Thompson Sampling: An Asymptotically Optimal Finite Time Analysis
  The question of the optimality of Thompson Sampling for solving the stochastic multi-armed bandit problem had been open since 1933. In this paper we answer it positively for the case of Bernoulli rewards by providing the first finite-time analysis that matches the asymptotic rate given in the Lai and Robbins lower bound for the cumulative regret. The proof is accompanied by a numerical comparison with other optimal policies, experiments that have been lacking in the literature until now for the Bernoulli case. 
Emilie Kaufmann, Nathaniel Korda and R\'emi Munos
stat.ML cs.LG