2023/07/16 by Heng Zhu, Zhu, Heng, Avishek Ghosh +3
Computer Science · Engineering · #Distributed #FOS: Computer and information sciences #Information Theory (cs.IT) #Machine Learning (cs.LG) #Parallel #Sparse and Compressive Sensing Techniques #Stochastic Gradient Optimization Techniques #Wireless Communication Security Techniques #and Cluster Computing (cs.DC)
paper · pdf · doi:10.48550/arxiv.2307.07941
openalex publication_date 2023/07/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Motivated by the need for communication-efficient distributed learning, we investigate the method for compressing a unit norm vector into the minimum number of bits, while still allowing for some acceptable level of distortion in recovery. This problem has been explored in the rate-distortion/covering code literature, but our focus is exclusively on the "high-distortion" regime. We approach this problem in a worst-case scenario, without any prior information on the vector, but allowing for the use of randomized compression maps. Our study considers both biased and unbiased compression methods and determines the optimal compression rates. It turns out that simple compression schemes are nearly optimal in this scenario. While the results are a mix of new and known, they are compiled in this paper for completeness.