  Model-based reinforcement learning (MBRL) algorithms can attain significant
sample efficiency but require an appropriate network structure to represent
system dynamics. Current approaches include white-box modeling using analytic
parameterizations and black-box modeling using deep neural networks. However,
both can suffer from a bias-variance trade-off in the learning process, and
neither provides a structured method for injecting domain knowledge into the
network. As an alternative, gray-box modeling leverages prior knowledge in
neural network training but only for simple systems. In this paper, we devise a
nested mixture of experts (NMOE) for representing and learning hybrid dynamical
systems. An NMOE combines both white-box and black-box models while optimizing
bias-variance trade-off. Moreover, an NMOE provides a structured method for
incorporating various types of prior knowledge by training the associative
experts cooperatively or competitively. The prior knowledge includes
information on robots' physical contacts with the environments as well as their
kinematic and dynamic properties. In this paper, we demonstrate how to
incorporate prior knowledge into our NMOE in various continuous control
domains, including hybrid dynamical systems. We also show the effectiveness of
our method in terms of data-efficiency, generalization to unseen data, and
bias-variance trade-off. Finally, we evaluate our NMOE using an MBRL setup,
where the model is integrated with a model-based controller and trained online.

Machine Learning;Robotics