Breaking the Total Variance Barrier: Sharp Sample Complexity for Linear Heteroscedastic Bandits with Fixed Action Set
Recent years have witnessed increasing interests in tackling heteroscedastic noise in bandits and reinforcement learning. In these works, the cumulative variance of the noise $Λ= \sum_{t=1}^T σ_t^2$, where $σ_t^2$ is the variance of the noise at round $t$, is used to characterize the statistical complexity of the problem, yielding \emph{simple regret} bounds of order $\tilde{\cal{O}}(d \sqrt{Λ/ T^2})$ for $d$-dimensional linear bandits with heteroscedastic noise. However, with a closer look, $Λ$ remains the same order even if the noise is close to zero at half of the rounds, which indicates that the $Λ$-dependence is not optimal. In this paper, we revisit the stochastic linear bandit prob...
| Authors | Heyang Zhao, Tianyuan Jin, Weixin Wang et al. |
|---|---|
| Primary category | cs.LG |
| Published | 26 July 2026 |
| Last updated at source | 26 July 2026 |
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