{"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/thompson-sampling-for-linearly-constrained","title":"Thompson Sampling for Linearly Constrained Bandits","arxiv_id":"2004.09258","date":"2020-04-20","proceeding":null,"authors":["Vidit Saxena","Joseph E. Gonzalez","Joakim Jaldén"],"abstract":"We address multi-armed bandits (MAB) where the objective is to maximize the cumulative reward under a probabilistic linear constraint. For a few real-world instances of this problem, constrained extensions of the well-known Thompson Sampling (TS) heuristic have recently been proposed. However, finite-time analysis of constrained TS is challenging; as a result, only O(\\sqrt{T}) bounds on the cumulative reward loss (i.e., the regret) are available. In this paper, we describe LinConTS, a TS-based algorithm for bandits that place a linear constraint on the probability of earning a reward in every round. We show that for LinConTS, the regret as well as the cumulative constraint violations are upper bounded by O(\\log T) for the suboptimal arms. We develop a proof technique that relies on careful analysis of the dual problem and combine it with recent theoretical work on unconstrained TS. Through numerical experiments on two real-world datasets, we demonstrate that LinConTS outperforms an asymptotically optimal upper confidence bound (UCB) scheme in terms of simultaneously minimizing the regret and the violation.","url_abs":"https://arxiv.org/abs/2004.09258v2","url_pdf":"https://arxiv.org/pdf/2004.09258v2.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":"thompson-sampling-for-linearly-constrained","repo_url":"https://github.com/vidits-kth/LinConTS","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"multi-armed-bandits","task_name":"Multi-Armed Bandits"},{"task_slug":"thompson-sampling","task_name":"Thompson Sampling"}],"methods":[{"method_slug":"ts","method_name":"TS"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}