{"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/risk-sensitive-control-as-inference-with","title":"Risk-sensitive control as inference with Rényi divergence","arxiv_id":"2411.01827","date":"2024-11-04","proceeding":null,"authors":["Kaito Ito","Kenji Kashima"],"abstract":"This paper introduces the risk-sensitive control as inference (RCaI) that extends CaI by using R\\'{e}nyi divergence variational inference. RCaI is shown to be equivalent to log-probability regularized risk-sensitive control, which is an extension of the maximum entropy (MaxEnt) control. We also prove that the risk-sensitive optimal policy can be obtained by solving a soft Bellman equation, which reveals several equivalences between RCaI, MaxEnt control, the optimal posterior for CaI, and linearly-solvable control. Moreover, based on RCaI, we derive the risk-sensitive reinforcement learning (RL) methods: the policy gradient and the soft actor-critic. As the risk-sensitivity parameter vanishes, we recover the risk-neutral CaI and RL, which means that RCaI is a unifying framework. Furthermore, we give another risk-sensitive generalization of the MaxEnt control using R\\'{e}nyi entropy regularization. We show that in both of our extensions, the optimal policies have the same structure even though the derivations are very different.","url_abs":"https://arxiv.org/abs/2411.01827v1","url_pdf":"https://arxiv.org/pdf/2411.01827v1.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":"risk-sensitive-control-as-inference-with","repo_url":"https://github.com/kaito-1111/risk-sensitive-sac","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[{"task_slug":"reinforcement-learning-1","task_name":"Reinforcement Learning (RL)"},{"task_slug":"variational-inference","task_name":"Variational Inference"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2411.01827","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}