A Framework for Bilevel Optimization on Riemannian Manifolds
Abstract
Bilevel optimization has gained prominence in various applications. In this study, we introduce a framework for solving bilevel optimization problems, where the variables in both the lower and upper levels are constrained on Riemannian manifolds. We present several hypergradient estimation strategies on manifolds and analyze their estimation errors. Furthermore, we provide comprehensive convergence and complexity analyses for the proposed hypergradient descent algorithm on manifolds. We also extend our framework to encompass stochastic bilevel optimization and incorporate the use of general retraction. The efficacy of the proposed framework is demonstrated through several applications.
Cite
Text
Han et al. "A Framework for Bilevel Optimization on Riemannian Manifolds." Neural Information Processing Systems, 2024. doi:10.52202/079017-3299Markdown
[Han et al. "A Framework for Bilevel Optimization on Riemannian Manifolds." Neural Information Processing Systems, 2024.](https://mlanthology.org/neurips/2024/han2024neurips-framework/) doi:10.52202/079017-3299BibTeX
@inproceedings{han2024neurips-framework,
title = {{A Framework for Bilevel Optimization on Riemannian Manifolds}},
author = {Han, Andi and Mishra, Bamdev and Jawanpuria, Pratik and Takeda, Akiko},
booktitle = {Neural Information Processing Systems},
year = {2024},
doi = {10.52202/079017-3299},
url = {https://mlanthology.org/neurips/2024/han2024neurips-framework/}
}