Differential Error Feedback for Communication-Efficient Decentralized Learning
Roula Nassif, Stefan Vlaski, Marco Carpentiero, Vincenzo Matta, Ali H. Sayed · IEEE Transactions on Signal Processing · 2025
Communication-constrained algorithms for decentralized learning and optimization rely on local updates coupled with the exchange of compressed signals. In this context,differential quantizationis an effective technique to mitigate the negative impact of compression by leveraging correlations between successive iterates. In addition, the use oferror 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 newdecentralizedcommunication-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-sizesμ, the resulting communication-efficient strategy is stable both in terms of mean-square error and average bit rate: by reducingμ, it is possible to keep theestimation errors small (on the order ofμ) without increasing indefinitely the bit rate asμ→ 0. The results establish that, in thesmall step-size regimeand with afinite number of bits, it is possible to attain the performance achievable in the absence of compression.