Reflective agents achieve reliable long-term decisions with formal guarantees
Counterfactual Regret for Reflective Agents with Lean-Verified Guarantees
Artificial Intelligence
Summary
Some language agents can think about their own past actions and improve without changing their core programming. The authors found ways to mathematically guarantee that these agents will do well over time, even when using limited resources and imperfect information. They proved many results using a formal tool called Lean to make sure everything is correct. This work helps understand when and why such adaptive agents can be trusted to perform well.
What this means in practice
- •For ai system designers: Ensure adaptive AI agents maintain reliable long-term behavior under limited computational budgets.
- •For automated decision systems: Improve confidence in reflective agent deployments by verifying performance guarantees through formal proofs.
A theory result. No direct application yet.
Authors
Zhongnian Li, Shi Xu, Mengting Xu, Peng Ying, Xinzheng Xu
Abstract
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.