Lingzhi Kong

Linfeng Zhao, Lingzhi Kong, Robin Walters et al.

Compositional generalization is a critical ability in learning and decision-making. We focus on the setting of reinforcement learning in object-oriented environments to study compositional generalization in world modeling. We (1) formalize the compositional generalization problem with an algebraic approach and (2) study how a world model can achieve that. We introduce a conceptual environment, Object Library, and two instances, and deploy a principled pipeline to measure the generalization ability. Motivated by the formulation, we analyze several methods with exact or no compositional generalization ability using our framework, and design a differentiable approach, Homomorphic Object-oriented World Model (HOWM), that achieves soft but more efficient compositional generalization.

Linfeng Zhao, Xupeng Zhu, Lingzhi Kong et al.

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.