  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.
