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

What the math gives to ML

The paper provides a practical way to differentiate through a converged constrained optimization solver without storing its entire trajectory. Its key asset is the separation between the full forward solve and a short backward trace: detach a warm-started iterate and retain only the final r primal-dual updates, yielding an exact gradient of a finite-trajectory surrogate while approaching the implicit equilibrium gradient as r grows under a locally fixed active set. This is directly transferable to neural networks containing optimization layers, differentiable physics modules, optimal transport blocks, resource-allocation layers, and constrained latent inference. The most promising experiment is to replace full unrolling in a primal-dual optimization layer with JFB-r and measure gradient fidelity, memory, runtime, and downstream task accuracy as r varies.