Calibrating Policy Covers for Nash Equilibrium Learning

A policy cover can reach every important state while its uniform mixture provides poor data for equilibrium learning. We study how to calibrate a finite cover in zero-sum Block games without identifying the latent-state decoder. Under common emissions and a finite evaluable decoder class containing the true decoder, constraints on all candidate-decoder events are equivalent at the population level to latent coverage constraints. Incorrect candidates therefore do not require a more conservative population mixture. Every library admits a coverage factor R\leq\min \ {M,S\}, where $M$ is its size and $S$ the latent state count. We estimate the event constraints from shared rollouts and implement them by linear programming. Under finite-class fitting conditions, the resulting Nash guarantee replaces $M$ by $R$ in the sufficient fitting budget, while charging cover construction and calibration. A hidden-coordinate class gives a polynomial-time implementation. In a three-stage family with an unknown entrance, $\tilde{O}(M+{\epsilon }^{-2})$ episodes match an adaptive lower bound up to logarithms, whereas uniform sampling of the same library requires $\Omega (M{\epsilon }^{-2})$. Fixed-budget experiments distinguish distribution quality from the costs and best-response errors that determine downstream performance.