{"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/adaptive-smooth-non-stationary-bandits","title":"Adaptive Smooth Non-Stationary Bandits","arxiv_id":"2407.08654","date":"2024-07-11","proceeding":null,"authors":["Joe Suk"],"abstract":"We study a $K$-armed non-stationary bandit model where rewards change smoothly, as captured by H\\\"{o}lder class assumptions on rewards as functions of time. Such smooth changes are parametrized by a H\\\"{o}lder exponent $\\beta$ and coefficient $\\lambda$. While various sub-cases of this general model have been studied in isolation, we first establish the minimax dynamic regret rate generally for all $K,\\beta,\\lambda$. Next, we show this optimal dynamic regret can be attained adaptively, without knowledge of $\\beta,\\lambda$. To contrast, even with parameter knowledge, upper bounds were only previously known for limited regimes $\\beta\\leq 1$ and $\\beta=2$ (Slivkins, 2014; Krishnamurthy and Gopalan, 2021; Manegueu et al., 2021; Jia et al.,2023). Thus, our work resolves open questions raised by these disparate threads of the literature. We also study the problem of attaining faster gap-dependent regret rates in non-stationary bandits. While such rates are long known to be impossible in general (Garivier and Moulines, 2011), we show that environments admitting a safe arm (Suk and Kpotufe, 2022) allow for much faster rates than the worst-case scaling with $\\sqrt{T}$. While previous works in this direction focused on attaining the usual logarithmic regret bounds, as summed over stationary periods, our new gap-dependent rates reveal new optimistic regimes of non-stationarity where even the logarithmic bounds are pessimistic. We show our new gap-dependent rate is tight and that its achievability (i.e., as made possible by a safe arm) has a surprisingly simple and clean characterization within the smooth H\\\"{o}lder class model.","url_abs":"https://arxiv.org/abs/2407.08654v2","url_pdf":"https://arxiv.org/pdf/2407.08654v2.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":"adaptive-smooth-non-stationary-bandits","repo_url":"https://github.com/joesuk/smoothbandits","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"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}