Functionally Constrained Algorithm Solves Convex Simple Bilevel Problems
<|reference_start|>Functionally Constrained Algorithm Solves Convex Simple Bilevel Problems: 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.<|reference_end|>
@article{zhang2024functionally,
    title={Functionally Constrained Algorithm Solves Convex Simple Bilevel Problems},
    author={Huaqing Zhang, Lesi Chen, Jing Xu, Jingzhao Zhang},
    journal={arXiv preprint arXiv:2409.06530},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.06530},
    primaryClass={math.OC cs.LG stat.ML}
}