A Primal-Dual-Assisted Penalty Approach to Bilevel Optimization with Coupled Constraints
Liuyuan Jiang, Quan Xiao, Victor M. Tenorio, Fernando Real-Rojas, Antonio Marques, Tianyi Chen
Abstract
Interest in bilevel optimization has grown in recent years, partially due to its relevance for challenging machine-learning problems. Several exciting recent works have been centered around developing efficient gradient-based algorithms that can solve bilevel optimization problems with provable guarantees. However, the existing literature mainly focuses on bilevel problems either without constraints, or featuring only simple constraints that do not couple variables across the upper and lower levels, excluding a range of complex applications. Our paper studies this challenging but less explored scenario and develops a (fully) first-order algorithm, which we term BLOCC, to tackle BiLevel Optimization problems with Coupled Constraints. We establish rigorous convergence theory for the proposed algorithm and demonstrate its effectiveness on two well-known real-world applications - support vector machine (SVM) - based model training and infrastructure planning in transportation networks.
BibTeX
@inproceedings{
jiang2024a,
title={A Primal-Dual-Assisted Penalty Approach to Bilevel Optimization with Coupled Constraints},
author={Liuyuan Jiang and Quan Xiao and Victor M. Tenorio and Fernando Real-Rojas and Antonio Marques and Tianyi Chen},
booktitle={The Thirty-eighth Annual Conference on Neural Information Processing Systems},
year={2024},
url={https://openreview.net/forum?id=uZi7H5Ac0X}
}