A Tight Theory of Error Feedback Algorithms in Distributed Optimization
2026-05-29 • Machine Learning
Machine Learning
AI summaryⓘ
The authors study ways to reduce communication costs in distributed learning by compressing the information shared between agents. They focus on two error feedback methods, EF and EF21, which help fix problems caused by compression. By carefully analyzing these methods, the authors find the best step sizes and mathematical tools to prove how well they work. Their results apply regardless of how many agents are involved and match the best known results when there is only one agent.
distributed learninggradient compressionerror feedbackEF methodEF21 methodconvergence analysisstep sizeLyapunov functionfirst-order optimizationcommunication cost
Authors
Daniel Berg Thomsen, Adrien Taylor, Aymeric Dieuleveut
Abstract
Communication costs are a major bottleneck in distributed learning and first-order optimization. A common approach to alleviate this issue is to compress the gradient information exchanged between agents. However, such compression typically degrades the convergence guarantees of gradient-based methods. Error feedback mechanisms provide a simple and computationally cheap remedy for this issue, but numerous variants have been proposed, and their relative performance remains poorly understood. This paper provides tight convergence analyses for two of the main error-feedback algorithms from the literature, the classic Error Feedback method (EF) and Error Feedback 21 (EF21), by identifying optimal step-size choices and constructing optimal Lyapunov functions tailored to each method. The results hold independently of the number of agents and recover the known best guarantees possible in the single-agent regime.