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No Spurious Local Minima in Full-Order Linear Quadratic Gaussian Control
Yang Zheng, Yujie Tang
This paper studies the nonconvex optimization landscape of Linear Quadratic Gaussian (LQG) control under direct state-space parameterization. Although the LQG cost may possess subo…
Policy Optimization of Mixed H2/H-infinity Control: Benign Nonconvexity and Global Optimality
Chih-Fan Pai, Yuto Watanabe, Yujie Tang +1
Mixed H2/H-infinity control balances performance and robustness by minimizing an H2 cost bound subject to an H-infinity constraint. However, classical Riccati/LMI solutions offer l…
Semidefinite Programming Duality in Infinite-Horizon Linear Quadratic Differential Games
Yuto Watanabe, Chih-Fan Pai, Yang Zheng
Semidefinite programs (SDPs) play a crucial role in control theory, traditionally as a computational tool. Beyond computation, the duality theory in convex optimization also provid…
Revisiting Strong Duality, Hidden Convexity, and Gradient Dominance in the Linear Quadratic Regulator
Yuto Watanabe, Yang Zheng
The Linear Quadratic Regulator (LQR) is a cornerstone of optimal control theory, widely studied in both model-based and model-free approaches. Despite its well-established nature,…
Benign Nonconvex Landscapes in Optimal and Robust Control, Part II: Extended Convex Lifting
Yang Zheng, Chih-Fan Pai, Yujie Tang
Many optimal and robust control problems are nonconvex and potentially nonsmooth in their policy optimization forms. In Part II of this paper, we introduce a new and unified Extend…
Benign Nonconvex Landscapes in Optimal and Robust Control, Part I: Global Optimality
Yang Zheng, Chih-fan Pai, Yujie Tang
Direct policy search has achieved great empirical success in reinforcement learning. Many recent studies have revisited its theoretical foundation for continuous control, which rev…