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arXiv · 1903.07890

On First-Order Bounds, Variance and Gap-Dependent Bounds for Adversarial Bandits

Roman Pogodin·Tor Lattimore
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Abstract

We make three contributions to the theory of k-armed adversarial bandits. First, we prove a first-order bound for a modified variant of the INF strategy by Audibert and Bubeck [2009], without sacrificing worst case optimality or modifying the loss estimators. Second, we provide a variance analysis for algorithms based on follow the regularised leader, showing that without adaptation the variance of the regret is typically {\Omega}(n^2) where n is the horizon. Finally, we study bounds that depend on the degree of separation of the arms, generalising the results by Cowan and Katehakis [2015] from the stochastic setting to the adversarial and improving the result of Seldin and Slivkins [2014] by a factor of log(n)/log(log(n)).

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Roman Pogodin, Tor Lattimore. 2019-03-19. On First-Order Bounds, Variance and Gap-Dependent Bounds for Adversarial Bandits. https://arxiv.org/abs/1903.07890

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