  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.
