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
Hlavní autoři: Yuan, Yulan, Tsang, Danny H. K., Lau, Vincent K. N.
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York IEEE 2025
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:
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
ISSN:1053-587X, 1941-0476
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Shrnutí: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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ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2025.3592678