Regime Switching BanditsDownload PDF

Published: 09 Nov 2021, Last Modified: 05 May 2023NeurIPS 2021 PosterReaders: Everyone
Keywords: regime switching, POMDP, hidden state, exploration-exploitation, spectral method, multi-armed bandit
Abstract: We study a multi-armed bandit problem where the rewards exhibit regime switching. Specifically, the distributions of the random rewards generated from all arms are modulated by a common underlying state modeled as a finite-state Markov chain. The agent does not observe the underlying state and has to learn the transition matrix and the reward distributions. We propose a learning algorithm for this problem, building on spectral method-of-moments estimations for hidden Markov models, belief error control in partially observable Markov decision processes and upper-confidence-bound methods for online learning. We also establish an upper bound $O(T^{2/3}\sqrt{\log T})$ for the proposed learning algorithm where $T$ is the learning horizon. Finally, we conduct proof-of-concept experiments to illustrate the performance of the learning algorithm.
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