Counterfactual Regret for Reflective Agents with Lean-Verified Guarantees

Zhongnian Li, Shi Xu, Mengting Xu, Peng Ying, Xinzheng Xu

Reflective language agents reuse feedback and memory to adapt across tasks without updating model weights. However, existing guarantees for policy selection and action generation do not by themselves establish when local reflection yields long-term performance guarantees for the complete agent under resource constraints. In this paper, we address this gap by deriving sufficient conditions for sublinear counterfactual regret from local generation and deployment guarantees, while retaining the native controller. Specifically, we establish a resource-sensitive transfer that bounds full-state deployment discrepancies along actual execution paths and preserves the own-history laws of both learner and comparator. Besides, local generation reliability yields a cumulative generation opportunity bound, linking policy acquisition to long-term performance through an explicit quality, coverage, and hard-budget tradeoff. To verify these guarantees, we formalize the conditional proof chain for all thirteen numbered theoretical results in Lean, including a native instance with repeated policy growth and imperfect validation.