Learning Multiple Markov Chains via Adaptive Allocation - Archive ouverte HAL
Conference Papers Year : 2019

Learning Multiple Markov Chains via Adaptive Allocation

Abstract

We study the problem of learning the transition matrices of a set of Markov chains from a single stream of observations on each chain. We assume that the Markov chains are ergodic but otherwise unknown. The learner can sample Markov chains sequentially to observe their states. The goal of the learner is to sequentially select various chains to learn transition matrices uniformly well with respect to some loss function. We introduce a notion of loss that naturally extends the squared loss for learning distributions to the case of Markov chains, and further characterize the notion of being uniformly good in all problem instances. We present a novel learning algorithm that efficiently balances exploration and exploitation intrinsic to this problem, without any prior knowledge of the chains. We provide finite-sample PAC-type guarantees on the performance of the algorithm. Further, we show that our algorithm asymptotically attains an optimal loss.
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Dates and versions

hal-02387345 , version 1 (29-11-2019)

Identifiers

  • HAL Id : hal-02387345 , version 1

Cite

Mohammad Sadegh Talebi, Odalric-Ambrym Maillard. Learning Multiple Markov Chains via Adaptive Allocation. Advances in Neural Information Processing Systems 32 (NIPS 2019), Dec 2019, Vancouver, Canada. ⟨hal-02387345⟩
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