Efficient Gradient Approximation Method for Constrained Bilevel Optimization

Bilevel optimization has been developed for many machine learning tasks with large-scale and high-dimensional data. This paper considers a constrained bilevel optimization problem, where the lower-level optimization problem is convex with equality and inequality constraints and the upper-level optim...

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Bibliographic Details
Published in:arXiv.org 2023-02
Main Authors: Xu, Siyuan, Zhu, Minghui
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Cognitive tasks
Constraints
Machine learning
Mathematical analysis
Optimization
Online Access:Get full text
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Summary:Bilevel optimization has been developed for many machine learning tasks with large-scale and high-dimensional data. This paper considers a constrained bilevel optimization problem, where the lower-level optimization problem is convex with equality and inequality constraints and the upper-level optimization problem is non-convex. The overall objective function is non-convex and non-differentiable. To solve the problem, we develop a gradient-based approach, called gradient approximation method, which determines the descent direction by computing several representative gradients of the objective function inside a neighborhood of the current estimate. We show that the algorithm asymptotically converges to the set of Clarke stationary points, and demonstrate the efficacy of the algorithm by the experiments on hyperparameter optimization and meta-learning.
ISSN:2331-8422
DOI:10.48550/arxiv.2302.01970