Zeroth-Order Stochastic Compositional Algorithms for Risk-Aware Learning

We present Free-MESSAGEp, the first zeroth-order algorithm for convex mean-semideviation-based risk-aware learning, which is also three-level compositional stochastic optimization algorithm, whatsoever. Using a non-trivial extension of Nesterov's classical results on Gaussian smoothing, we develop Free-MESSAGEp from principles, and show that it essentially solves smoothed surrogate to original problem, former being uniform approximation latter, in useful, convenient sense. then complete analysis establishes convergence user-tunable neighborhood optimal solutions as well explicit rates both strongly costs. Orderwise, fixed problem parameters, our demonstrate no sacrifice speed compared existing first-order methods, while striking certain balance among condition its dimensionality, accuracy obtained results, naturally extending previous risk-neutral learning.