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Main Authors: Zhang, Yixuan, Zhu, Ruihao, Xie, Qiaomin
Format: Preprint
Published: 2026
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Online Access:https://arxiv.org/abs/2603.18514
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author Zhang, Yixuan
Zhu, Ruihao
Xie, Qiaomin
author_facet Zhang, Yixuan
Zhu, Ruihao
Xie, Qiaomin
contents 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 reference} construction. This framework strictly extends the classical Fano method for passive estimation as well as recent interactive Fano techniques for stationary bandits. As a complement, we also discuss a special regime in which constant satisficing regret is again possible.
format Preprint
id arxiv_https___arxiv_org_abs_2603_18514
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle On the Peril of (Even a Little) Nonstationarity in Satisficing Regret Minimization
Zhang, Yixuan
Zhu, Ruihao
Xie, Qiaomin
Machine Learning
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 reference} construction. This framework strictly extends the classical Fano method for passive estimation as well as recent interactive Fano techniques for stationary bandits. As a complement, we also discuss a special regime in which constant satisficing regret is again possible.
title On the Peril of (Even a Little) Nonstationarity in Satisficing Regret Minimization
topic Machine Learning
url https://arxiv.org/abs/2603.18514