Designing optimal Bayes filters for nonlinear non-Gaussian systems is a challenging task. The main difficulties are: 1) representing complex beliefs, 2) handling non-Gaussian noise, and 3) marginalizing past states. To address these challenges, we focus on polynomial systems and propose the Max Entropy Moment Kalman Filter (MEM-KF). To address 1), we represent arbitrary beliefs by a MomentConstrained Max-Entropy Distribution (MED). The MED can asymptotically approximate almost any distribution given an increasing number of moment constraints. To address 2), we model the noise in the process and observation model as MED. To address 3), we propagate the moments through the process model and recover the distribution as MED, thus avoiding symbolic integration, which is generally intractable. All the steps in MEM-KF, including the extraction of a point estimate, can be solved via convex optimization.

A.1 Source code Upon request, we will provide an anonymized version of our code in the rebuttal. We replicated our experiments using the codebase provided by Shah et al. [ 2022 ], which can be found at github . To ensure consistency, we used the same hyperparameters as mentioned in the code or article for the baselines. This helps ensure the stability of metric learning. We initialize the parameters in such a way that the predicted metric is close to the Euclidean metric.

Model-free reinforcement learning aims to offer off-the-shelf solutions for controlling dynamical systems without requiring models of the system dynamics.

We study a distributionally robust mean square error estimation problem over a nonconvexWasserstein ambiguity set containing only normal distributions.

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