Equivariant $Q$ Learning in Spatial Action Spaces
This work addresses sample efficiency issues in robotics for tasks with spatial symmetries, representing an incremental improvement by applying known equivariant architectures to a specific Q-learning setting.
The paper tackled the problem of improving sample efficiency in Q-learning for robotics by leveraging equivariant neural network architectures that respect rotational and translational symmetries in visual state and spatial action spaces, and experimentally demonstrated that this approach outperforms standard methods in challenging manipulation tasks.
Recently, a variety of new equivariant neural network model architectures have been proposed that generalize better over rotational and reflectional symmetries than standard models. These models are relevant to robotics because many robotics problems can be expressed in a rotationally symmetric way. This paper focuses on equivariance over a visual state space and a spatial action space -- the setting where the robot action space includes a subset of $\rm{SE}(2)$. In this situation, we know a priori that rotations and translations in the state image should result in the same rotations and translations in the spatial action dimensions of the optimal policy. Therefore, we can use equivariant model architectures to make $Q$ learning more sample efficient. This paper identifies when the optimal $Q$ function is equivariant and proposes $Q$ network architectures for this setting. We show experimentally that this approach outperforms standard methods in a set of challenging manipulation problems.