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Learning to Detect an Odd Markov Arm

Karthik, PN and Sundaresan, R (2020) Learning to Detect an Odd Markov Arm. In: IEEE Transactions on Information Theory, 66 (7). pp. 4324-4348.

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Official URL: https://dx.doi.org/10.1109/TIT.2020.2972875


A multi-armed bandit with finitely many arms is studied when each arm is a homogeneous Markov process on an underlying finite state space. The transition law of one of the arms, referred to as the odd arm, is different from the common transition law of all other arms. A learner, who has no knowledge of the above transition laws, has to devise a sequential test to identify the index of the odd arm as quickly as possible, subject to an upper bound on the probability of error. For this problem, we derive an asymptotic lower bound on the expected stopping time of any sequential test of the learner, where the asymptotics is as the probability of error vanishes. Furthermore, we propose a sequential test, and show that the asymptotic behaviour of its expected stopping time comes arbitrarily close to that of the lower bound. Prior works deal with independent and identically distributed arms, whereas our work deals with Markov arms. Our analysis of the rested Markov setting is a key first step in understanding the difficult case of restless Markov setting, which is still open. © 1963-2012 IEEE.

Item Type: Journal Article
Publication: IEEE Transactions on Information Theory
Publisher: Institute of Electrical and Electronics Engineers Inc.
Additional Information: The copyright for the article belongs to the Authors.
Keywords: Computer applications; Information theory, Asymptotic behaviour; Asymptotics; Finite state spaces; Lower bounds; Multi armed bandit; Probability of errors; Sequential tests; Stopping time, Markov processes
Department/Centre: Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited: 22 Sep 2021 10:02
Last Modified: 19 Oct 2022 10:24
URI: https://eprints.iisc.ac.in/id/eprint/66043

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