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.
After revision:  In this paper, we consider stochastic zeroth-order optimization over Riemannian submanifolds embedded in Euclidean space, an important but less studied area, and propose four algorithms for solving this class of problems under different settings.