Deviations of Stochastic Bandit Regret

  • Antoine Salomon
  • Jean-Yves Audibert
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6925)


This paper studies the deviations of the regret in a stochastic multi-armed bandit problem. When the total number of plays n is known beforehand by the agent, Audibert et al. (2009) exhibit a policy such that with probability at least 1-1/n, the regret of the policy is of order logn. They have also shown that such a property is not shared by the popular ucb1 policy of Auer et al. (2002). This work first answers an open question: it extends this negative result to any anytime policy. The second contribution of this paper is to design anytime robust policies for specific multi-armed bandit problems in which some restrictions are put on the set of possible distributions of the different arms.


Neural Information Processing System Impossibility Result Bandit Problem Cumulative Reward Robust Policy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Antoine Salomon
    • 1
  • Jean-Yves Audibert
    • 1
    • 2
  1. 1.Imagine, LIGMÉcole des Ponts ParisTech Université Paris EstFrance
  2. 2.Sierra, CNRS/ENS/INRIAParisFrance

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