Statistical Reinforcement Learning: Adaptive Control of LQ Systems

Instructor: Nan Jiang

Reproduced and analyzed the core results of “Regret Bounds for the Adaptive Control of Linear Quadratic Systems” by Abbasi-Yadkori and Szepesvári. The work presents key theorems, lemmas, and an algorithm for solving Linear Quadratic (LQ) control problems with unknown model parameters — commonly referred to as adaptive control — aiming to minimize regret. The proposed algorithm estimates parameters using high-probability confidence sets and achieves a regret bound of $\tilde{O}(\sqrt{T})$.