Progressive Residual Symbolic Interpretation of Multi-Agent Reinforcement Learning Policies

Symbolic policy surrogates expose learned decision rules, but a single selected formula can obscure explanatory multiplicity and residual decision structure. We introduce a progressive residual symbolic interpretation framework for multi-agent reinforcement learning policies that characterizes a population of low-complexity symbolic explanations and then allocates residual symbolic corrections path by path using minimum description length (MDL). The resulting population is structurally diverse but functionally organized. After compression to 24 representative paths, MDL selects nonzero residual refinements for 20 and retains the Stage-I form for four. On 200 independently generated nominal episodes, the frozen refinements reduce agent-balanced NMSE by $0.0709$ (95% CI: $0.0662$–$0.0757$), showing that the gains persist beyond the discovery trajectories. The discovered symbolic structures transfer without structural rediscovery: on held-out matched states from four independently trained target MATD3 policies, fixed-structure coefficient recalibration achieves an agent-balanced NRMSE of $0.321$ and $R^2=0.827$. Finally, six selected symbolic controllers jointly replace all neural agents and preserve the principal closed-loop voltage-control profile across nominal and unseen $\pm 10$% and $\pm 30$% operating shifts. Across $1.29$ million raw symbolic-action evaluations, the final controller produces no native action clamps, non-finite evaluations, or rollout failures. Together, this establishes population-level characterization, progressive residual refinement, cross-policy structural reuse, and closed-loop functional validation.