Gap-free Bounds for Stochastic Multi-Armed Bandit
Résumé
We consider the stochastic multi-armed bandit problem with unknown horizon. We present a randomized decision strategy which is based on updating a probability distribution through a stochastic mirror descent/exponentiated gradient type algorithm. We consider separately two assumptions: nonnegative losses or arbitrary losses with an exponential moment condition. We prove optimal (up to logarithmic factors) gap-free bounds on the excess risk of the average over time of the instantaneous losses induced by the choice of a specific action.