Exact Bayes Regret and Asymptotic Optimality in High-Dimensional Gaussian Bandits
高维高斯多臂老虎机的精确贝叶斯遗憾与渐近最优性
We study Bayesian linear bandits with an isotropic Gaussian parameter, independent Gaussian candidate arms, and Gaussian reward noise when the horizon is proportional to the dimension. The normalized posterior uncertainty has an explicit limit that is uniform over all causal policies. Gaussian posterior identities then determine the limiting parameter overlaps without an assumed closure of the adaptive recursion. These results yield exact regret curves for Thompson sampling,…