Safety Aware Changepoint Detection for Piecewise i.i.d. Bandits
This work addresses safety-critical applications in bandit algorithms, such as medical trials or financial systems, by ensuring performance does not fall below a safe baseline, though it is incremental as it extends prior safe bandit and changepoint detection frameworks.
The paper tackles the problem of piecewise i.i.d. bandits with safety constraints, where cumulative rewards must stay above a threshold relative to a default action, and introduces two algorithms that detect changepoints and restart without prior knowledge, achieving regret bounds comparable to existing methods and providing matching lower bounds.
In this paper, we consider the setting of piecewise i.i.d. bandits under a safety constraint. In this piecewise i.i.d. setting, there exists a finite number of changepoints where the mean of some or all arms change simultaneously. We introduce the safety constraint studied in \citet{wu2016conservative} to this setting such that at any round the cumulative reward is above a constant factor of the default action reward. We propose two actively adaptive algorithms for this setting that satisfy the safety constraint, detect changepoints, and restart without the knowledge of the number of changepoints or their locations. We provide regret bounds for our algorithms and show that the bounds are comparable to their counterparts from the safe bandit and piecewise i.i.d. bandit literature. We also provide the first matching lower bounds for this setting. Empirically, we show that our safety-aware algorithms perform similarly to the state-of-the-art actively adaptive algorithms that do not satisfy the safety constraint.