@inproceedings{
zhang2024functionally,
title={Functionally Constrained Algorithm Solves Convex Simple Bilevel Problem},
author={Huaqing Zhang and Lesi Chen and Jing Xu and Jingzhao Zhang},
booktitle={The Thirty-eighth Annual Conference on Neural Information Processing Systems},
year={2024},
url={https://openreview.net/forum?id=PAiGHJppam}
}
This paper studies simple bilevel problems, where a convex upper-level function is minimized over the optimal solutions of a convex lower-level problem. We first show the fundamental difficulty of simple bilevel problems, that the approximate optimal value of such problems is not obtainable by first-order zero-respecting algorithms. Then we follow recent works to pursue the weak approximate solutions. For this goal, we propose novel near-optimal methods for smooth and nonsmooth problems by reformulating them into functionally constrained problems.
Functionally Constrained Algorithm Solves Convex Simple Bilevel Problem
Huaqing Zhang Lesi Chen Jing Xu Jingzhao Zhang