A Generalized Alternating Method for Bilevel Optimization under the Polyak-Łojasiewicz Condition

Bilevel optimization has recently regained interest owing to its applications in emerging machine learning fields such as hyperparameter optimization, meta-learning, and reinforcement learning. Recent results have shown that simple alternating (implicit) gradient-based algorithms can match the convergence rate of single-level gradient descent (GD) when addressing bilevel problems with a strongly convex lower-level objective. However, it remains unclear whether this result can be generalized to bilevel problems beyond this basic setting.