# Adversarial Estimators

arXiv: https://arxiv.org/abs/2204.10495 · HTML: https://mlsanity.com/paper/2204.10495/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 64 references that are in the map.
- First posted on arXiv 22 Apr 2022.

## Builds on (most cited first, 18 of 18)

- [Generative Adversarial Imitation Learning](https://mlsanity.com/paper/1606.03476/) (2016)
- [Error bounds for approximations with deep ReLU networks](https://mlsanity.com/paper/1610.01145/) (2016)
- [f-GAN: Training Generative Neural Samplers using Variational Divergence Minimization](https://mlsanity.com/paper/1606.00709/) (2016)
- [Generalization and Equilibrium in Generative Adversarial Nets (GANs)](https://mlsanity.com/paper/1703.00573/) (2017)
- [A Survey on Generative Adversarial Networks: Variants, Applications, and Training](https://mlsanity.com/paper/2006.05132/) (2020)
- [Deep Generalized Method of Moments for Instrumental Variable Analysis](https://mlsanity.com/paper/1905.12495/) (2019)
- [Minimax Estimation of Conditional Moment Models](https://mlsanity.com/paper/2006.07201/) (2020)
- [How Well Generative Adversarial Networks Learn Distributions](https://mlsanity.com/paper/1811.03179/) (2018)
- [Double/Debiased/Neyman Machine Learning of Treatment Effects](https://mlsanity.com/paper/1701.08687/) (2017)
- [Two-Player Games for Efficient Non-Convex Constrained Optimization](https://mlsanity.com/paper/1804.06500/) (2018)
- [Off-Policy Evaluation via Adaptive Weighting with Data from Contextual Bandits](https://mlsanity.com/paper/2106.02029/) (2021)
- [Adversarial Estimation of Riesz Representers](https://mlsanity.com/paper/2101.00009/) (2020)
- [Adversarial Generalized Method of Moments](https://mlsanity.com/paper/1803.07164/) (2018)
- [Using Wasserstein Generative Adversarial Networks for the Design of Monte Carlo Simulations](https://mlsanity.com/paper/1909.02210/) (2019)
- [Nonparametric Density Estimation under Adversarial Losses](https://mlsanity.com/paper/1805.08836/) (2018)
- [The Variational Method of Moments](https://mlsanity.com/paper/2012.09422/) (2020)
- [A Generalised Method for Empirical Game Theoretic Analysis](https://mlsanity.com/paper/1803.06376/) (2018)
- [An Adversarial Approach to Structural Estimation](https://mlsanity.com/paper/2007.06169/) (2020)

## Built on by (most cited first, 2 of 2)

- [Falsification of Internal and External Validity in Observational Studies via Conditional Moment Restrictions](https://mlsanity.com/paper/2301.13133/) (2023)
- [On Neural Network approximation of ideal adversarial attack and convergence of adversarial training](https://mlsanity.com/paper/2307.16099/) (2023)

## Abstract (arXiv)

We develop an asymptotic theory of adversarial estimators ('A-estimators'). They generalize maximum-likelihood-type estimators ('M-estimators') as their average objective is maximized by some parameters and minimized by others. This class subsumes the continuous-updating Generalized Method of Moments, Generative Adversarial Networks and more recent proposals in machine learning and econometrics. In these examples, researchers state which aspects of the problem may in principle be used for estimation, and an adversary learns how to emphasize them optimally. We derive the convergence rates of A-estimators under pointwise and partial identification, and the normality of functionals of their parameters. Unknown functions may be approximated via sieves such as deep neural networks, for which we provide simplified low-level conditions. As a corollary, we obtain the normality of neural-net M-estimators, overcoming technical issues previously identified by the literature. Our theory yields novel results about a variety of A-estimators, providing intuition and formal justification for their success in recent applications.