Learning Mixtures of Markov Chains and MDPs

We present an algorithm for use in learning mixtures of both Markov chains (MCs) and Markov decision processes (offline latent MDPs) from trajectories, with roots dating back to the work of Vempala and Wang. This amounts to handling Markov chains with optional control input. The method is modular in nature and amounts to (1) a subspace estimation step, (2) spectral clustering of trajectories, and (3) a few iterations of the EM algorithm. We provide end-to-end performance guarantees where we only explicitly require the number of trajectories to be linear in states and the trajectory length to be linear in mixing time. Experimental results suggest it outperforms both EM (95.4% on average) and a previous method by Gupta et al. (54.1%), obtaining 100% permuted accuracy on an 8x8 gridworld.