{"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/koopman-spectrum-nonlinear-regulator-and","title":"Koopman Spectrum Nonlinear Regulators and Efficient Online Learning","arxiv_id":"2106.15775","date":"2021-06-30","proceeding":null,"authors":["Motoya Ohnishi","Isao Ishikawa","Kendall Lowrey","Masahiro Ikeda","Sham Kakade","Yoshinobu Kawahara"],"abstract":"Most modern reinforcement learning algorithms optimize a cumulative single-step cost along a trajectory. The optimized motions are often 'unnatural', representing, for example, behaviors with sudden accelerations that waste energy and lack predictability. In this work, we present a novel paradigm of controlling nonlinear systems via the minimization of the Koopman spectrum cost: a cost over the Koopman operator of the controlled dynamics. This induces a broader class of dynamical behaviors that evolve over stable manifolds such as nonlinear oscillators, closed loops, and smooth movements. We demonstrate that some dynamics characterizations that are not possible with a cumulative cost are feasible in this paradigm, which generalizes the classical eigenstructure and pole assignments to nonlinear decision making. Moreover, we present a sample efficient online learning algorithm for our problem that enjoys a sub-linear regret bound under some structural assumptions.","url_abs":"https://arxiv.org/abs/2106.15775v2","url_pdf":"https://arxiv.org/pdf/2106.15775v2.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":"koopman-spectrum-nonlinear-regulator-and","repo_url":"https://github.com/Mohnishi/KSNR","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"decision-making","task_name":"Decision Making"},{"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":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}