{"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/weighted-linear-bandits-for-non-stationary","title":"Weighted Linear Bandits for Non-Stationary Environments","arxiv_id":"1909.09146","date":"2019-09-19","proceeding":"NeurIPS 2019 12","authors":["Yoan Russac","Claire Vernade","Olivier Cappé"],"abstract":"We consider a stochastic linear bandit model in which the available actions correspond to arbitrary context vectors whose associated rewards follow a non-stationary linear regression model. In this setting, the unknown regression parameter is allowed to vary in time. To address this problem, we propose D-LinUCB, a novel optimistic algorithm based on discounted linear regression, where exponential weights are used to smoothly forget the past. This involves studying the deviations of the sequential weighted least-squares estimator under generic assumptions. As a by-product, we obtain novel deviation results that can be used beyond non-stationary environments. We provide theoretical guarantees on the behavior of D-LinUCB in both slowly-varying and abruptly-changing environments. We obtain an upper bound on the dynamic regret that is of order d^{2/3} B\\_T^{1/3}T^{2/3}, where B\\_T is a measure of non-stationarity (d and T being, respectively, dimension and horizon). This rate is known to be optimal. We also illustrate the empirical performance of D-LinUCB and compare it with recently proposed alternatives in simulated environments.","url_abs":"https://arxiv.org/abs/1909.09146v2","url_pdf":"https://arxiv.org/pdf/1909.09146v2.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":"weighted-linear-bandits-for-non-stationary","repo_url":"https://github.com/YRussac/WeightedLinearBandits","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"BSD-3-Clause"}}],"tasks":[{"task_slug":"regression-1","task_name":"regression"}],"methods":[{"method_slug":"linear-regression","method_name":"Linear Regression"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1909.09146","atlas_url":"https://app.syntology.ai/?focus=1909.09146","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1909.09146"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-25T09:33:49+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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