Robust Analysis of Almost Sure Convergence of Zeroth-Order Mirror Descent Algorithm

This letter presents an almost sure convergence of the zeroth-order mirror descent (ZOMD) algorithm. The algorithm admits non-smooth convex functions and a biased oracle which only provides noisy function value at any desired point. We approximate subgradient objective using Nesterov’s Gaussian Approximation (NGA) with certain alternations suggested by some practical applications. prove iterates’ to neighbourhood optimal value, can not be made arbitrarily small, manifestation oracle. ends concentration inequality, is finite time analysis that predicts likelihood iterates in iteration.