Step Size Adaptation for Accelerated Stochastic Momentum Algorithm Using SDE Modeling and Lyapunov Drift Minimization

IF 5.8 2区 工程技术 Q1 ENGINEERING, ELECTRICAL & ELECTRONIC
Yulan Yuan;Danny H. K. Tsang;Vincent K. N. Lau
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引用次数: 0

Abstract

Training machine learning models often involves solving high-dimensional stochastic optimization problems, where stochastic gradient-based algorithms are hindered by slow convergence. Although momentum-based methods perform well in deterministic settings, their effectiveness diminishes under gradient noise. In this paper, we introduce a novel accelerated stochastic momentum algorithm. Specifically, we first model the trajectory of discrete-time momentum-based algorithms using continuous-time stochastic differential equations (SDEs). By leveraging a tailored Lyapunov function, we derive 2-D adaptive step sizes through Lyapunov drift minimization, which significantly enhance both convergence speed and noise stability. The proposed algorithm not only accelerates convergence but also eliminates the need for hyperparameter fine-tuning, consistently achieving robust accuracy in machine learning tasks.
基于SDE建模和Lyapunov漂移最小化的加速随机动量算法步长自适应
训练机器学习模型通常涉及解决高维随机优化问题,其中基于随机梯度的算法被缓慢收敛所阻碍。尽管基于动量的方法在确定性设置下表现良好,但在梯度噪声下其有效性降低。本文介绍了一种新的加速随机动量算法。具体来说,我们首先使用连续时间随机微分方程(SDEs)对离散时间动量算法的轨迹进行建模。通过利用定制的Lyapunov函数,我们通过Lyapunov漂移最小化推导出二维自适应步长,这大大提高了收敛速度和噪声稳定性。该算法不仅加快了收敛速度,而且消除了超参数微调的需要,在机器学习任务中始终如一地实现鲁棒精度。
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
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing 工程技术-工程:电子与电气
CiteScore
11.20
自引率
9.30%
发文量
310
审稿时长
3.0 months
期刊介绍: The IEEE Transactions on Signal Processing covers novel theory, algorithms, performance analyses and applications of techniques for the processing, understanding, learning, retrieval, mining, and extraction of information from signals. The term “signal” includes, among others, audio, video, speech, image, communication, geophysical, sonar, radar, medical and musical signals. Examples of topics of interest include, but are not limited to, information processing and the theory and application of filtering, coding, transmitting, estimating, detecting, analyzing, recognizing, synthesizing, recording, and reproducing signals.
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