Nesterov acceleration despite very noisy gradients

• URL: http://arxiv.org/abs/2302.05515v3
• Date: Thu, 31 Oct 2024 15:44:26 GMT
• Title: Nesterov acceleration despite very noisy gradients
• Authors: Kanan Gupta, Jonathan W. Siegel, Stephan Wojtowytsch,
• Abstract summary: We present a generalization of Nesterov's accelerated gradient descent algorithm. AGNES achieves acceleration for smooth convex and strongly convex minimization tasks.
• Score: 2.048226951354646
• License:
• Abstract: We present a generalization of Nesterov's accelerated gradient descent algorithm. Our algorithm (AGNES) provably achieves acceleration for smooth convex and strongly convex minimization tasks with noisy gradient estimates if the noise intensity is proportional to the magnitude of the gradient at every point. Nesterov's method converges at an accelerated rate if the constant of proportionality is below 1, while AGNES accommodates any signal-to-noise ratio. The noise model is motivated by applications in overparametrized machine learning. AGNES requires only two parameters in convex and three in strongly convex minimization tasks, improving on existing methods. We further provide clear geometric interpretations and heuristics for the choice of parameters.

Related papers

• Gradient Normalization with(out) Clipping Ensures Convergence of Nonconvex SGD under Heavy-Tailed Noise with Improved Results [60.92029979853314]
  This paper investigates Gradient Normalization without (NSGDC) its gradient reduction variant (NSGDC-VR) We present significant improvements in the theoretical results for both algorithms.
  arXiv  Detail & Related papers  (2024-10-21T22:40:42Z)
• From Gradient Clipping to Normalization for Heavy Tailed SGD [19.369399536643773]
  Recent empirical evidence indicates that machine learning applications involve heavy-tailed noise, which challenges the standard assumptions of bounded variance in practice. In this paper, we show that it is possible to achieve tightness of the gradient-dependent noise convergence problem under tailed noise.
  arXiv  Detail & Related papers  (2024-10-17T17:59:01Z)
• Flattened one-bit stochastic gradient descent: compressed distributed optimization with controlled variance [55.01966743652196]
  We propose a novel algorithm for distributed gradient descent (SGD) with compressed gradient communication in the parameter-server framework. Our gradient compression technique, named flattened one-bit gradient descent (FO-SGD), relies on two simple algorithmic ideas.
  arXiv  Detail & Related papers  (2024-05-17T21:17:27Z)
• Adaptive Federated Learning Over the Air [108.62635460744109]
  We propose a federated version of adaptive gradient methods, particularly AdaGrad and Adam, within the framework of over-the-air model training. Our analysis shows that the AdaGrad-based training algorithm converges to a stationary point at the rate of $mathcalO( ln(T) / T 1 - frac1alpha ).
  arXiv  Detail & Related papers  (2024-03-11T09:10:37Z)
• Tradeoffs between convergence rate and noise amplification for momentum-based accelerated optimization algorithms [8.669461942767098]
  We study momentum-based first-order optimization algorithms in which the iterations are subject to an additive white noise. For strongly convex quadratic problems, we use the steady-state variance of the error in the optimization variable to quantify noise amplification. We introduce two parameterized families of algorithms that strike a balance between noise amplification and settling time.
  arXiv  Detail & Related papers  (2022-09-24T04:26:30Z)
• Accelerated SGD for Non-Strongly-Convex Least Squares [14.010916616909743]
  We consider approximation for the least squares regression problem in the non-strongly convex setting. We present the first practical algorithm that achieves the optimal prediction error rates in terms of dependence on the noise of the problem.
  arXiv  Detail & Related papers  (2022-03-03T14:39:33Z)
• Nesterov Accelerated Shuffling Gradient Method for Convex Optimization [15.908060383231371]
  We show that our algorithm has an improved rate of $mathcalO (1/T)$ using unified shuffling schemes. Our convergence analysis does not require an assumption on bounded domain or a bounded gradient condition. Numerical simulations demonstrate the efficiency of our algorithm.
  arXiv  Detail & Related papers  (2022-02-07T21:23:17Z)
• A Unified Analysis of First-Order Methods for Smooth Games via Integral Quadratic Constraints [10.578409461429626]
  In this work, we adapt the integral quadratic constraints theory to first-order methods for smooth and strongly-varying games and iteration. We provide emphfor the first time a global convergence rate for the negative momentum method(NM) with an complexity $mathcalO(kappa1.5)$, which matches its known lower bound. We show that it is impossible for an algorithm with one step of memory to achieve acceleration if it only queries the gradient once per batch.
  arXiv  Detail & Related papers  (2020-09-23T20:02:00Z)
• Hessian-Free High-Resolution Nesterov Acceleration for Sampling [55.498092486970364]
  Nesterov's Accelerated Gradient (NAG) for optimization has better performance than its continuous time limit (noiseless kinetic Langevin) when a finite step-size is employed. This work explores the sampling counterpart of this phenonemon and proposes a diffusion process, whose discretizations can yield accelerated gradient-based MCMC methods.
  arXiv  Detail & Related papers  (2020-06-16T15:07:37Z)
• Stochastic Optimization with Heavy-Tailed Noise via Accelerated Gradient Clipping [69.9674326582747]
  We propose a new accelerated first-order method called clipped-SSTM for smooth convex optimization with heavy-tailed distributed noise in gradients. We prove new complexity that outperform state-of-the-art results in this case. We derive the first non-trivial high-probability complexity bounds for SGD with clipping without light-tails assumption on the noise.
  arXiv  Detail & Related papers  (2020-05-21T17:05:27Z)
• Towards Better Understanding of Adaptive Gradient Algorithms in Generative Adversarial Nets [71.05306664267832]
  Adaptive algorithms perform gradient updates using the history of gradients and are ubiquitous in training deep neural networks. In this paper we analyze a variant of OptimisticOA algorithm for nonconcave minmax problems. Our experiments show that adaptive GAN non-adaptive gradient algorithms can be observed empirically.
  arXiv  Detail & Related papers  (2019-12-26T22:10:10Z)

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.