学习样本重要性：在无处不在学习中对偶变量的参数化

中文摘要 AI 辅助

无处不在学习提供了一个原则性框架，用于在必须贯穿整个数据分布的约束下训练人工智能模型。在对偶域中，这些逐点约束产生了函数对偶变量。在这项工作中，我们提出学习这些对偶变量，其动机在于它们的值编码了关于底层约束问题的有用信息。通过将对偶变量表示为每个样本的参数化函数，我们使得学习到的乘子能够在新的、未见过的样本上进行评估。这与标准的经验对偶公式形成对比，后者为每个训练样本分配一个独立的乘子。我们刻画了将对偶变量限制在参数化函数类中所引起的恢复原始解误差，并表明该误差由该函数类逼近最优统计乘子的程度所控制。此外，我们表明学习到的参数化乘子保留了最优统计乘子的敏感性解释，从而提供了超越训练样本的近似敏感性保证。我们在各种无处不在学习任务上实证验证了我们的理论，表明由此产生的约束问题可以高效求解，并且学习到的对偶变量提供了样本级敏感性的有意义表示。

英文摘要

Everywhere learning provides a principled framework for training AI models under constraints that must hold throughout the data distribution. In the dual domain, these pointwise constraints give rise to functional dual variables. In this work, we propose to learn these dual variables, motivated by the fact that their values encode useful information about the underlying constrained problem. By representing the dual variable as a parametric function of each sample, we enable the learned multiplier to be evaluated on new, unseen samples. This contrasts with standard empirical dual formulations, which assign an independent multiplier to each training sample. We characterize the error in the recovered primal solution induced by restricting the dual variable to a parametric function class and show that it is controlled by how well this class approximates the optimal statistical multiplier. Moreover, we show that the learned parametric multiplier retains the sensitivity interpretation of the optimal statistical multiplier, yielding approximate sensitivity guarantees that extend beyond the samples used for training. We empirically validate our theory across a variety of everywhere learning tasks, showing that the resulting constrained problems can be solved efficiently and that the learned dual variables provide meaningful representations of sample-level sensitivity.

发表机构

• University of Pennsylvania（宾夕法尼亚大学）

机构由 AI 辅助整理，请以论文原文为准。