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 $α_E$, 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.