Beyond Global Symmetry: State-Conditioned Graph-Structured Partial Equivariance for Reinforcement Learning

Symmetry provides an effective inductive bias for reinforcement learning by enabling generalization across equivalent states, actions, and entities. However, in structured environments such as multi-agent systems and articulated robots, a fixed global symmetry can become unreliable, because dynamics variations, actuation constraints, and interaction changes may break symmetry selectively across entities and states. To address this, we propose Graph-Structured Partial Equivariance (GSPE), a framework that represents candidate symmetry relations using a state-conditioned symmetry graph. Each edge estimates the reliability of applying an equivariant inductive bias between two entities under the current state. Based on this framework, we introduce Graph-Conditioned Policy Decomposition (GCPD), which decomposes policy computation into graph-conditioned equivariant and residual components, preserving reliable symmetries while enabling adaptive symmetry breaking when relations become unreliable. Experiments on MuJoCo, MPE, and three-robot real-world deployment show that GSPE consistently improves robustness and generalization under structured symmetry violations compared with baselines.