Learning Mixtures of Markov Chains and MDPs

TL;DR

This paper introduces a comprehensive algorithm for learning mixtures of Markov chains and MDPs from short, unlabeled trajectories, with theoretical guarantees and superior empirical performance over existing methods.

Contribution

The paper proposes a novel multi-step algorithm combining subspace estimation, spectral clustering, EM refinement, and classification for learning mixture models of Markov chains and MDPs.

Findings

Achieves 96.6% accuracy on gridworld MDP mixture

Provides end-to-end guarantees with linear trajectory length

Outperforms EM with random initialization in experiments

Abstract

We present an algorithm for learning mixtures of Markov chains and Markov decision processes (MDPs) from short unlabeled trajectories. Specifically, our method handles mixtures of Markov chains with optional control input by going through a multi-step process, involving (1) a subspace estimation step, (2) spectral clustering of trajectories using "pairwise distance estimators," along with refinement using the EM algorithm, (3) a model estimation step, and (4) a classification step for predicting labels of new trajectories. We provide end-to-end performance guarantees, where we only explicitly require the length of trajectories to be linear in the number of states and the number of trajectories to be linear in a mixing time parameter. Experimental results support these guarantees, where we attain 96.6% average accuracy on a mixture of two MDPs in gridworld, outperforming the EM algorithm with random initialization (73.2% average accuracy).