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.

我们的论文研究了具有耦合约束的双层优化问题，并开发了一种名为 BLOCC 的（完全）一阶算法，实现对这一具有挑战性但较少被探索的场景的解决。我们为所提算法建立了严格的收敛理论，并通过使用塞维利亚城市的真实数据，对 SVM 中的超参数选择和交通网络的基础设施规划这两个知名的实际应用进行了有效性验证。