{"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-b-testing-and-best-arm-identification-for","title":"A/B Testing and Best-arm Identification for Linear Bandits with Robustness to Non-stationarity","arxiv_id":"2307.15154","date":"2023-07-27","proceeding":null,"authors":["Zhihan Xiong","Romain Camilleri","Maryam Fazel","Lalit Jain","Kevin Jamieson"],"abstract":"We investigate the fixed-budget best-arm identification (BAI) problem for linear bandits in a potentially non-stationary environment. Given a finite arm set $\\mathcal{X}\\subset\\mathbb{R}^d$, a fixed budget $T$, and an unpredictable sequence of parameters $\\left\\lbrace\\theta_t\\right\\rbrace_{t=1}^{T}$, an algorithm will aim to correctly identify the best arm $x^* := \\arg\\max_{x\\in\\mathcal{X}}x^\\top\\sum_{t=1}^{T}\\theta_t$ with probability as high as possible. Prior work has addressed the stationary setting where $\\theta_t = \\theta_1$ for all $t$ and demonstrated that the error probability decreases as $\\exp(-T /\\rho^*)$ for a problem-dependent constant $\\rho^*$. But in many real-world $A/B/n$ multivariate testing scenarios that motivate our work, the environment is non-stationary and an algorithm expecting a stationary setting can easily fail. For robust identification, it is well-known that if arms are chosen randomly and non-adaptively from a G-optimal design over $\\mathcal{X}$ at each time then the error probability decreases as $\\exp(-T\\Delta^2_{(1)}/d)$, where $\\Delta_{(1)} = \\min_{x \\neq x^*} (x^* - x)^\\top \\frac{1}{T}\\sum_{t=1}^T \\theta_t$. As there exist environments where $\\Delta_{(1)}^2/ d \\ll 1/ \\rho^*$, we are motivated to propose a novel algorithm $\\mathsf{P1}$-$\\mathsf{RAGE}$ that aims to obtain the best of both worlds: robustness to non-stationarity and fast rates of identification in benign settings. We characterize the error probability of $\\mathsf{P1}$-$\\mathsf{RAGE}$ and demonstrate empirically that the algorithm indeed never performs worse than G-optimal design but compares favorably to the best algorithms in the stationary setting.","url_abs":"https://arxiv.org/abs/2307.15154v2","url_pdf":"https://arxiv.org/pdf/2307.15154v2.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-b-testing-and-best-arm-identification-for","repo_url":"https://github.com/fftypezero/bobw_linear","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[{"method_slug":"fail","method_name":"fail"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}