Non-convex Stochastic Composite Optimization with Polyak Momentum

• URL: http://arxiv.org/abs/2403.02967v3
• Date: Mon, 18 Nov 2024 09:44:08 GMT
• Title: Non-convex Stochastic Composite Optimization with Polyak Momentum
• Authors: Yuan Gao, Anton Rodomanov, Sebastian U. Stich,
• Abstract summary: The generalization proximal gradient is a powerful generalization of the widely used gradient descent (SGD) method. However, it is notoriously known that method fails to converge in numerous applications in Machine.
• Score: 25.060477077577154
• License:
• Abstract: The stochastic proximal gradient method is a powerful generalization of the widely used stochastic gradient descent (SGD) method and has found numerous applications in Machine Learning. However, it is notoriously known that this method fails to converge in non-convex settings where the stochastic noise is significant (i.e. when only small or bounded batch sizes are used). In this paper, we focus on the stochastic proximal gradient method with Polyak momentum. We prove this method attains an optimal convergence rate for non-convex composite optimization problems, regardless of batch size. Additionally, we rigorously analyze the variance reduction effect of the Polyak momentum in the composite optimization setting and we show the method also converges when the proximal step can only be solved inexactly. Finally, we provide numerical experiments to validate our theoretical results.

Related papers

• An Adaptive Stochastic Gradient Method with Non-negative Gauss-Newton Stepsizes [17.804065824245402]
  In machine learning applications, each loss function is non-negative and can be expressed as the composition of a square and its real-valued square root. We show how to apply the Gauss-Newton method or the Levssquardt method to minimize the average of smooth but possibly non-negative functions.
  arXiv  Detail & Related papers  (2024-07-05T08:53:06Z)
• On the Stochastic (Variance-Reduced) Proximal Gradient Method for Regularized Expected Reward Optimization [10.36447258513813]
  We consider a regularized expected reward optimization problem in the non-oblivious setting that covers many existing problems in reinforcement learning (RL) In particular, the method has shown to admit an $O(epsilon-4)$ sample to an $epsilon$-stationary point, under standard conditions. Our analysis shows that the sample complexity can be improved from $O(epsilon-4)$ to $O(epsilon-3)$ under additional conditions.
  arXiv  Detail & Related papers  (2024-01-23T06:01:29Z)
• High-Probability Convergence for Composite and Distributed Stochastic Minimization and Variational Inequalities with Heavy-Tailed Noise [96.80184504268593]
  gradient, clipping is one of the key algorithmic ingredients to derive good high-probability guarantees. Clipping can spoil the convergence of the popular methods for composite and distributed optimization.
  arXiv  Detail & Related papers  (2023-10-03T07:49:17Z)
• Variance reduction techniques for stochastic proximal point algorithms [5.374800961359305]
  In this work, we propose the first unified study of variance reduction techniques for proximal point algorithms. We introduce a generic proximal-based algorithm that can be specified to give the proximal version of SVRG, SAGA, and some of their variants. Our experiments demonstrate the advantages of the proximal variance reduction methods over their gradient counterparts.
  arXiv  Detail & Related papers  (2023-08-18T05:11:50Z)
• Convex and Non-convex Optimization Under Generalized Smoothness [69.69521650503431]
  An analysis of convex and non- optimization methods often requires the Lipsitzness gradient, which limits the analysis by this trajectorys. Recent work generalizes the gradient setting via the non-uniform smoothness condition.
  arXiv  Detail & Related papers  (2023-06-02T04:21:59Z)
• Differentiable Annealed Importance Sampling and the Perils of Gradient Noise [68.44523807580438]
  Annealed importance sampling (AIS) and related algorithms are highly effective tools for marginal likelihood estimation. Differentiability is a desirable property as it would admit the possibility of optimizing marginal likelihood as an objective. We propose a differentiable algorithm by abandoning Metropolis-Hastings steps, which further unlocks mini-batch computation.
  arXiv  Detail & Related papers  (2021-07-21T17:10:14Z)
• On the Convergence of Stochastic Extragradient for Bilinear Games with Restarted Iteration Averaging [96.13485146617322]
  We present an analysis of the ExtraGradient (SEG) method with constant step size, and present variations of the method that yield favorable convergence. We prove that when augmented with averaging, SEG provably converges to the Nash equilibrium, and such a rate is provably accelerated by incorporating a scheduled restarting procedure.
  arXiv  Detail & Related papers  (2021-06-30T17:51:36Z)
• Constrained and Composite Optimization via Adaptive Sampling Methods [3.4219044933964944]
  The motivation for this paper stems from the desire to develop an adaptive sampling method for solving constrained optimization problems. The method proposed in this paper is a proximal gradient method that can also be applied to the composite optimization problem min f(x) + h(x), where f is convex (but not necessarily differentiable)
  arXiv  Detail & Related papers  (2020-12-31T02:50:39Z)
• Zeroth-Order Hybrid Gradient Descent: Towards A Principled Black-Box Optimization Framework [100.36569795440889]
  This work is on the iteration of zero-th-order (ZO) optimization which does not require first-order information. We show that with a graceful design in coordinate importance sampling, the proposed ZO optimization method is efficient both in terms of complexity as well as as function query cost.
  arXiv  Detail & Related papers  (2020-12-21T17:29:58Z)
• Convergence of a Stochastic Gradient Method with Momentum for Non-Smooth Non-Convex Optimization [25.680334940504405]
  This paper establishes the convergence of the rate of a non-smooth subient method with momentum for constrained problems. For problems, we show how the unconstrained case can be analyzed under weaker assumptions than the state-of-the-art.
  arXiv  Detail & Related papers  (2020-02-13T12:10:17Z)
• Complexity Guarantees for Polyak Steps with Momentum [76.97851351276165]
  We study a class of methods, based on Polyak steps, where this knowledge is substituted by that of the optimal value, $f_*$. We first show slightly improved convergence bounds than previously known for the classical case of simple gradient descent with Polyak steps, we then derive an accelerated gradient method with Polyak steps and momentum, along with convergence guarantees.
  arXiv  Detail & Related papers  (2020-02-03T17:50:28Z)

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.