首个面向非平稳场景的函数级优化算法，理论与实践兼备。
Non-Stationary Functional Bilevel Optimization
- 引入时间平滑的随机超梯度估计，降低方差提升稳定性。
- 外层更新实现次线性后悔，非平稳场景下性能显著优于现有方法。
- 适用于在线超参优化与模型强化学习，兼具理论保障与可扩展性。
函数级双层优化（FBO）为函数空间中的层级学习提供了强大框架，但现有方法仅限于静态离线设置，在在线、非平稳场景中表现不佳。我们提出SmoothFBO，首个针对非平稳FBO的算法，兼具理论保证与实际可扩展性。SmoothFBO引入时间平滑的随机超梯度估计器，通过窗口参数降低方差，实现稳定的外层更新并达到次线性后悔。经典参数化双层优化是本框架的特例，使SmoothFBO自然扩展至在线、非平稳场景。实验表明，SmoothFBO在非平稳超参数优化和基于模型的强化学习中持续优于现有FBO方法，验证了其实际有效性。这些结果共同确立SmoothFBO为在线、非平稳场景下双层优化的一般性、理论坚实且实用的基础。
原文摘要 · Abstract (English)
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.
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