A Semismooth Newton Stochastic Proximal Point Algorithm with Variance Reduction

• URL: http://arxiv.org/abs/2204.00406v3
• Date: Tue, 26 Mar 2024 08:48:53 GMT
• Title: A Semismooth Newton Stochastic Proximal Point Algorithm with Variance Reduction
• Authors: Andre Milzarek, Fabian Schaipp, Michael Ulbrich,
• Abstract summary: We develop an implementable proximal point (SPP) method for a class of weakly convex, composite optimization problems. The proposed algorithm incorporates a variance reduction mechanism and the resulting updates are solved using an inexact semismooth Newton framework.
• Score: 2.048226951354646
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We develop an implementable stochastic proximal point (SPP) method for a class of weakly convex, composite optimization problems. The proposed stochastic proximal point algorithm incorporates a variance reduction mechanism and the resulting SPP updates are solved using an inexact semismooth Newton framework. We establish detailed convergence results that take the inexactness of the SPP steps into account and that are in accordance with existing convergence guarantees of (proximal) stochastic variance-reduced gradient methods. Numerical experiments show that the proposed algorithm competes favorably with other state-of-the-art methods and achieves higher robustness with respect to the step size selection.

Related papers

• Trust-Region Sequential Quadratic Programming for Stochastic Optimization with Random Models [57.52124921268249]
  We propose a Trust Sequential Quadratic Programming method to find both first and second-order stationary points. To converge to first-order stationary points, our method computes a gradient step in each iteration defined by minimizing a approximation of the objective subject. To converge to second-order stationary points, our method additionally computes an eigen step to explore the negative curvature the reduced Hessian matrix.
  arXiv  Detail & Related papers  (2024-09-24T04:39:47Z)
• A Unified Theory of Stochastic Proximal Point Methods without Smoothness [52.30944052987393]
  Proximal point methods have attracted considerable interest owing to their numerical stability and robustness against imperfect tuning. This paper presents a comprehensive analysis of a broad range of variations of the proximal point method (SPPM)
  arXiv  Detail & Related papers  (2024-05-24T21:09:19Z)
• Variance Reduction and Low Sample Complexity in Stochastic Optimization via Proximal Point Method [5.025654873456757]
  The paper establishes a low sample complexity to obtain a high probability guarantee on the convergence of the proposed method. A subroutine is developed to solve the proximal subproblem, which also serves as a novel technique for variance reduction.
  arXiv  Detail & Related papers  (2024-02-14T07:34:22Z)
• 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)
• A relaxed proximal gradient descent algorithm for convergent plug-and-play with proximal denoiser [6.2484576862659065]
  This paper presents a new convergent Plug-and-fidelity Descent (Play) algorithm. The algorithm converges for a wider range of regular convexization parameters, thus allowing more accurate restoration of an image.
  arXiv  Detail & Related papers  (2023-01-31T16:11:47Z)
• Robust empirical risk minimization via Newton's method [9.797319790710711]
  A new variant of Newton's method for empirical risk minimization is studied. The gradient and Hessian of the objective function are replaced by robust estimators. An algorithm for obtaining robust Newton directions based on the conjugate gradient method is also proposed.
  arXiv  Detail & Related papers  (2023-01-30T18:54:54Z)
• Faster One-Sample Stochastic Conditional Gradient Method for Composite Convex Minimization [61.26619639722804]
  We propose a conditional gradient method (CGM) for minimizing convex finite-sum objectives formed as a sum of smooth and non-smooth terms. The proposed method, equipped with an average gradient (SAG) estimator, requires only one sample per iteration. Nevertheless, it guarantees fast convergence rates on par with more sophisticated variance reduction techniques.
  arXiv  Detail & Related papers  (2022-02-26T19:10:48Z)
• A Stochastic Newton Algorithm for Distributed Convex Optimization [62.20732134991661]
  We analyze a Newton algorithm for homogeneous distributed convex optimization, where each machine can calculate gradients of the same population objective. We show that our method can reduce the number, and frequency, of required communication rounds compared to existing methods without hurting performance.
  arXiv  Detail & Related papers  (2021-10-07T17:51:10Z)
• Momentum Accelerates the Convergence of Stochastic AUPRC Maximization [80.8226518642952]
  We study optimization of areas under precision-recall curves (AUPRC), which is widely used for imbalanced tasks. We develop novel momentum methods with a better iteration of $O (1/epsilon4)$ for finding an $epsilon$stationary solution. We also design a novel family of adaptive methods with the same complexity of $O (1/epsilon4)$, which enjoy faster convergence in practice.
  arXiv  Detail & Related papers  (2021-07-02T16:21:52Z)
• IDEAL: Inexact DEcentralized Accelerated Augmented Lagrangian Method [64.15649345392822]
  We introduce a framework for designing primal methods under the decentralized optimization setting where local functions are smooth and strongly convex. Our approach consists of approximately solving a sequence of sub-problems induced by the accelerated augmented Lagrangian method. When coupled with accelerated gradient descent, our framework yields a novel primal algorithm whose convergence rate is optimal and matched by recently derived lower bounds.
  arXiv  Detail & Related papers  (2020-06-11T18:49:06Z)
• Distributed Stochastic Nonconvex Optimization and Learning based on Successive Convex Approximation [26.11677569331688]
  We introduce a novel framework for the distributed algorithmic minimization of the sum of the sum of the agents in a network. We show that the proposed method can be applied to distributed neural networks.
  arXiv  Detail & Related papers  (2020-04-30T15:36:46Z)

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.