Game-Theoretic Algorithms for Conditional Moment Matching
This work provides a scalable and efficient method for problems like instrumental variable regression and Bellman residual minimization, though it appears incremental by building on prior frameworks.
The authors tackled the problem of satisfying conditional moment restrictions in econometrics and machine learning by developing a general game-theoretic strategy that scales to nonlinear problems, is amenable to gradient-based optimization, and accounts for finite sample uncertainty, recovering existing approaches as special cases.
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.