Online Linear Quadratic Regulator

Online Linear Quadratic Regulator (LQR) research focuses on designing control strategies for systems with dynamically changing cost functions, aiming to minimize cumulative error over time. Current work emphasizes developing algorithms with strong theoretical guarantees, such as regret bounds, often employing techniques like optimistic online optimization and manifold optimization to handle constraints or improve efficiency. These advancements are significant for applications requiring adaptive control in uncertain environments, such as robotics and autonomous systems, by enabling more robust and efficient control policies in the face of unpredictable changes. The development of sample-efficient methods and the exploration of multi-task learning further enhance the applicability and scalability of online LQR solutions.