{"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/learning-stabilizing-controllers-of-linear","title":"Learning Stabilizing Controllers of Linear Systems via Discount Policy Gradient","arxiv_id":"2112.09294","date":"2021-12-17","proceeding":null,"authors":["Feiran Zhao","Xingyun Fu","Keyou You"],"abstract":"Stability is one of the most fundamental requirements for systems synthesis. In this paper, we address the stabilization problem for unknown linear systems via policy gradient (PG) methods. We leverage a key feature of PG for Linear Quadratic Regulator (LQR), i.e., it drives the policy away from the boundary of the unstabilizing region along the descent direction, provided with an initial policy with finite cost. To this end, we discount the LQR cost with a factor, by adaptively increasing which gradient leads the policy to the stabilizing set while maintaining a finite cost. Based on the Lyapunov theory, we design an update rule for the discount factor which can be directly computed from data, rendering our method purely model-free. Compared to recent work \\citep{perdomo2021stabilizing}, our algorithm allows the policy to be updated only once for each discount factor. Moreover, the number of sampled trajectories and simulation time for gradient descent is significantly reduced to $\\mathcal{O}(\\log(1/\\epsilon))$ for the desired accuracy $\\epsilon$. Finally, we conduct simulations on both small-scale and large-scale examples to show the efficiency of our discount PG method.","url_abs":"https://arxiv.org/abs/2112.09294v1","url_pdf":"https://arxiv.org/pdf/2112.09294v1.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":"learning-stabilizing-controllers-of-linear","repo_url":"https://github.com/fuxy16/stabilize-via-pg","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"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}