Bilevel Optimization
Overview
Bilevel optimization models decisions in two levels: an outer problem evaluates choices using the solution of an inner problem, as in hyperparameter tuning, data selection, meta-learning, and neural architecture search. Common approaches differentiate through inner optimization using unrolling or implicit hypergradients, while single-loop stochastic, penalty-based, and derivative-free methods aim to reduce computation and handle larger or black-box problems. Applications also use the framework for decision-focused learning, reinforcement learning, and strategic settings where one agent responds to another. A central challenge is making these methods efficient and reliable when the inner problem is nonconvex or has multiple solutions, while establishing useful convergence and generalization guarantees without restrictive assumptions.
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