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One of the challenges in model-based control of stochastic dynamical systemsis that the state transition dynamics are involved, and it is not easy orefficient to make good-quality predictions of the states. Moreover, there arenot many representational models for the majority of autonomous systems, as itis not easy to build a compact model that captures the entire dynamicalsubtleties and uncertainties. In this work, we present a hierarchical Bayesianlinear regression model with local features to learn the dynamics of amicro-robotic system as well as two simpler examples, consisting of astochastic mass-spring damper and a stochastic double inverted pendulum on acart. The model is hierarchical since we assume non-stationary priors for themodel parameters. These non-stationary priors make the model more flexible byimposing priors on the priors of the model. To solve the maximum likelihood(ML) problem for this hierarchical model, we use the variational expectationmaximization (EM) algorithm, and enhance the procedure by introducing hiddentarget variables. The algorithm yields parsimonious model structures, andconsistently provides fast and accurate predictions for all our examplesinvolving large training and test sets. This demonstrates the effectiveness ofthe method in learning stochastic dynamics, which makes it suitable for futureuse in a paradigm, such as model-based reinforcement learning, to computeoptimal control policies in real time.

A Hierarchical Bayesian Linear Regression Model with Local Features for Stochastic Dynamics Approximation