Learning Mixtures of Markov Chains and MDPs

Chinmaya Kausik, Kevin Tan, Ambuj Tewari
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:15970-16017, 2023.

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). We also significantly outperform the EM algorithm on real data from the LastFM song dataset.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-kausik23a, title = {Learning Mixtures of {M}arkov Chains and {MDP}s}, author = {Kausik, Chinmaya and Tan, Kevin and Tewari, Ambuj}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {15970--16017}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/kausik23a/kausik23a.pdf}, url = {https://proceedings.mlr.press/v202/kausik23a.html}, 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). We also significantly outperform the EM algorithm on real data from the LastFM song dataset.} }
Endnote
%0 Conference Paper %T Learning Mixtures of Markov Chains and MDPs %A Chinmaya Kausik %A Kevin Tan %A Ambuj Tewari %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-kausik23a %I PMLR %P 15970--16017 %U https://proceedings.mlr.press/v202/kausik23a.html %V 202 %X 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). We also significantly outperform the EM algorithm on real data from the LastFM song dataset.
APA
Kausik, C., Tan, K. & Tewari, A.. (2023). Learning Mixtures of Markov Chains and MDPs. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:15970-16017 Available from https://proceedings.mlr.press/v202/kausik23a.html.

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