Large Stepsizes Accelerate Gradient Descent for Regularized Logistic Regression

• URL: http://arxiv.org/abs/2506.02336v1
• Date: Tue, 03 Jun 2025 00:21:22 GMT
• Title: Large Stepsizes Accelerate Gradient Descent for Regularized Logistic Regression
• Authors: Jingfeng Wu, Pierre Marion, Peter Bartlett,
• Abstract summary: We study gradient descent (GD) with a constant stepsize for $ell$-regularized logistic regression with linearly separable data.<n>We show that this can be accelerated to $widetildemathcalO(sqrtkappa)$ by simply using a large stepsize.
• Score: 9.15420898792103
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study gradient descent (GD) with a constant stepsize for $\ell_2$-regularized logistic regression with linearly separable data. Classical theory suggests small stepsizes to ensure monotonic reduction of the optimization objective, achieving exponential convergence in $\widetilde{\mathcal{O}}(\kappa)$ steps with $\kappa$ being the condition number. Surprisingly, we show that this can be accelerated to $\widetilde{\mathcal{O}}(\sqrt{\kappa})$ by simply using a large stepsize -- for which the objective evolves nonmonotonically. The acceleration brought by large stepsizes extends to minimizing the population risk for separable distributions, improving on the best-known upper bounds on the number of steps to reach a near-optimum. Finally, we characterize the largest stepsize for the local convergence of GD, which also determines the global convergence in special scenarios. Our results extend the analysis of Wu et al. (2024) from convex settings with minimizers at infinity to strongly convex cases with finite minimizers.

Related papers

• Stochastic Gradient Descent in Non-Convex Problems: Asymptotic Convergence with Relaxed Step-Size via Stopping Time Methods [13.677904140815386]
  Gradient Descent (SGD) is widely used in machine learning research.<n>This paper introduces a novel analytical method for convergence analysis of SGD under more relaxed step-size conditions.
  arXiv  Detail & Related papers  (2025-04-17T02:56:20Z)
• Gradient Descent on Logistic Regression with Non-Separable Data and Large Step Sizes [38.595892152591595]
  We study descent dynamics on logistic regression problems with large, constant step sizes. Local convergence is guaranteed for all step sizes less than the critical step size, but global convergence is not.
  arXiv  Detail & Related papers  (2024-06-07T15:53:06Z)
• Large Stepsize Gradient Descent for Logistic Loss: Non-Monotonicity of the Loss Improves Optimization Efficiency [47.8739414267201]
  We consider gradient descent (GD) with a constant stepsize applied to logistic regression with linearly separable data. We show that GD exits this initial oscillatory phase rapidly -- in $mathcalO(eta)$ steps -- and subsequently achieves an $tildemathcalO (1 / (eta t) )$ convergence rate. Our results imply that, given a budget of $T$ steps, GD can achieve an accelerated loss of $tildemathcalO (1/T2)$ with an aggressive stepsize
  arXiv  Detail & Related papers  (2024-02-24T23:10:28Z)
• 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)
• Last iterate convergence of SGD for Least-Squares in the Interpolation regime [19.05750582096579]
  We study the noiseless model in the fundamental least-squares setup. We assume that an optimum predictor fits perfectly inputs and outputs $langle theta_*, phi(X) rangle = Y$, where $phi(X)$ stands for a possibly infinite dimensional non-linear feature map.
  arXiv  Detail & Related papers  (2021-02-05T14:02:20Z)
• ROOT-SGD: Sharp Nonasymptotics and Near-Optimal Asymptotics in a Single Algorithm [71.13558000599839]
  We study the problem of solving strongly convex and smooth unconstrained optimization problems using first-order algorithms. We devise a novel, referred to as Recursive One-Over-T SGD, based on an easily implementable, averaging of past gradients. We prove that it simultaneously achieves state-of-the-art performance in both a finite-sample, nonasymptotic sense and an sense.
  arXiv  Detail & Related papers  (2020-08-28T14:46:56Z)
• Balancing Rates and Variance via Adaptive Batch-Size for Stochastic Optimization Problems [120.21685755278509]
  In this work, we seek to balance the fact that attenuating step-size is required for exact convergence with the fact that constant step-size learns faster in time up to an error. Rather than fixing the minibatch the step-size at the outset, we propose to allow parameters to evolve adaptively.
  arXiv  Detail & Related papers  (2020-07-02T16:02:02Z)
• On the Almost Sure Convergence of Stochastic Gradient Descent in Non-Convex Problems [75.58134963501094]
  This paper analyzes the trajectories of gradient descent (SGD) We show that SGD avoids saddle points/manifolds with $1$ for strict step-size policies.
  arXiv  Detail & Related papers  (2020-06-19T14:11:26Z)
• A Simple Convergence Proof of Adam and Adagrad [74.24716715922759]
  We show a proof of convergence between the Adam Adagrad and $O(d(N)/st)$ algorithms. Adam converges with the same convergence $O(d(N)/st)$ when used with the default parameters.
  arXiv  Detail & Related papers  (2020-03-05T01:56:17Z)

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.