单步内法线性收敛双层优化

IF 16.4 1区 化学 Q1 CHEMISTRY, MULTIDISCIPLINARY
Ensio Suonperä, Tuomo Valkonen
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引用次数: 2

摘要

摘要提出了一种求解双层优化问题的新方法,它介于用牛顿型方法求解全系统最优性条件和将内部问题作为隐函数处理之间。总体思想是解决全系统最优性条件,但前提条件是它们在内部问题,伴随方程和外部问题的简单传统方法步骤之间交替。虽然内部物镜必须是光滑的,但外部物镜在准收缩条件下可能是不光滑的。用伴随方程的精确解和不精确解证明了梯度下降法和正向后分裂法组合方法的线性收敛性。我们在学习正则化参数用于各向异性全变差图像去噪和卷积核用于图像反卷积方面表现出良好的性能。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Linearly convergent bilevel optimization with single-step inner methods

Linearly convergent bilevel optimization with single-step inner methods
Abstract We propose a new approach to solving bilevel optimization problems, intermediate between solving full-system optimality conditions with a Newton-type approach, and treating the inner problem as an implicit function. The overall idea is to solve the full-system optimality conditions, but to precondition them to alternate between taking steps of simple conventional methods for the inner problem, the adjoint equation, and the outer problem. While the inner objective has to be smooth, the outer objective may be nonsmooth subject to a prox-contractivity condition. We prove linear convergence of the approach for combinations of gradient descent and forward-backward splitting with exact and inexact solution of the adjoint equation. We demonstrate good performance on learning the regularization parameter for anisotropic total variation image denoising, and the convolution kernel for image deconvolution.
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来源期刊
Accounts of Chemical Research
Accounts of Chemical Research 化学-化学综合
CiteScore
31.40
自引率
1.10%
发文量
312
审稿时长
2 months
期刊介绍: Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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