Nonconvex Federated Learning on Compact Smooth Submanifolds With Heterogeneous Data
CoRR(2024)
摘要
Many machine learning tasks, such as principal component analysis and
low-rank matrix completion, give rise to manifold optimization problems.
Although there is a large body of work studying the design and analysis of
algorithms for manifold optimization in the centralized setting, there are
currently very few works addressing the federated setting. In this paper, we
consider nonconvex federated learning over a compact smooth submanifold in the
setting of heterogeneous client data. We propose an algorithm that leverages
stochastic Riemannian gradients and a manifold projection operator to improve
computational efficiency, uses local updates to improve communication
efficiency, and avoids client drift. Theoretically, we show that our proposed
algorithm converges sub-linearly to a neighborhood of a first-order optimal
solution by using a novel analysis that jointly exploits the manifold structure
and properties of the loss functions. Numerical experiments demonstrate that
our algorithm has significantly smaller computational and communication
overhead than existing methods.
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