Non-Stationary Functional Bilevel Optimization

Jason Bohne, Ieva Petrulionytė, Michael Arbel, Julien Mairal, Pawel Polak

TL;DR: SmoothFBO is a functional bilevel optimization algorithm for both stationary and non-stationary settings. It uses time-smoothing to stabilize updates, achieves sublinear regret, and outperforms existing methods under distribution shifts.

Abstract: 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.

Submission Number: 2419