When May a Bandit Leave Its Anchor? E-Process-Authorized Thompson Sampling under Non-stationarity

Title:When May a Bandit Leave Its Anchor? E-Process-Authorized Thompson Sampling under Non-stationarity

Abstract:Stationarity rewards memory, but after a change the same history can mislead. We ask when forgetting should be permitted. E-process-authorized Thompson sampling (e-ATS) gives each arm full-history and discounted Beta states. An anytime-valid e-process first authorizes the discounted state, then a reversible relevance score controls its influence. Before authorization, e-ATS exactly follows optimistic Thompson sampling (OTS). Under a Beta-Bernoulli prior-predictive stationary model, e-ATS's probability of ever departing from OTS is at most the chosen $\alpha_E$, without fitted thresholds. Relative to e-ATS, removing authorization increased mean normalized dynamic pseudo-regret by $38.4\%$ on the registered suite but reduced it by $7.5\%$ on the literature-derived replay suite. Therefore, evidence controls when adaptation begins, not whether it always helps.

25 pages, 3 figures. Accepted to the E-Values Workshop at NeurIPS 2026 (poster)

Machine Learning (cs.LG); Machine Learning (stat.ML)

arXiv:2610.03646 [cs.LG]

(or arXiv:2610.03646v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2610.03646 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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