The Restless Hidden Markov Bandit with Linear Rewards and Side Information

Michal Yemini*, Amir Leshem, Anelia Somekh-Baruch

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

In this paper we present a model for the hidden Markovian bandit problem with linear rewards. As opposed to current work on Markovian bandits, we do not assume that the state is known to the decision maker before making the decision. Furthermore, we assume structural side information where the decision maker knows in advance that there are two types of hidden states; one is common to all arms and evolves according to a Markovian distribution, and the other is unique to each arm and is distributed according to an i.i.d. process that is unique to each arm. We present an algorithm and regret analysis to this problem. Surprisingly, we can recover the hidden states and maintain logarithmic regret in the case of a convex polytope action set. Furthermore, we show that the structural side information leads to expected regret that does not depend on the number of extreme points in the action space. Therefore, we obtain practical solutions even in high dimensional problems.

Original languageAmerican English
Article number9335534
Pages (from-to)1108-1123
Number of pages16
JournalIEEE Transactions on Signal Processing
Volume69
DOIs
StatePublished - 2021
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 1991-2012 IEEE.

Keywords

  • Linear bandit
  • Markov decision process
  • hidden states
  • restless bandit
  • side information

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