On the Peril of (Even a Little) Nonstationarity in Satisficing Regret Minimization
Motivated by the principle of satisficing in decision-making, we study satisficing regret guarantees for nonstationary $K$-armed bandits. We show that in the general realizable, piecewise-stationary setting with $L$ stationary segments, the optimal regret is $Θ(L\log T)$ as long as $L\geq 2$. This stands in sharp contrast to the case of $L=1$ (i.e., the stationary setting), where a $T$-independent $Θ(1)$ satisficing regret is achievable under realizability. In other words, the optimal regret has to scale with $T$ even if just a little nonstationarity presents. A key ingredient in our analysis is a novel Fano-based framework tailored to nonstationary bandits via a \emph{post-interaction re...
| Authors | Yixuan Zhang, Ruihao Zhu, Qiaomin Xie |
|---|---|
| Primary category | stat.ML |
| Published | 19 March 2026 |
| Last updated at source | 25 April 2026 |
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