In practice, many machine learning (ML) problems come with constraints, and their applied domains involve distributed sensitive data that cannot be shared with others, e.g., in healthcare. Collaborative learning in such practical scenarios entails federated learning (FL) for ML problems with constraints, or FL with constraints for short. Despite the extensive developments of FL techniques in recent years, these techniques only deal with unconstrained FL problems or FL problems with simple constraints that are amenable to easy projections. There is little work dealing with FL problems with general constraints. To fill this gap, we take the first step toward building an algorithmic framework for solving FL problems with general constraints. In particular, we propose a new FL algorithm for constrained ML problems based on the proximal augmented Lagrangian (AL) method. Assuming convex objective and convex constraints plus other mild conditions, we establish the worst-case complexity of the proposed algorithm. Our numerical experiments show the effectiveness of our algorithm in performing Neyman-Pearson classification and fairness-aware learning with nonconvex constraints, in an FL setting.

翻译：在实际应用中，许多机器学习问题都带有约束条件，且其相关领域（如医疗健康）涉及无法与他人共享的分布式敏感数据。此类实际场景下的协作学习需要针对带约束机器学习问题的联邦学习（简称带约束联邦学习）。尽管近年来联邦学习技术取得了广泛发展，但这些技术仅能处理无约束联邦学习问题或可通过简单投影解决的带简单约束的联邦学习问题。针对具有一般约束的联邦学习问题的研究工作甚少。为填补这一空白，我们率先迈出了构建求解一般约束联邦学习问题算法框架的第一步。具体而言，我们基于近端增广拉格朗日方法提出了一种适用于带约束机器学习问题的新型联邦学习算法。在假设目标函数和约束条件均为凸函数及其他温和条件下，我们建立了所提算法的最坏情况复杂度。数值实验表明，该算法在联邦学习场景下进行Neyman-Pearson分类与非凸约束公平性学习时具有有效性。