Before revision: We propose and analyze zeroth-order algorithms for optimization over Riemannian manifolds, where we observe only potentially noisy evaluations of the objective function. Our approach is based on estimating the Riemannian gradient from the objective function evaluations .
After revision: We propose and analyze zeroth-order optimization concerns problems where only noisy function evaluations are available. Such problems arises frequently in many important applications. In this paper, we consider stochastic zeroth-order optimization over Riemannian submanifolds embedded in an Euclidean space, an important but less studied area, and propose four algorithms for solving this class of problems under different settings. Our algorithms are based on estimating the Riemannian gradient from the objective function evaluations .