{"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/stochastic-optimal-control-via-hilbert-space","title":"Stochastic Optimal Control via Hilbert Space Embeddings of Distributions","arxiv_id":"2103.12759","date":"2021-03-23","proceeding":null,"authors":["Adam J. Thorpe","Meeko M. K. Oishi"],"abstract":"Kernel embeddings of distributions have recently gained significant attention in the machine learning community as a data-driven technique for representing probability distributions. Broadly, these techniques enable efficient computation of expectations by representing integral operators as elements in a reproducing kernel Hilbert space. We apply these techniques to the area of stochastic optimal control theory and present a method to compute approximately optimal policies for stochastic systems with arbitrary disturbances. Our approach reduces the optimization problem to a linear program, which can easily be solved via the Lagrangian dual, without resorting to gradient-based optimization algorithms. We focus on discrete-time dynamic programming, and demonstrate our proposed approach on a linear regulation problem, and on a nonlinear target tracking problem. This approach is broadly applicable to a wide variety of optimal control problems, and provides a means of working with stochastic systems in a data-driven setting.","url_abs":"https://arxiv.org/abs/2103.12759v1","url_pdf":"https://arxiv.org/pdf/2103.12759v1.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":"stochastic-optimal-control-via-hilbert-space","repo_url":"https://github.com/unm-hscl/ajthor-CDC2021","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}