Step Size Adaptation for Accelerated Stochastic Momentum Algorithm Using SDE Modeling and Lyapunov Drift Minimization
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 gradien...
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| Vydáno v: | IEEE transactions on signal processing Ročník 73; s. 3124 - 3139 |
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2025
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| 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. |
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| AbstractList | 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. |
| Author | Yuan, Yulan Tsang, Danny H. K. Lau, Vincent K. N. |
| Author_xml | – sequence: 1 givenname: Yulan orcidid: 0009-0004-6817-0310 surname: Yuan fullname: Yuan, Yulan email: yyuan202@connect.hkust-gz.edu.cn organization: Internet of Things Thrust, The Hong Kong University of Science and Technology (Guangzhou), Guangzhou, Guangdong, China – sequence: 2 givenname: Danny H. K. orcidid: 0000-0003-0135-7098 surname: Tsang fullname: Tsang, Danny H. K. email: eetsang@ece.ust.hk organization: Internet of Things Thrust, The Hong Kong University of Science and Technology (Guangzhou), Guangzhou, Guangdong, China – sequence: 3 givenname: Vincent K. N. orcidid: 0000-0001-7769-6008 surname: Lau fullname: Lau, Vincent K. N. email: eeknlau@ece.ust.hk organization: Department of Electronic and Computer Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong SAR, China |
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| SubjectTerms | Algorithms Approximation algorithms Cognitive tasks Convergence Differential equations Heuristic algorithms Liapunov functions Lyapunov drift Machine learning Mathematical models Momentum Noise Optimization Signal processing algorithms Stability analysis stochastic differential equation Stochastic momentum Stochastic processes Trajectory |
| Title | Step Size Adaptation for Accelerated Stochastic Momentum Algorithm Using SDE Modeling and Lyapunov Drift Minimization |
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