Game-Theoretic Algorithms for Conditional Moment Matching

TL;DR

This paper introduces a game-theoretic framework for solving conditional moment restrictions in econometrics and machine learning, enabling scalable, gradient-based optimization that accounts for finite sample uncertainty.

Contribution

It presents a unified, general approach to conditional moment matching that extends previous methods and improves scalability and robustness.

Findings

Framework recovers existing methods as special cases

Enables efficient gradient-based optimization

Addresses finite sample uncertainty

Abstract

A variety of problems in econometrics and machine learning, including instrumental variable regression and Bellman residual minimization, can be formulated as satisfying a set of conditional moment restrictions (CMR). We derive a general, game-theoretic strategy for satisfying CMR that scales to nonlinear problems, is amenable to gradient-based optimization, and is able to account for finite sample uncertainty. We recover the approaches of Dikkala et al. and Dai et al. as special cases of our general framework before detailing various extensions and how to efficiently solve the game defined by CMR.