LoDAdaC: a unified local training-based decentralized framework with adaptive gradients and compressed communication

In the decentralized distributed learning, achieving fast convergence and low communication cost is essential for scalability and high efficiency. Adaptive gradient methods, such as Adam, have demonstrated strong practical performance in deep learning and centralized distributed settings. However, their convergence properties remain largely unexplored in decentralized settings involving multiple local training steps, such as federated learning. To address this limitation, we propose LoDAdaC, a unified multiple Local Training (MLT) Decentralized framework with Adam-type updates and Compressed communication (CC). LoDAdaC accommodates a broad class of optimizers for its local adaptive updates, including AMSGrad, Adam, and AdaGrad; it is compatible with standard (possibly biased) compressors such as low-bit quantization and sparsification. MLT and CC enable LoDAdaC to achieve multiplied reduction of communication cost, while the technique of adaptive updates enables fast convergence. We rigorously prove the combined advantage through complexity analysis. In addition, experiments on image classification and GPT-style language model training validate our theoretical findings and show that LoDAdaC significantly outperforms existing decentralized algorithms in terms of convergence speed and communication efficiency.

Compressed Decentralized Momentum Stochastic Gradient Methods for Nonconvex Optimization

In this paper, we design two compressed decentralized algorithms for solving nonconvex stochastic optimization under two different scenarios. Both algorithms adopt a momentum technique to achieve fast convergence and a message-compression technique to save communication costs. Though momentum acceleration and compressed communication have been used in literature, it is highly nontrivial to theoretically prove the effectiveness of their composition in a decentralized algorithm that can maintain the benefits of both sides, because of the need to simultaneously control the consensus error, the compression error, and the bias from the momentum gradient. For the scenario where gradients are bounded, our proposal is a compressed decentralized adaptive method. To the best of our knowledge, this is the first decentralized adaptive stochastic gradient method with compressed communication. For the scenario of data heterogeneity without bounded gradients, our proposal is a compressed decentralized heavy-ball method, which applies a gradient tracking technique to address the challenge of data heterogeneity. Notably, both methods achieve an optimal convergence rate, and they can achieve linear speed up and adopt topology-independent algorithmic parameters within a certain regime of the user-specified error tolerance. Superior empirical performance is observed over state-of-the-art methods on training deep neural networks (DNNs) and Transformers.