Equivariant Ensembles and Regularization for Reinforcement Learning in Map-Based Path Planning

In reinforcement learning (RL), exploiting en- vironmental symmetries can significantly enhance efficiency, robustness, and performance. However, ensuring that the deep RL policy and value networks are respectively equivariant and invariant to exploit these symmetries is a substantial challenge. Related works try to design networks that are equivariant and invariant by construction, limiting them to a very restricted library of components, which in turn hampers the expres- siveness of the networks. This paper proposes a method to construct equivariant policies and invariant value functions without specialized neural network components, which we term equivariant ensembles. We further add a regularization term for adding inductive bias during training. In a map-based path planning case study, we show how equivariant ensembles and regularization benefit sample efficiency and performance.