Learning Mixtures of Markov Chains and MDPs
This addresses the challenge of clustering and modeling sequential data with hidden components for applications in robotics or reinforcement learning, but it is incremental as it builds on existing spectral and EM methods.
The paper tackles the problem of learning mixtures of Markov chains and MDPs from short unlabeled trajectories, achieving 96.6% average accuracy on a mixture of two MDPs in gridworld, outperforming EM with random initialization at 73.2%.
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).