Federated Equilibrium Solutions for Generalized Method of Moments applied to Instrumental Variable Analysis

ICLR 2026 Conference Submission18817 Authors

Keywords: Federated Learning, Generalized Method of Moments, Equilibrium Solutions, Instrumental Variable Analysis, GMM

TL;DR: Existence results for federated zero-sum game equilibrium and consistent federated GMM estimators.

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 IV analysis (FedIV) via federated GMM (FedGMM). We formulate FedGMM as a federated zero-sum game defined by a non-convex non-concave minimax optimization problem. We characterize the solutions to the federated game using Stackelberg equilibrium and show that it satisfies client-local equilibria up to a heterogeneity bias. Thereby, we show that the consistency of the federated GMM estimator across clients closely depends on the heterogeneity bias. Our experiments demonstrate that the federated framework for IV analysis efficiently recovers the consistent GMM estimators for low and high-dimensional data.

Primary Area: optimization

Submission Number: 18817