2022/07/24 by Chen, Can, Chen, Xi, Ma, Chen +2
#FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.2207.11719
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.