Regularized Model Predictive Control via Contractivity and Implicit Lur'e Analysis

What the math gives to ML

The paper's transferable asset is a certificate for making an implicitly defined feedback map contractive in a non-Euclidean metric, rather than merely penalizing parameter norms or spectral radii. This can be transplanted to recurrent, state-space, and latent world-model transitions by constraining the one-step Jacobian of the learned state update, yielding bounded sensitivity to initialization and perturbations. The most practical first implementation is a sampled Jacobian contraction regularizer with a fixed or learned positive-definite metric P; the full multiplier/Lur'e machinery could later support nonsmooth or implicit neural blocks. The likely benefit is improved long-horizon stability and less exploding sensitivity, at the cost of potentially reducing dynamical expressivity.