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LancBiO: dynamic Lanczos-aided bilevel optimization via Krylov subspace
April 5, 2024, 4:42 a.m. | Bin Gao, Yan Yang, Ya-xiang Yuan
cs.LG updates on arXiv.org arxiv.org
Abstract: Bilevel optimization, with broad applications in machine learning, has an intricate hierarchical structure. Gradient-based methods have emerged as a common approach to large-scale bilevel problems. However, the computation of the hyper-gradient, which involves a Hessian inverse vector product, confines the efficiency and is regarded as a bottleneck. To circumvent the inverse, we construct a sequence of low-dimensional approximate Krylov subspaces with the aid of the Lanczos process. As a result, the constructed subspace is able …
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