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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.18514 |
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| _version_ | 1866917436082618368 |
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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 |