Neural Parameter Calibration for Finite-State Mean Field Games
2026-06-22 • Computer Science and Game Theory
Computer Science and Game TheoryMachine Learning
AI summaryⓘ
The authors created a method to learn how large groups of decision-makers behave over time by using neural networks to adjust the hidden rules that guide them. Instead of needing to see each individual's choices, their approach looks only at how the whole group changes and works backward to figure out the game parameters. They use advanced math techniques to precisely calculate how to improve these guesses, making the process fully differentiable. The authors tested their method on simple theoretical examples and real city traffic data, showing it can handle different complexities.
mean field gamesneural networksinverse problemimplicit differentiationequilibriumparameter calibrationtrajectory estimationdiscrete-time modelspopulation dynamicsurban mobility
Authors
Anna C. M. Thöni, Grégoire Lambrecht, Gökçe Dayanıklı, Yonathan Efroni, Tal Kachman, Mathieu Laurière
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.