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In decentralized optimization, it is common algorithmic practice to have nodes interleave (local) gradient descent iterations with gossip (i.e. averaging over the network) steps. Motivated by the training of large-scale machine learning models, it is also increasingly common to require that messages be {em lossy compresse
Decentralized optimization and communication compression have exhibited their great potential in accelerating distributed machine learning by mitigating the communication bottleneck in practice. While existing decentralized algorithms with communicat
A central question in federated learning (FL) is how to design optimization algorithms that minimize the communication cost of training a model over heterogeneous data distributed across many clients. A popular technique for reducing communication is
Various bias-correction methods such as EXTRA, gradient tracking methods, and exact diffusion have been proposed recently to solve distributed {em deterministic} optimization problems. These methods employ constant step-sizes and converge linearly to
Communication compression has become a key strategy to speed up distributed optimization. However, existing decentralized algorithms with compression mainly focus on compressing DGD-type algorithms. They are unsatisfactory in terms of convergence rat
Decentralized federated learning (DFL) is a powerful framework of distributed machine learning and decentralized stochastic gradient descent (SGD) is a driving engine for DFL. The performance of decentralized SGD is jointly influenced by communicatio