Adaptive Proximal Methods for Weakly Convex Optimization with Unknown Parameter: Deterministic and Stochastic Guarantees (opens in new tab)

Many nonsmooth, nonconvex objectives in learning and signal recovery are $\rho$-weakly convex. We minimize such a function in deterministic and stochastic settings when the weak-convexity parameter $\rho$ is unknown. The objective is not required to be globally Lipschitz continuous or smooth. We propose the Adaptive Prox-Guided Scheme (APS), a one-trial proximal algorithm that adapts the proximal parameter online and bidirectionally through a ...