Self-Identifying Internal Model-Based Online Optimization

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.