Gap-free bounds for multi-armed stochastic bandit.
Anatoli Juditsky, Alexander Nazin, Alexandre Tsybakov and Nicolas Vayatis
In: World Congress of IFAC 2008, Jul 2008, Korea.

Abstract

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 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.

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