On The Complexity of Best-Arm Identification in Non-Stationary Linear Bandits
We study the fixed-budget best-arm identification (BAI) problem in non-stationary linear bandits. Concretely, given a fixed time budget $T\in \mathbb{N}$, finite arm set $\mathcal{X} \subset \mathbb{R}^d$, and a potentially adversarial sequence of unknown parameters $\lbrace θ_t\rbrace_{t=1}^{T}$ (hence non-stationary), a learner aims to identify the arm with the largest cumulative reward $x_* = \arg\max_{x \in \mathcal{X}} x^\top\sum_{t=1}^T θ_t$ with high probability. In this setting, it is well-known that uniformly sampling arms from the G-optimal design yields a minimax-optimal error probability of $\exp\left(-Θ\left(T / H_{G}\right)\right)$, where $H_{G}$ scales proportionally with t...
| Authors | Leo Maynard-Zhang, Zhihan Xiong, Kevin Jamieson et al. |
|---|---|
| Primary category | stat.ML |
| Published | 11 March 2026 |
| Last updated at source | 11 March 2026 |
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