aiqbench analysis
This research introduces SmoothFBO, a novel algorithm addressing the limitations of functional bilevel optimization in dynamic, non-stationary environments. By leveraging time-smoothed stochastic hypergradient estimators, it achieves sublinear regret and outperforms existing methods in online hyperparameter tuning and reinforcement learning tasks. The work establishes a theoretically grounded foundation for handling hierarchical learning scenarios where data distributions shift over time.
Non-Stationary Functional Bilevel Optimization
arXiv:2601.15363v2 Announce Type: replace-cross 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.
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.
Machine Learning (stat.ML); Machine Learning (cs.LG)
arXiv:2601.15363 [stat.ML]
(or arXiv:2601.15363v2 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2601.15363 Focus to learn more arXiv-issued DOI via DataCite
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