Extended stochastic derivative-free optimization on riemannian manifolds

In this work we study the generalization of Stochastic Derivative-Free Optimization (SDFO) algorithms from Euclidean spaces to Riemannian manifolds. In the literature, Riemannian adaptations of SDFO relies on the Riemannian exponential map, which imposes local restrictions. We aim to address this restriction using only the intrinsic geometry of the Riemannian manifold.