# Neural Parameter Calibration for Finite-State Mean Field Games

arXiv: https://arxiv.org/abs/2606.23155 · HTML: https://mlsanity.com/paper/2606.23155/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 49 references that are in the map.
- First posted on arXiv 22 Jun 2026.

## Builds on (most cited first, 22 of 22)

- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [Efficient and Modular Implicit Differentiation](https://mlsanity.com/paper/2105.15183/) (2021)
- [Policy Mirror Ascent for Efficient and Independent Learning in Mean Field Games](https://mlsanity.com/paper/2212.14449/) (2022)
- [Mean Field Game of Controls and An Application To Trade Crowding](https://mlsanity.com/paper/1610.09904/) (2016)
- [Numerical Methods for Mean Field Games and Mean Field Type Control](https://mlsanity.com/paper/2106.06231/) (2021)
- [Neural parameter calibration for large-scale multi-agent models](https://mlsanity.com/paper/2209.13565/) (2022)
- [Finite State Graphon Games with Applications to Epidemics](https://mlsanity.com/paper/2106.07859/) (2021)
- [Individual-Level Inverse Reinforcement Learning for Mean Field Games](https://mlsanity.com/paper/2202.06401/) (2022)
- [Optimal incentives to mitigate epidemics: a Stackelberg mean field game approach](https://mlsanity.com/paper/2011.03105/) (2020)
- [Model-Based RL for Mean-Field Games is not Statistically Harder than Single-Agent RL](https://mlsanity.com/paper/2402.05724/) (2024)
- [Mean-field-game model for Botnet defense in Cyber-security](https://mlsanity.com/paper/1511.06642/) (2015)
- [Adversarial Inverse Reinforcement Learning for Mean Field Games](https://mlsanity.com/paper/2104.14654/) (2021)
- [Linear-Quadratic Mean Field Games](https://mlsanity.com/paper/1404.5741/) (2014)
- [Deep Backward and Galerkin Methods for the Finite State Master Equation](https://mlsanity.com/paper/2403.04975/) (2024)
- [Linearly Solvable Mean-Field Traffic Routing Games](https://mlsanity.com/paper/1903.01449/) (2019)
- [Maximum Causal Entropy IRL in Mean-Field Games and GNEP Framework for Forward RL](https://mlsanity.com/paper/2401.06566/) (2024)
- [Kernel Based Maximum Entropy Inverse Reinforcement Learning for Mean-Field Games](https://mlsanity.com/paper/2507.14529/) (2025)
- [A Mean Field Games approach for multi-lane traffic management](https://mlsanity.com/paper/1711.04116/) (2017)
- [Stabilizing Traffic via Autonomous Vehicles: A Continuum Mean Field Game Approach](https://mlsanity.com/paper/1906.01554/) (2019)
- [Operator Learning for Families of Finite-State Mean-Field Games](https://mlsanity.com/paper/2602.13169/) (2026)
- [Behavioral patterns and mean-field games in epidemiological models](https://mlsanity.com/paper/2512.20547/) (2025)
- [Modeling Epidemic Spread with Strategic Vaccination and Socialization: a Mean Field Game Analysis](https://mlsanity.com/paper/2604.22946/) (2026)

## Abstract (arXiv)

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.