Memory-Efficient Gradient Unrolling for Large-Scale Bi-level Optimization

• URL: http://arxiv.org/abs/2406.14095v1
• Date: Thu, 20 Jun 2024 08:21:52 GMT
• Title: Memory-Efficient Gradient Unrolling for Large-Scale Bi-level Optimization
• Authors: Qianli Shen, Yezhen Wang, Zhouhao Yang, Xiang Li, Haonan Wang, Yang Zhang, Jonathan Scarlett, Zhanxing Zhu, Kenji Kawaguchi,
• Abstract summary: Traditional gradient-based bi-level optimization algorithms are ill-suited to meet the demands of large-scale applications. We introduce $(textFG)2textU$, which achieves an unbiased approximation of the meta gradient for bi-level optimization. $(textFG)2textU$ is inherently designed to support parallel computing, enabling it to effectively leverage large-scale distributed computing systems.
• Score: 71.35604981129838
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Bi-level optimization (BO) has become a fundamental mathematical framework for addressing hierarchical machine learning problems. As deep learning models continue to grow in size, the demand for scalable bi-level optimization solutions has become increasingly critical. Traditional gradient-based bi-level optimization algorithms, due to their inherent characteristics, are ill-suited to meet the demands of large-scale applications. In this paper, we introduce $\textbf{F}$orward $\textbf{G}$radient $\textbf{U}$nrolling with $\textbf{F}$orward $\textbf{F}$radient, abbreviated as $(\textbf{FG})^2\textbf{U}$, which achieves an unbiased stochastic approximation of the meta gradient for bi-level optimization. $(\text{FG})^2\text{U}$ circumvents the memory and approximation issues associated with classical bi-level optimization approaches, and delivers significantly more accurate gradient estimates than existing large-scale bi-level optimization approaches. Additionally, $(\text{FG})^2\text{U}$ is inherently designed to support parallel computing, enabling it to effectively leverage large-scale distributed computing systems to achieve significant computational efficiency. In practice, $(\text{FG})^2\text{U}$ and other methods can be strategically placed at different stages of the training process to achieve a more cost-effective two-phase paradigm. Further, $(\text{FG})^2\text{U}$ is easy to implement within popular deep learning frameworks, and can be conveniently adapted to address more challenging zeroth-order bi-level optimization scenarios. We provide a thorough convergence analysis and a comprehensive practical discussion for $(\text{FG})^2\text{U}$, complemented by extensive empirical evaluations, showcasing its superior performance in diverse large-scale bi-level optimization tasks.

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