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In robotic tasks, changes in reference frames typically do not influence theunderlying physical properties of the system, which has been known asinvariance of physical laws.These changes, which preserve distance, encompassisometric transformations such as translations, rotations, and reflections,collectively known as the Euclidean group. In this work, we delve into thedesign of improved learning algorithms for reinforcement learning and planningtasks that possess Euclidean group symmetry. We put forth a theory on thatunify prior work on discrete and continuous symmetry in reinforcement learning,planning, and optimal control. Algorithm side, we further extend the 2D pathplanning with value-based planning to continuous MDPs and propose a pipelinefor constructing equivariant sampling-based planning algorithms. Our work issubstantiated with empirical evidence and illustrated through examples thatexplain the benefits of equivariance to Euclidean symmetry in tackling naturalcontrol problems.

Can Euclidean Symmetry be Leveraged in Reinforcement Learning and Planning?