A Primal-Dual-Assisted Penalty Approach to Bilevel Optimization with Coupled Constraints
This addresses a gap in bilevel optimization for complex applications with coupled constraints, though it appears incremental as an extension of existing gradient-based methods to a more general constraint setting.
The paper tackles bilevel optimization problems with coupled constraints between upper and lower levels, developing a first-order algorithm called BLOCC with rigorous convergence theory and demonstrating effectiveness on hyperparameter selection in SVM and transportation infrastructure planning with real Seville data.
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.