Variance-Aware Sparse Linear Bandits. (arXiv:2205.13450v1 [cs.LG])

It is well-known that the worst-case minimax regret for sparse linear bandits
is $\widetilde{\Theta}\left(\sqrt{dT}\right)$ where $d$ is the ambient
dimension and $T$ is the number of time steps (ignoring the dependency on
sparsity). On the other hand, in the benign setting where there is no noise and
the action set is the unit sphere, one can use divide-and-conquer to achieve an
$\widetilde{\mathcal O}(1)$ regret, which is (nearly) independent of $d$ and
$T$. In this paper, we present the first variance-aware …

arxiv linear variance