Non-Stationary Functional Bilevel Optimization
This addresses the need for scalable and stable bilevel optimization in dynamic environments, such as online learning and reinforcement learning, representing a novel extension rather than an incremental improvement.
The paper tackled the problem of functional bilevel optimization (FBO) in online, non-stationary settings, where existing methods are limited and suboptimal, and proposed SmoothFBO, which outperforms existing FBO methods in tasks like hyperparameter optimization and model-based reinforcement learning.
Functional bilevel optimization (FBO) provides a powerful framework for hierarchical learning in function spaces, yet current methods are limited to static offline settings and perform suboptimally in online, non-stationary scenarios. We propose SmoothFBO, the first algorithm for non-stationary FBO with both theoretical guarantees and practical scalability. SmoothFBO introduces a time-smoothed stochastic hypergradient estimator that reduces variance through a window parameter, enabling stable outer-loop updates with sublinear regret. Importantly, the classical parametric bilevel case is a special reduction of our framework, making SmoothFBO a natural extension to online, non-stationary settings. Empirically, SmoothFBO consistently outperforms existing FBO methods in non-stationary hyperparameter optimization and model-based reinforcement learning, demonstrating its practical effectiveness. Together, these results establish SmoothFBO as a general, theoretically grounded, and practically viable foundation for bilevel optimization in online, non-stationary scenarios.