Symmetry is ubiquitous in nature and has been used in physics and mathematics to help make models tractable for centuries. Although Reinforcement Learning (RL) has achieved success in ATARI, GO, robots, and flow control in recent years, RL cannot guarantee to satisfy symmetry. Researchers have shown that for a system with symmetry, the performance of RL is limited without forcing symmetry to be respected. This paper develops a generally applicable Neural Network (NN) module with symmetry to achieve an NN-based model that enforces symmetry to be respected. A symmetry-informed Model-Based RL (MBRL) approach that satisfies symmetry is established based on the NN module with symmetry. This paper paves a way for integrating ubiquitous symmetry into MBRL to improve the performance of MBRL in learning and deployment and improves the feasibility of deploying RL in the real world.

Symmetry is ubiquitous in nature, physics, and mathematics. However, a classical symmetry-agnostic reinforcement learning (RL) approach cannot guarantee to respect symmetry. Researchers have shown that if the symmetry of a system cannot be respected, the performance of a symmetry-agnostic RL approach can be inhibited. To this end, this article develops a generally applicable neural network (NN) module with symmetry that can enforce the symmetry of a system to be respected. Based on the NN module with symmetry, this article proposes a symmetry-informed model-based RL (MBRL) approach that respects symmetry and improves data efficiency. The symmetry-informed MBRL approach is applied to the attitude control of a quadrotor in simulation to evaluate the effectiveness of the approach. The simulation results show that the data efficiency of the symmetry-informed MBRL approach is much superior to that of a symmetry-agnostic MBRL approach. An NN module with symmetry can respect the symmetry of a quadrotor while a naive NN cannot enforce the symmetry of a quadrotor to be respected.