An Improved Parametrization and Analysis of the EXP3++ Algorithm for Stochastic and Adversarial Bandits

Abstract

We present a new strategy for gap estimation in randomized algorithms for multiarmed bandits and combine it with the EXP3++ algorithm of Seldin and Slivkins (2014). In the stochastic regime the strategy reduces dependence of regret on a time horizon from $(\ln t{)}^3$ to $(\ln t{)}^2$ and eliminates an additive factor of order $\Delta e^{1/{\Delta }^2}$, where $\Delta$ is the minimal gap of a problem instance. In the adversarial regime regret guarantee remains unchanged.

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