Online learning of nonlinear parametric models under non-smooth regularization using EKF and ADMM

This paper proposes a novel combination of extended Kalman filtering (EKF) with the alternating direction method of multipliers (ADMM) for learning parametric nonlinear models online under non-smooth regularization terms, including ℓ1 and ℓ0 penalties and bound constraints on model parameters. For the case of linear time-varying models and non-smooth convex regularization terms, we provide a sublinear regret bound that ensures the proper behavior of the online learning strategy. The approach is computationally efficient for a wide range of regularization terms, which makes it appealing for its use in embedded control applications for online model adaptation. We show the performance of the proposed method in three simulation examples, highlighting its effectiveness compared to other batch and online algorithms.