Asymptotic Theory and Sequential Testing for Adaptive Bandits

Statistics > Methodology [Submitted on 26 Feb 2026 (v1), last revised 30 May 2026 (this version, v2)] Title:Asymptotic Theory and Sequential Testing for Adaptive Bandits View PDF HTML (experimental)Abstract:Multi-armed bandit (MAB) processes constitute a foundational subclass of reinforcement learning problems and represent a central topic in statistical decision theory. Yet, conducting valid sequential testing under adaptive allocation remains challenging due to the lack of asymptotic theory under non-i.i.d. reward sequences and sublinear sample sizes for some arms. To address this open challenge, we propose an Urn Bandit (UNB) process to integrate the reinforcement mechanism of urn probabilistic models with MAB principles, ensuring almost sure concentration of allocation proportions on optimal arms. We establish a joint functional central limit theorem (FCLT) for consistent estimators of expected rewards under non-i.i.d. reward sequences with non-sub-Gaussian tails and pairwise cross-arm dependence. To overcome the limitations of existing methods that focus mainly on cumulative regret and therefore provide only algorithmic performance guarantees without supporting valid sequential testing, we develop an asymptotic theory for sequential test statistics under the proposed UNB process. The resulting framework enables a broad class of sequential inference procedures, such as A/B testing and policy evaluation. Simulation studies and real data analysis demonstrate that UNB maintains testing performance comparable to that of the equal randomization (ER) design while achieving improved reward accumulation relative to ER. Submission history From: Li Yang [view email][v1] Thu, 26 Feb 2026 08:59:20 UTC (98 KB) [v2] Sat, 30 May 2026 08:32:28 UTC (98 KB) References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer (What is the Explorer?) Connected Papers (What is Connected Papers?) Litmaps (What is Litmaps?) scite Smart Citations (What are Smart Citations?) Code, Data and Media Associated with this Article alphaXiv (What is alphaXiv?) CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub (What is DagsHub?) Gotit.pub (What is GotitPub?) Hugging Face (What is Huggingface?) ScienceCast (What is ScienceCast?) Demos Recommenders and Search Tools Influence Flower (What are Influence Flowers?) CORE Recommender (What is CORE?) arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.