OSCC: Certified Observation-Safe Coupling Optimization for Gradient-Noise Control in Imperfect-Information Learning

Coupled rollouts can reduce the noise of counterfactual action comparisons, but standard common-random-number constructions are not directly applicable to imperfect-information learning due to information leakage, invalid stochastic synchronization, and mismatch between scalar variance reduction and policy-gradient optimization objectives. We introduce Observation-Safe Counterfactual Coupling (OSCC), a framework that defines valid couplings through marginal preservation, information-state safety, branch-local policy randomness, semantic event alignment, and trace-before-oracle replay. We derive a gradient-aware coupling criterion showing that, under marginal-preserving transformations, policy-gradient noise is governed by policy-Jacobian-weighted off-diagonal return covariance rather than return-contrast variance alone. Based on this analysis, we propose OSCC-Select, a calibration-only selector that evaluates candidate coupling strategies using certified safety constraints, projected gradient-noise reduction, and physical sampling cost, while reverting to independent sampling when improvement cannot be statistically guaranteed. We instantiate the framework with CP-GRPO, a fully coupled rollout design for imperfect-information reinforcement learning. On 100,000 fixed-root Leduc comparisons, CP-GRPO reduces return-contrast variance from 41.1158 to 18.1441 (55.87% reduction) while preserving branch marginals. Extensive analyses across optimization, transfer, safety, noise transfer, and cost surfaces demonstrate how observation-safe coupling improves estimator reliability without violating information constraints.