Reviews: Regret Bounds for Robust Adaptive Control of the Linear Quadratic Regulator

The central element of the paper is a (novel) algorithm that utilizes a convex optimization approach (the so-called System Level Synthesis approach, SLS) for synthesizing LQR controllers using estimated dynamics models. The SLS approach allows for an analysis of how the error in the matrix estimation affects the regret of the LQR controller. Using this controller synthesis, upper bounds on the estimation error of the dynamics matrices as well as upper and lower bounds for the expected loss are provided. The method is compared to existing approaches on a benchmark system. This computational study shows a comparable performance of all methods, with the presented method giving the nicest theoretical guarantees (e.g.