Before revision:  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 and Hessian from noisy objective function evaluations, based on a Riemannian version of the Gaussian smoothing technique.
After revision:  In this paper, we consider stochastic zeroth-order optimization over Riemannian submanifolds embedded in an Euclidean space, where the task is to solve Riemannian optimization problem with only noisy objective function evaluations. Towards this, our main contribution is to propose estimators of the Riemannian gradient and Hessian from noisy objective function evaluations, based on a Riemannian version of the Gaussian smoothing technique.