  This paper introduces MDP homomorphic networks for deep reinforcement
learning. MDP homomorphic networks are neural networks that are equivariant
under symmetries in the joint state-action space of an MDP. Current approaches
to deep reinforcement learning do not usually exploit knowledge about such
structure. By building this prior knowledge into policy and value networks
using an equivariance constraint, we can reduce the size of the solution space.
We specifically focus on group-structured symmetries (invertible
transformations). Additionally, we introduce an easy method for constructing
equivariant network layers numerically, so the system designer need not solve
the constraints by hand, as is typically done. We construct MDP homomorphic
MLPs and CNNs that are equivariant under either a group of reflections or
rotations. We show that such networks converge faster than unstructured
baselines on CartPole, a grid world and Pong.
