Proximal Gradient Method for Solving Bilevel Optimization Problems

Yimer, Seifu Endris; Gebrie, Anteneh Getachew

doi:10.3390/mca25040066

Cited by 2 publications

(1 citation statement)

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“…However, bi-level model's complexity makes it difficult to be solved in practice using the conventional approaches and computing devices. Specially, they may fail in the face of large-scale, highdimensional applications, especially in machine learning and computer vision fields [48], [49].…”

Section: Introductionmentioning

confidence: 99%

Investigating Bi-Level Optimization for Learning and Vision from a Unified Perspective: A Survey and Beyond

Liu¹,

Gao²,

Zhang³

et al. 2021

Preprint

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Bi-Level Optimization (BLO) is originated from the area of economic game theory and then introduced into the optimization community. BLO is able to handle problems with a hierarchical structure, involving two levels of optimization tasks, where one task is nested inside the other. In machine learning and computer vision fields, despite the different motivations and mechanisms, a lot of complex problems, such as hyper-parameter optimization, multi-task and meta-learning, neural architecture search, adversarial learning and deep reinforcement learning, actually all contain a series of closely related subproblms. In this paper, we first uniformly express these complex learning and vision problems from the perspective of BLO. Then we construct a value-function-based single-level reformulation and establish a unified algorithmic framework to understand and formulate mainstream gradient-based BLO methodologies, covering aspects ranging from fundamental automatic differentiation schemes to various accelerations, simplifications, extensions and their convergence and complexity properties. Last but not least, we discuss the potentials of our unified BLO framework for designing new algorithms and point out some promising directions for future research.

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Section: Introductionmentioning

confidence: 99%