Integrating Symmetry into Differentiable Planning with Steerable Convolutions
This work addresses data efficiency and generalization issues in end-to-end differentiable planning for decision-making tasks with symmetry, representing an incremental improvement over existing methods like VINs.
The paper tackled the problem of improving data efficiency and generalization in differentiable planning algorithms by integrating group symmetry, specifically rotation and reflection, into path planning tasks. The result showed that symmetric planning algorithms significantly enhanced training efficiency and generalization compared to non-equivariant methods like VIN and GPPN across tasks such as 2D navigation and manipulation.
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.