Work

Truncated Differentiation Through Primal-Dual Solvers for Inverse Potential Mean-Field Games

Year: 2026

Type: preprint

Abstract: We study inverse potential mean-field games (MFGs), in which an unknown spatial inverse-cost (mobility) map is inferred from observed population densities. We solve the forward MFG with a preconditioned primal-dual hybrid gradient (PDHG) method and develop Jacobian-free backpropagation (JFB-$r$), which records only the final $r$ iterations from a detached warm start while retaining the full forward solve. To analyze this truncated differentiation method, we show that the exact-proximal dual-extrapolated PDHG map is a metric resolvent of the maximal monotone KKT operator. This resolvent view shows that JFB-$r$ exactly differentiates a finite-trajectory surrogate and, under a locally fixed active set at an exact equilibrium detach point, converges to the implicit gradient as the tracked depth increases. Across several inverse-MFG settings, numerical experiments show that JFB-r at moderate tracked depths can achieve recovery accuracy comparable to full unrolling while reducing memory and runtime.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2608.00217

Authors: Liu, Siting, Chow, Yat Tin, Fung, Samy Wu

Institutions: University of California, Riverside, Colorado School of Mines

Topic: Optimization and Variational Analysis

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Office of Naval Research

Awards: G4353487559, Development of novel numerical methods for forward and inverse problems in mean field games, Optimization-based Implicit Deep Learning, Theory and Applications, G8876996369

OpenAlex ID: W7172376945

Cites:

Cited by:

Related to: