Towards Understanding the Generalizability of Delayed Stochastic Gradient Descent

• URL: http://arxiv.org/abs/2308.09430v2
• Date: Mon, 18 Dec 2023 03:09:54 GMT
• Title: Towards Understanding the Generalizability of Delayed Stochastic Gradient Descent
• Authors: Xiaoge Deng, Li Shen, Shengwei Li, Tao Sun, Dongsheng Li, and Dacheng Tao
• Abstract summary: A gradient descent performed in an asynchronous manner plays a crucial role in training large-scale machine learning models. Existing generalization error bounds are rather pessimistic and cannot reveal the correlation between asynchronous delays and generalization. Our theoretical results indicate that asynchronous delays reduce the generalization error of the delayed SGD algorithm.
• Score: 63.43247232708004
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Stochastic gradient descent (SGD) performed in an asynchronous manner plays a crucial role in training large-scale machine learning models. However, the generalization performance of asynchronous delayed SGD, which is an essential metric for assessing machine learning algorithms, has rarely been explored. Existing generalization error bounds are rather pessimistic and cannot reveal the correlation between asynchronous delays and generalization. In this paper, we investigate sharper generalization error bound for SGD with asynchronous delay $\tau$. Leveraging the generating function analysis tool, we first establish the average stability of the delayed gradient algorithm. Based on this algorithmic stability, we provide upper bounds on the generalization error of $\tilde{\mathcal{O}}(\frac{T-\tau}{n\tau})$ and $\tilde{\mathcal{O}}(\frac{1}{n})$ for quadratic convex and strongly convex problems, respectively, where $T$ refers to the iteration number and $n$ is the amount of training data. Our theoretical results indicate that asynchronous delays reduce the generalization error of the delayed SGD algorithm. Analogous analysis can be generalized to the random delay setting, and the experimental results validate our theoretical findings.

Related papers

• Distributed Stochastic Gradient Descent with Staleness: A Stochastic Delay Differential Equation Based Framework [56.82432591933544]
  Distributed gradient descent (SGD) has attracted considerable recent attention due to its potential for scaling computational resources, reducing training time, and helping protect user privacy in machine learning. This paper presents the run time and staleness of distributed SGD based on delay differential equations (SDDEs) and the approximation of gradient arrivals. It is interestingly shown that increasing the number of activated workers does not necessarily accelerate distributed SGD due to staleness.
  arXiv  Detail & Related papers  (2024-06-17T02:56:55Z)
• Stochastic Approximation with Delayed Updates: Finite-Time Rates under Markovian Sampling [73.5602474095954]
  We study the non-asymptotic performance of approximation schemes with delayed updates under Markovian sampling. Our theoretical findings shed light on the finite-time effects of delays for a broad class of algorithms.
  arXiv  Detail & Related papers  (2024-02-19T03:08:02Z)
• Sharper Convergence Guarantees for Asynchronous SGD for Distributed and Federated Learning [77.22019100456595]
  We show a training algorithm for distributed computation workers with varying communication frequency. In this work, we obtain a tighter convergence rate of $mathcalO!!!(sigma2-2_avg!! . We also show that the heterogeneity term in rate is affected by the average delay within each worker.
  arXiv  Detail & Related papers  (2022-06-16T17:10:57Z)
• Asynchronous SGD Beats Minibatch SGD Under Arbitrary Delays [8.46491234455848]
  We prove much better guarantees for the same asynchronous gradient regardless of the delays in steps, depending instead just on the number of steps. For our analysis, we introduce a novel based on "virtual steps" and delay iterations, which allow us to derive state-of-the-art guarantees for both convex non-adaptive gradients.
  arXiv  Detail & Related papers  (2022-06-15T16:28:37Z)
• Distributed stochastic optimization with large delays [59.95552973784946]
  One of the most widely used methods for solving large-scale optimization problems is distributed asynchronous gradient descent (DASGD) We show that DASGD converges to a global optimal implementation model under same delay assumptions.
  arXiv  Detail & Related papers  (2021-07-06T21:59:49Z)
• Guided parallelized stochastic gradient descent for delay compensation [0.0]
  gradient descent (SGD) algorithm and its variations have been effectively used to optimize neural network models. With the rapid growth of big data and deep learning, SGD is no longer the most suitable choice due to its natural behavior of sequential optimization of the error function. This has led to the development of parallel SGD algorithms, such as asynchronous SGD (ASGD) and synchronous SGD (SSGD) to train deep neural networks.
  arXiv  Detail & Related papers  (2021-01-17T23:12:40Z)
• Direction Matters: On the Implicit Bias of Stochastic Gradient Descent with Moderate Learning Rate [105.62979485062756]
  This paper attempts to characterize the particular regularization effect of SGD in the moderate learning rate regime. We show that SGD converges along the large eigenvalue directions of the data matrix, while GD goes after the small eigenvalue directions.
  arXiv  Detail & Related papers  (2020-11-04T21:07:52Z)
• Stochastic Gradient Langevin with Delayed Gradients [29.6870062491741]
  We show that the rate of convergence in measure is not significantly affected by the error caused by the delayed gradient information used for computation. We show that the rate of convergence in measure is not significantly affected by the error caused by the delayed gradient information used for computation, suggesting significant potential for speedup in wall clock time.
  arXiv  Detail & Related papers  (2020-06-12T17:51:30Z)
• Slow and Stale Gradients Can Win the Race [39.750046808758526]
  Distributed Gradient Descent (SGD) when run in a synchronous manner, suffers from delays in runtime as it waits for the slowest workers (stragglers) Asynchronous methods can alleviate stragglers, but cause gradient staleness that can adversely affect the convergence error. We present a novel theoretical characterization of the speedup offered by asynchronous methods by analyzing the trade-off between the error in the trained model and the actual training runtime.
  arXiv  Detail & Related papers  (2020-03-23T23:27:50Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.