MDP Homomorphic Networks: Group Symmetries in Reinforcement Learning

TL;DR

This paper presents MDP homomorphic networks that incorporate group symmetry equivariance into reinforcement learning models, leading to faster convergence by reducing solution complexity.

Contribution

It introduces a method to embed group-structured symmetries into neural networks for reinforcement learning, including an easy construction of equivariant layers.

Findings

Faster convergence on CartPole, grid world, and Pong.

Networks are equivariant under reflections and rotations.

Reduces solution space by leveraging symmetry constraints.

Abstract

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.