Boosting Accelerated Proximal Gradient Method with Adaptive Sampling for Stochastic Composite Optimization

Dongxuan Zhu; Weihuan Huang; Caihua Chen

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arXiv · 2507.18277

Boosting Accelerated Proximal Gradient Method with Adaptive Sampling for Stochastic Composite Optimization

Dongxuan Zhu·Weihuan Huang·Caihua Chen

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Abstract

We develop an adaptive Nesterov accelerated proximal gradient (adaNAPG) algorithm for stochastic composite optimization problems, boosting the Nesterov accelerated proximal gradient (NAPG) algorithm through the integration of an adaptive sampling strategy for gradient estimation. We provide a complexity analysis demonstrating that the new algorithm, adaNAPG, achieves both the optimal iteration complexity and the optimal sample complexity as outlined in the existing literature. Additionally, we establish a central limit theorem for the iteration sequence of the new algorithm adaNAPG, elucidating its convergence rate and efficiency.

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Dongxuan Zhu, Weihuan Huang, Caihua Chen. 2025-07-24. Boosting Accelerated Proximal Gradient Method with Adaptive Sampling for Stochastic Composite Optimization. https://arxiv.org/abs/2507.18277

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