# Regret bounds for restless Markov bandits

2 SEQUEL - Sequential Learning
LIFL - Laboratoire d'Informatique Fondamentale de Lille, LAGIS - Laboratoire d'Automatique, Génie Informatique et Signal, Inria Lille - Nord Europe
Abstract : We consider the restless Markov bandit problem, in which the state of each arm evolves according to a Markov process independently of the learner's actions. We suggest an algorithm, that first represents the setting as an MDP which exhibits some special structural properties. In order to grasp this information we introduce the notion of $\epsilon$-structured MDPs, which are a generalization of concepts like (approximate) state aggregation and MDP homomorphisms. We propose a general algorithm for learning $\epsilon$-structured MDPs and show regret bounds that demonstrate that additional structural information enhances learning. Applied to the restless bandit setting, this algorithm achieves after any $T$ steps regret of order $\tilde{O}(\sqrt{T})$ with respect to the best policy that knows the distributions of all arms. We make no assumptions on the Markov chains underlying each arm except that they are irreducible. In addition, we show that index-based policies are necessarily suboptimal for the considered problem.
Type de document :
Article dans une revue
Journal of Theoretical Computer Science (TCS), Elsevier, 2014, 558, pp.62-76. 〈10.1016/j.tcs.2014.09.026〉

https://hal.inria.fr/hal-01074077
Contributeur : Daniil Ryabko <>
Soumis le : dimanche 12 octobre 2014 - 17:29:16
Dernière modification le : jeudi 11 janvier 2018 - 01:49:34

### Citation

Ronald Ortner, Daniil Ryabko, Peter Auer, Rémi Munos. Regret bounds for restless Markov bandits. Journal of Theoretical Computer Science (TCS), Elsevier, 2014, 558, pp.62-76. 〈10.1016/j.tcs.2014.09.026〉. 〈hal-01074077〉

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