Gradient-based Bi-level Optimization for Deep Learning: A Survey

• URL: http://arxiv.org/abs/2207.11719v4
• Date: Sun, 9 Jul 2023 21:53:45 GMT
• Title: Gradient-based Bi-level Optimization for Deep Learning: A Survey
• Authors: Can Chen, Xi Chen, Chen Ma, Zixuan Liu, Xue Liu
• Abstract summary: Bi-level optimization, especially the gradient-based category, has been widely used in the deep learning community. We first give a formal definition of the gradient-based bi-level optimization. We then discuss four bi-level optimization solvers to update the outer variable.
• Score: 14.39891675968109
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Bi-level optimization, especially the gradient-based category, has been widely used in the deep learning community including hyperparameter optimization and meta-knowledge extraction. Bi-level optimization embeds one problem within another and the gradient-based category solves the outer-level task by computing the hypergradient, which is much more efficient than classical methods such as the evolutionary algorithm. In this survey, we first give a formal definition of the gradient-based bi-level optimization. Next, we delineate criteria to determine if a research problem is apt for bi-level optimization and provide a practical guide on structuring such problems into a bi-level optimization framework, a feature particularly beneficial for those new to this domain. More specifically, there are two formulations: the single-task formulation to optimize hyperparameters such as regularization parameters and the distilled data, and the multi-task formulation to extract meta-knowledge such as the model initialization. With a bi-level formulation, we then discuss four bi-level optimization solvers to update the outer variable including explicit gradient update, proxy update, implicit function update, and closed-form update. Finally, we wrap up the survey by highlighting two prospective future directions: (1) Effective Data Optimization for Science examined through the lens of task formulation. (2) Accurate Explicit Proxy Update analyzed from an optimization standpoint.

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