Direct policy search has been widely applied in modern reinforcement learning and continuous control. However, the performance of direct policy search on nonsmooth robust control synthesis has not been well understood. The optimal ℋ_∞ control framework aims at designing a policy to minimize the closed-loop ℋ_∞ norm, and is arguably the most important robust control paradigm. In this work, we show that direct policy search is guaranteed to find the global solution of the robust ℋ_∞ state-feedback…