  Recent work in reinforcement learning has leveraged symmetries in the model
to improve sample efficiency in training a policy. A commonly used simplifying
assumption is that the dynamics and reward both exhibit the same symmetry.
However, in many real-world environments, the dynamical model exhibits symmetry
independent of the reward model: the reward may not satisfy the same symmetries
as the dynamics. In this paper, we investigate scenarios where only the
dynamics are assumed to exhibit symmetry, extending the scope of problems in
reinforcement learning and learning in control theory where symmetry techniques
can be applied. We use Cartan's moving frame method to introduce a technique
for learning dynamics which, by construction, exhibit specified symmetries. We
demonstrate through numerical experiments that the proposed method learns a
more accurate dynamical model.
