Batch Stationary Distribution Estimation

• URL: http://arxiv.org/abs/2003.00722v1
• Date: Mon, 2 Mar 2020 09:10:01 GMT
• Title: Batch Stationary Distribution Estimation
• Authors: Junfeng Wen, Bo Dai, Lihong Li, Dale Schuurmans
• Abstract summary: We consider the problem of approximating the stationary distribution of an ergodic Markov chain given a set of sampled transitions. We propose a consistent estimator that is based on recovering a correction ratio function over the given data.
• Score: 98.18201132095066
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider the problem of approximating the stationary distribution of an ergodic Markov chain given a set of sampled transitions. Classical simulation-based approaches assume access to the underlying process so that trajectories of sufficient length can be gathered to approximate stationary sampling. Instead, we consider an alternative setting where a fixed set of transitions has been collected beforehand, by a separate, possibly unknown procedure. The goal is still to estimate properties of the stationary distribution, but without additional access to the underlying system. We propose a consistent estimator that is based on recovering a correction ratio function over the given data. In particular, we develop a variational power method (VPM) that provides provably consistent estimates under general conditions. In addition to unifying a number of existing approaches from different subfields, we also find that VPM yields significantly better estimates across a range of problems, including queueing, stochastic differential equations, post-processing MCMC, and off-policy evaluation.

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