There has been substantial recent progress on the theoretical understanding of model-free approaches to Linear Quadratic Regulator (LQR) problems. Much attention has been devoted to the special case when the goal is to drive the state close to a zero target. In this work, we consider the general case where the target is allowed to be arbitrary, which we refer to as the LQR tracking problem. We study the optimization landscape of this problem, and show that similar to the zero-target LQR problem, the LQR tracking problem also satisfies gradient dominance and local smoothness properties. This allows us to develop a zeroth-order policy gradient algorithm that achieves global convergence. We support our arguments with numerical simulations on a linear system.
Asynchronous Distributed Reinforcement Learning for LQR Control via Zeroth-Order Block Coordinate Descent
Chongqing University（重庆大学）；North Carolina State University（北卡罗来纳州立大学）；Oklahoma State University（俄克拉荷马州立大学）；DEVCOM Army Research Laboratory（DEVCOM陆军研究实验室）
Harnessing Data from Clustered LQR Systems: Personalized and Collaborative Policy Optimization
Department of Electrical and Computer Engineering（电气与计算机工程系）；North Carolina State University（北卡罗来纳州立大学）；The Elmore Family School of Electrical and Computer Engineering（埃尔莫尔家族电气与计算机工程学院）；Purdue University（普渡大学）
Zeroth-Order Actor-Critic: An Evolutionary Framework for Sequential Decision Problems
The University of Hong Kong（香港大学）；Tsinghua University（清华大学）；SunRising AI Ltd.（森瑞昇人工智能有限公司）；Institute for Interdisciplinary Information Sciences, Tsinghua University（清华大学交叉信息研究院）；Shanghai Qi Zhi Institute（上海期智研究院）
Distributed Zeroth-Order Optimization with Rademacher Perturbations and Momentum Gradient Tracking
School of Artificial Intelligence, Anhui University（安徽大学人工智能学院）；Engineering Research Center of Autonomous Unmanned System Technology, Ministry of Education（教育部无人系统技术工程研究中心）
Multi-objective LQR with Optimum Weight Selection to Design FOPID Controllers for Delayed Fractional Order Processes
School of Electronics and Computer Science, University of Southampton（南安普顿大学电子与计算机科学学院）；Department of Power Engineering, Jadavpur University（贾达普大学动力工程系）；Department of Earth Science and Engineering, Imperial College London（帝国理工学院地球科学与工程系）；Reactor Control Division, Bhabha Atomic Research Centre（巴哈原子研究中心反应堆控制部）
Forgetting-Factor Regret for Online Zero-Sum Games
Peking University（北京大学）；Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）；University of Chinese Academy of Sciences（中国科学院大学）
