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

arXiv: https://arxiv.org/abs/2610.03646 · HTML: https://mlsanity.com/paper/2610.03646/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 21 references that are in the map.
- First posted on arXiv 2 Oct 2026.

## Builds on (most cited first, 13 of 13)

- [Game-theoretic statistics and safe anytime-valid inference](https://mlsanity.com/paper/2210.01948/) (2022)
- [Safe Testing](https://mlsanity.com/paper/1906.07801/) (2019)
- [Weighted Linear Bandits for Non-Stationary Environments](https://mlsanity.com/paper/1909.09146/) (2019)
- [Conservative Bandits](https://mlsanity.com/paper/1602.04282/) (2016)
- [Nearly Optimal Adaptive Procedure with Change Detection for Piecewise-Stationary Bandit](https://mlsanity.com/paper/1802.03692/) (2018)
- [A Change-Detection based Framework for Piecewise-stationary Multi-Armed Bandit Problem](https://mlsanity.com/paper/1711.03539/) (2017)
- [Optimal Exploration-Exploitation in a Multi-Armed-Bandit Problem with Non-stationary Rewards](https://mlsanity.com/paper/1405.3316/) (2014)
- [Taming Non-stationary Bandits: A Bayesian Approach](https://mlsanity.com/paper/1707.09727/) (2017)
- [Testing exchangeability: fork-convexity, supermartingales, and e-processes](https://mlsanity.com/paper/2102.00630/) (2021)
- [E-detectors: a nonparametric framework for sequential change detection](https://mlsanity.com/paper/2203.03532/) (2022)
- [Sliding-Window Thompson Sampling for Non-Stationary Settings](https://mlsanity.com/paper/2409.05181/) (2024)
- [Thompson Sampling in Switching Environments with Bayesian Online Change Point Detection](https://mlsanity.com/paper/1302.3721/) (2013)
- [On Adaptive Estimation for Dynamic Bernoulli Bandits](https://mlsanity.com/paper/1712.03134/) (2017)

## Abstract (arXiv)

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 αE, 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.