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.

Gradient-based meta-learning and hyperparameter optimization have seen significant progress recently, enabling practical end-to-end training of neural networks together with many hyperparameters. Nevertheless, existing approaches are relatively expensive as they need to compute second-order derivatives and store a longer computational graph. This cost prevents scaling them to larger network architectures. We present EvoGrad, a new approach to meta-learning that draws upon evolutionary techniques to more efficiently compute hypergradients.

Text-to-image (T2I) diffusion models have achieved impressive image generation quality and are increasingly fine-tuned for personalized applications. However, these models often inherit unsafe behaviors from toxic pretraining data, raising growing safety concerns. While recent safety-driven unlearning methods have made promising progress in suppressing model toxicity, they are found to be fragile to downstream fine-tuning, as we reveal that state-of-the-art methods largely fail to retain their effectiveness even when fine-tuned on entirely benign datasets. To mitigate this problem, in this paper, we propose ResAlign, a safety-driven unlearning framework with enhanced resilience against downstream fine-tuning. By modeling downstream fine-tuning as an implicit optimization problem with a Moreau envelope-based reformulation, ResAlign enables efficient gradient estimation to minimize the recovery of harmful behaviors. Additionally, a meta-learning strategy is proposed to simulate a diverse distribution of fine-tuning scenarios to improve generalization. Extensive experiments across a wide range of datasets, fine-tuning methods, and configurations demonstrate that ResAlign consistently outperforms prior unlearning approaches in retaining safety, while effectively preserving benign generation capability. Our code and pretrained models are publicly available at https://github.com/AntigoneRandy/ResAlign.

The optimal policy in various real-world strategic decision-making problems depends both on the environmental configuration and exogenous events.

Bilevel optimization has gained prominence in various applications.

It is worth noting that, Eq. In Section 4.1, we have shown the experimental results of HPM on two population synthetic functions, It is worth noting that, since the synthetic function only simulates the validation loss function ( i.e., The same exploit strategy in PBT, i.e., truncation selection [ All the codes on the synthetic functions were implemented with Autograd. Same to the Figure 1 in Section 4.1, we show the mean performance We show the details of hyperparameters we tuned on the benchmark datasets as follows. The tied weight is used for the embedding and softmax layer.

Computing the gradient of model hyperparameters, i.e., hypergradient, enables a