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1. SQuARM-SGD: Communication-Efficient Momentum SGD for Decentralized Optimization

   Singh, Navjot ; Data, Deepesh ; George, Jemin ; Diggavi, Suhas N. ( July 2021 , IEEE International Symposium on Information Theory (ISIT))

   null (Ed.)

   In this paper, we study communication-efficient decentralized training of large-scale machine learning models over a network. We propose and analyze SQuARM-SGD, a decentralized training algorithm, employing momentum and compressed communication between nodes regulated by a locally computable triggering rule. In SQuARM-SGD, each node performs a fixed number of local SGD (stochastic gradient descent) steps using Nesterov's momentum and then sends sparisified and quantized updates to its neighbors only when there is a significant change in its model parameters since the last time communication occurred. We provide convergence guarantees of our algorithm for strongly-convex and non-convex smooth objectives. We believe that ours is the first theoretical analysis for compressed decentralized SGD with momentum updates. We show that SQuARM-SGD converges at rate O(1/nT) for strongly-convex objectives, while for non-convex objectives it converges at rate O(1/√nT), thus matching the convergence rate of \emphvanilla distributed SGD in both these settings. We corroborate our theoretical understanding with experiments and compare the performance of our algorithm with the state-of-the-art, showing that without sacrificing much on the accuracy, SQuARM-SGD converges at a similar rate while saving significantly in total communicated bits. 

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2. Cooperative SGD: A Unified Framework for the Design and Analysis of Local-Update SGD Algorithms

   Wang, Jianyu ; Joshi, Gauri ( January 2021 , Journal of machine learning research)

   When training machine learning models using stochastic gradient descent (SGD) with a large number of nodes or massive edge devices, the communication cost of synchronizing gradients at every iteration is a key bottleneck that limits the scalability of the system and hinders the benefit of parallel computation. Local-update SGD algorithms, where worker nodes perform local iterations of SGD and periodically synchronize their local models, can effectively reduce the communication frequency and save the communication delay. In this paper, we propose a powerful framework, named Cooperative SGD, that subsumes a variety of local-update SGD algorithms (such as local SGD, elastic averaging SGD, and decentralized parallel SGD) and provides a unified convergence analysis. Notably, special cases of the unified convergence analysis provided by the cooperative SGD framework yield 1) the first convergence analysis of elastic averaging SGD for general non-convex objectives, and 2) improvements upon previous analyses of local SGD and decentralized parallel SGD. Moreover, we design new algorithms such as elastic averaging SGD with overlapped computation and communication, and decentralized periodic averaging which are shown to be 4x or more faster than the baseline in reaching the same training loss. 

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3. Overlap Local-SGD: An Algorithmic Approach to Hide Communication Delays in Distributed SGD

   https://doi.org/10.1109/ICASSP40776.2020.9053834  

   Wang, Jianyu ; Liang, Hao ; Joshi, Gauri ( May 2020 , IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP))

   null (Ed.)

   Distributed stochastic gradient descent (SGD) is essential for scaling the machine learning algorithms to a large number of computing nodes. However, the infrastructures variability such as high communication delay or random node slowdown greatly impedes the performance of distributed SGD algorithm, especially in a wireless system or sensor networks. In this paper, we propose an algorithmic approach named Overlap Local-SGD (and its momentum variant) to overlap communication and computation so as to speedup the distributed training procedure. The approach can help to mitigate the straggler effects as well. We achieve this by adding an anchor model on each node. After multiple local updates, locally trained models will be pulled back towards the synchronized anchor model rather than communicating with others. Experimental results of training a deep neural network on CIFAR-10 dataset demonstrate the effectiveness of Overlap Local-SGD. We also provide a convergence guarantee for the proposed algorithm under non-convex objective functions. 

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4. On the Convergence of Communication-Efficient Local SGD for Federated Learning

   Hongchang Gao, An Xu ( February 2021 , 35th AAAI Conference on Artificial Intelligence (AAAI 2021))

   Federated Learning (FL) has attracted increasing attention in recent years. A leading training algorithm in FL is local SGD, which updates the model parameter on each worker and averages model parameters across different workers only once in a while. Although it has fewer communication rounds than the classical parallel SGD, local SGD still has large communication overhead in each communication round for large machine learning models, such as deep neural networks. To address this issue, we propose a new communicationefficient distributed SGD method, which can significantly reduce the communication cost by the error-compensated double compression mechanism. Under the non-convex setting, our theoretical results show that our approach has better communication complexity than existing methods and enjoys the same linear speedup regarding the number of workers as the full-precision local SGD. Moreover, we propose a communication-efficient distributed SGD with momentum, which also has better communication complexity than existing methods and enjoys a linear speedup with respect to the number of workers. At last, extensive experiments are conducted to verify the performance of our proposed methods. 

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5. Distributed Optimization over Time-Varying Networks: Imperfect Information with Feedback is as Good as Perfect Information

   https://doi.org/10.23919/ACC53348.2022.9867680  

   Reisizadeh, Hadi ; Touri, Behrouz ; Mohajer, Soheil ( January 2022 , 2022 American Control Conference (ACC))

   The convergence of an error-feedback algorithm is studied for decentralized stochastic gradient descent (DSGD) algorithm with compressed information sharing over time-varying graphs. It is shown that for both strongly-convex and convex cost functions, despite of imperfect information sharing, the convergence rates match those with perfect information sharing. To do so, we show that for strongly-convex loss functions, with a proper choice of a step-size, the state of each node converges to the global optimizer at the rate of O(T^{−1}). Similarly, for general convex cost functions, with a proper choice of step-size, we show that the value of loss function at a temporal average of each node’s estimates converges to the optimal value at the rate of O(T^{−1/2+ϵ }) for any ϵ > 0. 

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