Interest in bilevel optimization has grown in recent years, partially due to its applications to tackle 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 - hyperparameter selection in support vector machine (SVM) and infrastructure planning in transportation networks using the real data from the city of Seville.

翻译：近年来，双层优化研究兴趣日益增长，部分归因于其在应对具有挑战性的机器学习问题中的应用。近期若干重要研究工作集中于开发具有可证明保证的高效基于梯度的算法，以求解双层优化问题。然而，现有文献主要关注无约束或仅含简单约束（即不耦合上下层变量）的双层问题，这排除了一系列复杂应用场景。本文研究这一具有挑战性但尚未充分探索的情形，提出一种（完全）一阶算法（命名为BLOCC）来处理具有耦合约束的双层优化问题。我们为所提算法建立了严格的收敛理论，并在两个经典实际应用场景中验证了其有效性——支持向量机（SVM）的超参数选择，以及利用塞维利亚市真实数据进行的交通网络基础设施规划。