Theoretical Foundations and Effective Algorithms for Policy-Aware Simulator Learning

Abstract

Model-based reinforcement learning (MBRL) agents typically learn world models by minimizing predictive loss. However, powerful RL optimizers inevitably exploit minor model inaccuracies, leading to simulator exploitation and a reality gap where policies succeed in simulation but fail in the real world. We propose that the objective for learning simulators should be strategic robustness rather than predictive accuracy, and formulate this as a zero-sum minimax game between a model player and an adversarial policy player. We provide a comprehensive theoretical analysis: (1) an online learning guarantee showing the game is learnable with sublinear regret bounds; (2) a tractable critic-based simplification bounding the global policy-value gap by the local critic's loss; and (3) an Error-MDP duality, proving that finding the worst-case policy is formally dual to a standard RL problem where the reward is the one-step critic error. This duality yields a provably convergent active data selection algorithm. Experiments on continuous control tasks demonstrate that our approach reduces prediction error in strategically important regions by $1.5$-$2.2\times$ and enables policies trained purely in simulation to match near-optimal real-world performance.