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This paper introduces e-process-authorized Thompson sampling (e-ATS), a novel approach to multi-armed bandits that selectively permits forgetting under non-stationarity by maintaining both full-history and discounted Beta states. The core innovation lies in an anytime-valid e-process that authorizes the use of the discounted state, with a reversible relevance score modulating its influence, thereby enabling adaptive exploration without sacrificing performance in stationary environments. Empirical results demonstrate that e-ATS outperforms a version without authorization, highlighting the critical role of evidence-based adaptation initiation.
Forgetting is not always beneficial in non-stationary bandits; evidence, not just change, should trigger adaptation.
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.