Improving the Worst-Case Bidirectional Communication Complexity for Nonconvex Distributed Optimization Under Function Similarity
Abstract: Effective communication between the server and workers plays a key role in distributed optimization. In this paper, we focus on optimizing the server-to-worker communication, uncovering inefficiencies in prevalent downlink compression approaches.
Considering first the pure setup where the uplink communication costs are negligible, we introduce MARINA-P, a novel method for downlink compression, employing a collection of correlated compressors. Theoretical analysis demonstrates that MARINA-P with permutation compressors can achieve a server-to-worker communication complexity improving with the number of workers, thus being provably superior to existing algorithms.
We further show that MARINA-P can serve as a starting point for extensions such as methods supporting bidirectional compression. We introduce M3, a method combining MARINA-P with uplink compression and a momentum step, achieving bidirectional compression with provable improvements in total communication complexity as the number of workers increases. Theoretical findings align closely with empirical experiments, underscoring the efficiency of the proposed algorithms.
Bio: Kaja Gruntkowska is a Ph.D. student in Optimization for Machine Learning at King Abdullah University of Science and Technology. She completed her bachelor’s in Mathematics and Statistics at the University of Warwick and earned a master’s in Statistical Science from the University of Oxford.
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