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Title: Correlation Aware Sparsified Mean Estimation Using Random Projection
We study the problem of communication-efficient distributed vector mean estimation, which is a commonly used subroutine in distributed optimization and Federated Learning (FL). Rand-k sparsification is a commonly used technique to reduce communication cost, where each client sends of its coordinates to the server. However, Rand-k is agnostic to any correlations, that might exist between clients in practical scenarios. The recently proposed Rand-k-Spatial estimator leverages the cross-client correlation information at the server to improve Rand-k's performance. Yet, the performance of Rand-k-Spatial is suboptimal, and improving mean estimation is key to faster convergence in distributed optimization. We propose the Rand-Proj-Spatial estimator with a more flexible encoding-decoding procedure, which generalizes the encoding of Rand- by projecting the client vectors to a random k-dimensional subspace. We utilize Subsampled Randomized Hadamard Transform (SRHT) as the projection matrix and show that Rand-Proj-Spatial with SRHT outperforms Rand-k-Spatial, using the correlation information more efficiently. Furthermore, we propose an approach to incorporate varying degrees of correlation and suggest a practical variant of Rand-Proj-Spatial when the correlation information is not available to the server. Finally, experiments on real-world distributed optimization tasks showcase the superior performance of Rand-Proj-Spatial compared to Rand-k-Spatial and other more sophisticated sparsification techniques.  more » « less
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Publisher / Repository:
Proceedings on Machine Learning Research
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Journal Name:
Advances in neural information processing systems
Medium: X
Sponsoring Org:
National Science Foundation
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