On Regularized System Identification from a Martingale Distributional Robustness Perspective

In this work, we propose a novel martingale-based distributionally robust regression (MDRR) approach to system identification of uncertain dynamical systems. Under data uncertainty, the ridge regression offers a useful remedy, which can be interpreted as a min-max problem through the lens of distributionally robust optimization. However, ignoring the specific structural properties, RR amounts to robustifying against unrealistic perturbations with evident dynamics and thus leads to over-conservatism. By considering the Hankel structure of uncertainty and incorporating martingale constraints into the Wasserstein ambiguity set, the realistic data perturbation pattern can be Effectively captured, and this helps to considerably alleviate the conservatism. The induced min-max problem is solved by a subgradient-based algorithm. Empirical results on both simulation and real-world datasets validate the Effectiveness of MDRR, showcasing its out-performance over generic regression models and ease of parameter calibration.