Self-Identifying Internal Model-Based Online Optimization
Wouter J. A. van Weerelt, Lantian Zhang, Silun Zhang, Nicola Bastianello
TL;DR
The paper addresses online optimization with time-varying costs by introducing SIMBO, a two-phase method that first collects data via online gradient descent and then uses a self-identified internal dynamics model to implement a control-based optimizer. It combines Recursive Least Squares system identification with a structured controller to learn the internal model on the fly and switch from data-driven updates to model-based control as the model converges, enabling adaptation to changes in the problem. The main contributions are the SIMBO algorithm, a convergence analysis for quadratic costs, and extensive numerical validation showing robust tracking and adaptability even under model changes and time-varying Hessians. This approach reduces reliance on prior internal-model knowledge and offers practical benefits for tracking in non-stationary online optimization settings.
Abstract
In this paper, we propose a novel online optimization algorithm built by combining ideas from control theory and system identification. The foundation of our algorithm is a control-based design that makes use of the internal model of the online problem. Since such prior knowledge of this internal model might not be available in practice, we incorporate an identification routine that learns this model on the fly. The algorithm is designed starting from quadratic online problems but can be applied to general problems. For quadratic cases, we characterize the asymptotic convergence to the optimal solution trajectory. We compare the proposed algorithm with existing approaches, and demonstrate how the identification routine ensures its adaptability to changes in the underlying internal model. Numerical results also indicate strong performance beyond the quadratic setting.