Abstract
Instrumental variables (IV) analysis is an important applied tool for areas such as healthcare and consumer economics. For IV analysis in high-dimensional settings, the Generalized Method of Moments (GMM) using deep neural networks offers an efficient approach. With non-i.i.d. data sourced from scattered decentralized clients, federated learning is a popular paradigm for training the models while promising data privacy. However, to our knowledge, no federated algorithm for either GMM or IV analysis exists to date. In this work, we introduce federated instrumental variables analysis (FedIV) via federated generalized method of moments (FedGMM). We formulate FedGMM as a federated zero-sum game defined by a federated non-convex non-concave minimax optimization problem, which is solved using federated gradient descent ascent (FedGDA) algorithm. One key challenge arises in theoretically characterizing the federated local optimality. To address this, we present properties and existence results of clients' local equilibria via FedGDA limit points. Thereby, we show that the federated solution consistently estimates the local moment conditions of every participating client. The proposed algorithm is backed by extensive experiments to demonstrate the efficacy of our approach.
Abstract (translated)
工具变量（IV）分析在医疗保健和消费者经济学等领域中是一项重要的应用工具。对于高维环境下的IV分析，采用深度神经网络的广义矩方法（GMM）提供了一种高效的解决方案。面对非独立同分布（non-i.i.d.）的数据源，这些数据通常来自分散且去中心化的客户端，在这种情况下，联邦学习成为训练模型的一种流行范式，并保证了数据隐私的安全性。然而，据我们所知，至今为止还没有专门针对GMM或IV分析的联邦算法。 在本研究中，我们通过引入联邦广义矩方法（FedGMM）来提出联邦工具变量分析（FedIV）。我们将FedGMM定义为一个由联邦非凸非凹极小化极大化优化问题构成的联邦零和博弈，并采用联邦梯度下降上升（FedGDA）算法进行求解。在理论上刻画联邦局部最优性方面，出现了一个关键挑战。为应对这一挑战，我们通过分析FedGDA极限点来阐述客户端局部均衡的特性及其存在性结果，从而表明联邦解决方案能够一致估计每个参与客户的本地矩条件。 我们的方法得到了广泛的实验验证，证明了该算法的有效性和实用性。
URL
https://arxiv.org/abs/2505.21012
