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# Learning POMDP Models with Similarity Space Regularization: a Linear Gaussian Case Study

*Proceedings of The 4th Annual Learning for Dynamics and Control Conference*, PMLR 168:330-341, 2022.

#### Abstract

Partially observable Markov decision process (POMDP) is a principled framework for sequential decision making and control under uncertainty. Classical POMDP methods assume known system models, while in real-world applications, the true models are usually unknown. Recent researches propose learning POMDP models from the observation sequences rolled out by the true system using maximum likelihood estimation (MLE). However, we find that such methods usually fail to find a desirable solution. This paper makes a profound study of the POMDP model learning problem, focusing on the linear Gaussian case. We show the objective of MLE is a high-order polynomial function, which makes it easy to get stuck in local optima. We then prove that the global optimal models are not unique and constitute a similarity space of the true model. Based on this view, we propose Similarity Space Regularization (SimReg), an algorithm that smooths out the local optima but keeps all the global optima. Experiments show that given only a biased prior model, our algorithm achieves a higher log-likelihood, more accurate observation reconstruction and state estimation compared with the MLE-based method.