Infinite-Horizon Inverse Linear-Quadratic Differential Games with State- and Control-Dependent Noise

What the math gives to ML

The paper provides a constructive inverse mechanism for stochastic linear-quadratic Nash equilibria: once equilibrium feedback gains are observed, the compatible state and control cost parameters lie in an explicitly computable kernel intersected with admissibility constraints. The transferable asset is an identifiability certificate: equilibrium behavior generally determines a family of objectives rather than a unique objective, and the dimension of that family can be measured by a nullspace calculation. In neural networks, this can be adapted to infer or constrain local quadratic loss metrics and optimizer preconditioners from observed parameter-update trajectories, while explicitly exposing which curvature directions are unidentifiable.