Linear bandits with polylogarithmic minimax regret

arXiv:2402.12042v1 Announce Type: new
Abstract: We study a noise model for linear stochastic bandits for which the subgaussian noise parameter vanishes linearly as we select actions on the unit sphere closer and closer to the unknown vector. We introduce an algorithm for this problem that exhibits a minimax regret scaling as $\log^3(T)$ in the time horizon $T$, in stark contrast the square root scaling of this regret for typical bandit algorithms. Our strategy, based on weighted least-squares estimation, achieves the …

abstract algorithm arxiv cs.ai cs.lg linear minimax noise scaling sphere stat.ml stochastic study type vector