{"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/a-unifying-theory-of-thompson-sampling-for","title":"A Unifying Theory of Thompson Sampling for Continuous Risk-Averse Bandits","arxiv_id":"2108.11345","date":"2021-08-25","proceeding":null,"authors":["Joel Q. L. Chang","Vincent Y. F. Tan"],"abstract":"This paper unifies the design and the analysis of risk-averse Thompson sampling algorithms for the multi-armed bandit problem for a class of risk functionals $\\rho$ that are continuous and dominant. We prove generalised concentration bounds for these continuous and dominant risk functionals and show that a wide class of popular risk functionals belong to this class. Using our newly developed analytical toolkits, we analyse the algorithm $\\rho$-MTS (for multinomial distributions) and prove that they admit asymptotically optimal regret bounds of risk-averse algorithms under CVaR, proportional hazard, and other ubiquitous risk measures. More generally, we prove the asymptotic optimality of $\\rho$-MTS for Bernoulli distributions for a class of risk measures known as empirical distribution performance measures (EDPMs); this includes the well-known mean-variance. Numerical simulations show that the regret bounds incurred by our algorithms are reasonably tight vis-\\`a-vis algorithm-independent lower bounds.","url_abs":"https://arxiv.org/abs/2108.11345v4","url_pdf":"https://arxiv.org/pdf/2108.11345v4.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":"a-unifying-theory-of-thompson-sampling-for","repo_url":"https://github.com/joel-ql-chang/continuous-rho-ts","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok"}}],"tasks":[{"task_slug":"thompson-sampling","task_name":"Thompson Sampling"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=2108.11345","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}