Discovering How Agents Learn Using Few Data

Decentralized learning algorithms are an essential tool for designing multi-agent systems, as they enable agents to autonomously learn from their experience and past interactions. In this work, we propose a theoretical and algorithmic framework for real-time identification of the learning dynamics that govern agent behavior using a short burst of a single system trajectory. Our method identifies agent dynamics through polynomial regression, where we compensate for limited data by incorporating side-information constraints that capture fundamental assumptions or expectations about agent behavior. These constraints are enforced computationally using sum-of-squares optimization, leading to a hierarchy of increasingly better approximations of the true agent dynamics. Extensive experiments demonstrated that our approach, using only 5 samples from a short run of a single trajectory, accurately recovers the true dynamics across various benchmarks, including equilibrium selection and prediction of chaotic systems up to 10 Lyapunov times. These findings suggest that our approach has significant potential to support effective policy and decision-making in strategic multi-agent systems.