2024/06/26 by Roula Nassif, Stefan Vlaski, Nassif, Roula +7 · 2 citations
Computer Science · #Distributed Control Multi-Agent Systems #Distributed Sensor Networks and Detection Algorithms #FOS: Computer and information sciences #FOS: Electrical engineering #Machine Learning (cs.LG) #Multiagent Systems (cs.MA) #Neural Networks and Applications #Signal Processing (eess.SP) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2406.18418
openalex publication_date 2024/06/26 · openalex created_date 2024/06/28 · openalex updated_date 2026/07/28
Communication-constrained algorithms for decentralized learning and optimization rely on local updates coupled with the exchange of compressed signals. In this context, differential quantization is an effective technique to mitigate the negative impact of compression by leveraging correlations between successive iterates. In addition, the use of error feedback, which consists of incorporating the compression error into subsequent steps, is a powerful mechanism to compensate for the bias caused by the compression. Under error feedback, performance guarantees in the literature have so far focused on algorithms employing a fusion center or a special class of contractive compressors that cannot be implemented with a finite number of bits. In this work, we propose a new decentralized communication-efficient learning approach that blends differential quantization with error feedback. The approach is specifically tailored for decentralized learning problems where agents have individual risk functions to minimize subject to subspace constraints that require the minimizers across the network to lie in low-dimensional subspaces. This constrained formulation includes consensus or single-task optimization as special cases, and allows for more general task relatedness models such as multitask smoothness and coupled optimization. We show that, under some general conditions on the compression noise, and for sufficiently small step-sizes μ, the resulting communication-efficient strategy is stable both in terms of mean-square error and average bit rate: by reducing μ, it is possible to keep the estimation errors small (on the order of μ) without increasing indefinitely the bit rate as μ→ 0. The results establish that, in the small step-size regime and with a finite number of bits, it is possible to attain the performance achievable in the absence of compression.
DeepSqueeze: Decentralization Meets Error-Compensated Compression