  We propose the kl-UCB ++ algorithm for regret minimization in stochastic
bandit models with exponential families of distributions. We prove that it is
simultaneously asymptotically optimal (in the sense of Lai and Robbins' lower
bound) and minimax optimal. This is the first algorithm proved to enjoy these
two properties at the same time. This work thus merges two different lines of
research with simple and clear proofs.
