We study how group symmetry helps improve data efficiency and generalization for end-to-end differentiable planning algorithms when symmetry appears in decision-making tasks. Motivated by equivariant convolution networks, we treat the path planning problem as \textit{signals} over grids. We show that value iteration in this case is a linear equivariant operator, which is a (steerable) convolution. This extends Value Iteration Networks (VINs) on using convolutional networks for path planning with additional rotation and reflection symmetry. Our implementation is based on VINs and uses steerable convolution networks to incorporate symmetry. The experiments are performed on four tasks: 2D navigation, visual navigation, and 2 degrees of freedom (2DOFs) configuration space and workspace manipulation. Our symmetric planning algorithms improve training efficiency and generalization by large margins compared to non-equivariant counterparts, VIN and GPPN.

翻译：我们研究了在决策任务出现对称性时，群对称性如何帮助提升端到端可微分规划算法的数据效率与泛化能力。受等变卷积网络启发，我们将路径规划问题视为网格上的信号处理。我们发现，在此语境下，值迭代是一种线性等变算子，本质为（可引导）卷积。这扩展了值迭代网络利用卷积网络进行路径规划时对旋转和反射对称性的支持。我们的实现基于VIN，并采用可引导卷积网络融入对称性。实验在四个任务上展开：二维导航、视觉导航、二自由度构型空间及工作空间操作。相较于非等变方法VIN和GPPN，我们的对称规划算法在训练效率和泛化能力上均有大幅提升。