q-learning","method_name":"Q-Learning"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2010.14087","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}