A projection-based zeroth-order federated learning algorithm on Riemannian manifolds achieves sublinear convergence with linear speedup, using only Euclidean random perturbations.
From the Greene--Wu Convolution to Gradient Estimation over Riemannian Manifolds
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abstract
Over a complete Riemannian manifold of finite dimension, Greene and Wu introduced a convolution, known as Greene-Wu (GW) convolution. In this paper, we study properties of the GW convolution and apply it to non-Euclidean machine learning problems. In particular, we derive a new formula for how the curvature of the space would affect the curvature of the function through the GW convolution. Also, following the study of the GW convolution, a new method for gradient estimation over Riemannian manifolds is introduced.
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Federated Learning on Riemannian Manifolds: A Gradient-Free Projection-Based Approach
A projection-based zeroth-order federated learning algorithm on Riemannian manifolds achieves sublinear convergence with linear speedup, using only Euclidean random perturbations.