Optimal Algorithms for Nonsmooth Nonconvex Stochastic Optimization with Constraints
The paper presents new algorithms for solving nonsmooth, nonconvex optimization problems subject to convex constraints where traditional smooth or convex methods fail. It introduces optimal first-order and zeroth-order stochastic algorithms that achieve best possible convergence rates under various settings. The results show that the complexity is not worsened by the lack of smoothness or convexity when dealing with constraints.