Neural Parameter Calibration for Finite-State Mean Field Games

2026-06-22

AI Summary

This work addresses the challenge of calibrating parameters in finite-state mean field games when theoretical derivation or direct observation is infeasible—such as with latent preferences, constraints, or interaction structures—by formulating parameter calibration as an inverse problem. The authors propose a neural network–based, end-to-end differentiable framework that leverages implicit differentiation to accurately compute gradients of discrete-time mean field equilibria with respect to model parameters. This approach enables, for the first time, efficient optimization over state- and time-dependent parameter trajectories without requiring individual-level action or reward data. Empirical validation across four increasingly complex systems—including synthetic linear-quadratic benchmarks and real-world urban mobility datasets—demonstrates the method’s effectiveness and accuracy.

Abstract

Mean field games efficiently approximate a very large population of strategic agents. While these games can aid the understanding of complex systems, their deployment in real-world settings is challenged by the specification of their parameters: mean field games (MFGs) often involve hidden preferences, constraints, and interactions that can rarely be theoretically derived or directly observed. To address this gap, we present a neural network-based framework for learning parametric, finite-state MFGs from observed population dynamics. To do so, we formulate the parameter calibration as an inverse problem and use implicit differentiation to backpropagate through the games' equilibrium. The resulting approach is fully differentiable and enables us to estimate flexible trajectory-wise parameter paths, including state- and time-dependent specifications without requiring observations of the individual agents' actions or rewards. We provide a proof for the exactness of the gradient computation in a discrete-time formulation. We validate our framework through numerical experiments across four systems of increasing complexity, ranging from synthetic linear-quadratic benchmarks to real-world urban mobility datasets.

Problem

• Mean Field Games
• Parameter Calibration
• Inverse Problem
• Hidden Preferences
• Population Dynamics

Innovation

• neural parameter calibration
• mean field games
• implicit differentiation
• inverse problem
• finite-state MFGs