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Register a new userMinibatch vs Local SGD for Heterogeneous Distributed Learning
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Blake Woodworth
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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We analyze Local SGD (aka parallel or federated SGD) and Minibatch SGD in the heterogeneous distributed setting, where each machine has access to stochastic gradient estimates for a different, machine-specific, convex objective; the goal is to optimize w.r.t. the average objective; and machines can only communicate intermittently. We argue that, (i) Minibatch SGD (even without acceleration) dominates all existing analysis of Local SGD in this setting, (ii) accelerated Minibatch SGD is optimal when the heterogeneity is high, and (iii) present the first upper bound for Local SGD that improves over Minibatch SGD in a non-homogeneous regime.
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We study local SGD (also known as parallel SGD and federated averaging), a natural and frequently used stochastic distributed optimization method. Its theoretical foundations are currently lacking and we highlight how all existing error guarantees in the convex setting are dominated by a simple baseline, minibatch SGD. (1) For quadratic objectives we prove that local SGD strictly dominates minibatch SGD and that accelerated local SGD is minimax optimal for quadratics; (2) For general convex objectives we provide the first guarantee that at least sometimes improves over minibatch SGD; (3) We show that indeed local SGD does not dominate minibatch SGD by presenting a lower bound on the performance of local SGD that is worse than the minibatch SGD guarantee.
Gradient quantization is an emerging technique in reducing communication costs in distributed learning. Existing gradient quantization algorithms often rely on engineering heuristics or empirical observations, lacking a systematic approach to dynamically quantize gradients. This paper addresses this issue by proposing a novel dynamically quantized SGD (DQ-SGD) framework, enabling us to dynamically adjust the quantization scheme for each gradient descent step by exploring the trade-off between communication cost and convergence error. We derive an upper bound, tight in some cases, of the convergence error for a restricted family of quantization schemes and loss functions. We design our DQ-SGD algorithm via minimizing the communication cost under the convergence error constraints. Finally, through extensive experiments on large-scale natural language processing and computer vision tasks on AG-News, CIFAR-10, and CIFAR-100 datasets, we demonstrate that our quantization scheme achieves better tradeoffs between the communication cost and learning performance than other state-of-the-art gradient quantization methods.
There is an increasing realization that algorithmic inductive biases are central in preventing overfitting; empirically, we often see a benign overfitting phenomenon in overparameterized settings for natural learning algorithms, such as stochastic gradient descent (SGD), where little to no explicit regularization has been employed. This work considers this issue in arguably the most basic setting: constant-stepsize SGD (with iterate averaging) for linear regression in the overparameterized regime. Our main result provides a sharp excess risk bound, stated in terms of the full eigenspectrum of the data covariance matrix, that reveals a bias-variance decomposition characterizing when generalization is possible: (i) the variance bound is characterized in terms of an effective dimension (specific for SGD) and (ii) the bias bound provides a sharp geometric characterization in terms of the location of the initial iterate (and how it aligns with the data covariance matrix). We reflect on a number of notable differences between the algorithmic regularization afforded by (unregularized) SGD in comparison to ordinary least squares (minimum-norm interpolation) and ridge regression.
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 the 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.
Hogwild! implements asynchronous Stochastic Gradient Descent (SGD) where multiple threads in parallel access a common repository containing training data, perform SGD iterations and update shared state that represents a jointly learned (global) model. We consider big data analysis where training data is distributed among local data sets in a heterogeneous way -- and we wish to move SGD computations to local compute nodes where local data resides. The results of these local SGD computations are aggregated by a central aggregator which mimics Hogwild!. We show how local compute nodes can start choosing small mini-batch sizes which increase to larger ones in order to reduce communication cost (round interaction with the aggregator). We improve state-of-the-art literature and show $O(sqrt{K}$) communication rounds for heterogeneous data for strongly convex problems, where $K$ is the total number of gradient computations across all local compute nodes. For our scheme, we prove a textit{tight} and novel non-trivial convergence analysis for strongly convex problems for {em heterogeneous} data which does not use the bounded gradient assumption as seen in many existing publications. The tightness is a consequence of our proofs for lower and upper bounds of the convergence rate, which show a constant factor difference. We show experimental results for plain convex and non-convex problems for biased (i.e., heterogeneous) and unbiased local data sets.
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