Sharp Deviations Bounds for Dirichlet Weighted Sums with Application to analysis of Bayesian algorithms
The research derives sharp, non-asymptotic deviation bounds for weighted sums of Dirichlet random variables using a novel integral representation. This method yields Gaussian-like approximations and tight bounds that generalize previous results to Beta distributions. The findings significantly sharpen regret bounds for algorithms like Multinomial Thompson Sampling and provide new analysis for Bayesian bootstrap methods.