AI and the World's Hard Problems · Theoretical computer science · arXiv · 2026-10-23
Near-Optimal Regret for KL-Regularized Multi-Armed Bandits
The study examines regret for multi-armed bandits with KL-regularized objectives, a setting whose statistical efficiency was not well understood. Using a sharp analysis of KL-UCB with a novel peeling argument, the authors derive the first high-probability regret bound with linear dependence on the number of arms K, of order Õ(ηK log²T). They also give a lower bound of Ω(ηK log T) showing the analysis is nearly tight, and show that in the low-regularization regime the regret is independent of η and scales as Θ̃(√(KT)).