Can Euclidean Symmetry be Leveraged in Reinforcement Learning and Planning?
This work addresses the challenge of leveraging symmetry in robotic tasks for more efficient reinforcement learning and planning, representing a novel method for a known bottleneck rather than a broad breakthrough.
The paper tackles the problem of designing improved learning algorithms for reinforcement learning and planning tasks with Euclidean group symmetry, resulting in a unified theory and a pipeline for constructing equivariant sampling-based planning algorithms, supported by empirical evidence.
In robotic tasks, changes in reference frames typically do not influence the underlying physical properties of the system, which has been known as invariance of physical laws.These changes, which preserve distance, encompass isometric transformations such as translations, rotations, and reflections, collectively known as the Euclidean group. In this work, we delve into the design of improved learning algorithms for reinforcement learning and planning tasks that possess Euclidean group symmetry. We put forth a theory on that unify prior work on discrete and continuous symmetry in reinforcement learning, planning, and optimal control. Algorithm side, we further extend the 2D path planning with value-based planning to continuous MDPs and propose a pipeline for constructing equivariant sampling-based planning algorithms. Our work is substantiated with empirical evidence and illustrated through examples that explain the benefits of equivariance to Euclidean symmetry in tackling natural control problems.