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

02/20/2017

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by   Yevgeny Seldin, et al.

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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 ( t)^3 to ( t)^2 and eliminates an additive factor of order Δ e^1/Δ^2, where Δ is the minimal gap of a problem instance. In the adversarial regime regret guarantee remains unchanged.