Learning-Augmented Online Allocation under Unreliable Advice: Robustness, Exposure Fairness, and Distribution Shift

Learning-augmented algorithms improve online decisions using predictions, but unreliable advice may harm efficiency and fairness. We study an online allocation problem with finite candidate sets, irreversible decisions, and exposure constraints. We propose a robust and fair rule combining advice with a conservative fallback and fairness correction. Under bounded-error assumptions, we prove consistency and robustness with loss proportional to prediction error. Experiments show stability under adversarial advice and significant reductions in exposure disparity.

Lipschitz Continuity in Deep Learning: A Systematic Review of Theoretical Foundations, Estimation Methods, Regularization Approaches, and Certifiable Robustness

Lipschitz continuity is a fundamental property of neural networks that characterizes their sensitivity to input perturbations. It plays a pivotal role in deep learning, governing \textbf{robustness}, \textbf{generalization} and \textbf{optimization dynamics}. Despite its importance, research on Lipschitz continuity is scattered across various domains, lacking a unified perspective. This paper addresses this gap by providing a systematic review of Lipschitz continuity in deep learning. We explore its \textbf{theoretical foundations}, \textbf{estimation methods}, \textbf{regularization approaches}, and \textbf{certifiable robustness}. By reviewing existing research through the lens of Lipschitz continuity, this survey serves as a comprehensive reference for researchers and practitioners seeking a deeper understanding of Lipschitz continuity and its implications in deep learning.

Upper Bounds on the Generalization Error of Deep Learning Models via Local Robustness and Stability

Generalization is a critical property of data-driven models, particularly deep learning models deployed in safety-critical applications. Robustness-based generalization bounds have gained attention as a principled way to link robustness properties to generalization performance, often in a data-dependent manner. However, most existing bounds suffer from vacuousness in practical settings, yielding loose upper bounds that greatly exceed the actual error rates and limiting their usefulness for real-world evaluation. While this issue is often attributed to the uncertainty term, a substantial part of the problem originates from the robustness term itself, particularly for the 0-1 loss. Existing approaches typically treat the robustness term as a global measure, ignoring its variation across different sub-regions of the input space. In this work, we propose a generalization bound that addresses this limitation by scaling the robustness term according to the number of stable and unstable samples within each sub-region. Our bounds incorporate both data- and model-dependent factors while maintaining practical relevance (yielding tighter upper bounds on true error). Experiments on models trained on the ImageNet dataset show that our bounds remain consistently non-vacuous and achieve the tightest estimates among existing methods, closely aligning with empirical performance across a range of robust deep neural networks.