High probability bounds on AdaGrad for constrained weakly convex optimization

IF 1.8 2区数学 Q1 MATHEMATICS

Journal of Complexity Pub Date : 2024-07-31 DOI:10.1016/j.jco.2024.101889

Yusu Hong , Junhong Lin

引用次数: 0

Abstract

In this paper, we study the high probability convergence of AdaGrad-Norm for constrained, non-smooth, weakly convex optimization with bounded noise and sub-Gaussian noise cases. We also investigate a more general accelerated gradient descent (AGD) template (Ghadimi and Lan, 2016) encompassing the AdaGrad-Norm, the Nesterov's accelerated gradient descent, and the RSAG (Ghadimi and Lan, 2016) with different parameter choices. We provide a high probability convergence rate $\tilde{O} (1 / \sqrt{T})$ without knowing the information of the weak convexity parameter and the gradient bound to tune the step-sizes.

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受约束弱凸优化的 AdaGrad 高概率边界

在本文中，我们研究了 AdaGrad-Norm 对于有约束噪声和亚高斯噪声情况下的约束、非光滑、弱凸优化的高概率收敛性。我们还研究了一种更通用的加速梯度下降（AGD）模板（Ghadimi 和 Lan，2016 年），其中包含 AdaGrad-Norm、Nesterov 加速梯度下降和 RSAG（Ghadimi 和 Lan，2016 年），并有不同的参数选择。我们在不知道弱凸性参数和梯度约束信息的情况下提供了高概率收敛率，以调整步长。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Complexity 工程技术-计算机：理论方法

CiteScore

3.10

自引率

17.60%

发文量

审稿时长

>12 weeks

期刊介绍： The multidisciplinary Journal of Complexity publishes original research papers that contain substantial mathematical results on complexity as broadly conceived. Outstanding review papers will also be published. In the area of computational complexity, the focus is on complexity over the reals, with the emphasis on lower bounds and optimal algorithms. The Journal of Complexity also publishes articles that provide major new algorithms or make important progress on upper bounds. Other models of computation, such as the Turing machine model, are also of interest. Computational complexity results in a wide variety of areas are solicited. Areas Include: • Approximation theory • Biomedical computing • Compressed computing and sensing • Computational finance • Computational number theory • Computational stochastics • Control theory • Cryptography • Design of experiments • Differential equations • Discrete problems • Distributed and parallel computation • High and infinite-dimensional problems • Information-based complexity • Inverse and ill-posed problems • Machine learning • Markov chain Monte Carlo • Monte Carlo and quasi-Monte Carlo • Multivariate integration and approximation • Noisy data • Nonlinear and algebraic equations • Numerical analysis • Operator equations • Optimization • Quantum computing • Scientific computation • Tractability of multivariate problems • Vision and image understanding.