# Towards a Unified Analysis of Neural Networks in Nonparametric Instrumental Variable Regression: Optimization and Generalization

arXiv: https://arxiv.org/abs/2511.14710 · HTML: https://mlsanity.com/paper/2511.14710/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Nov 2025.

## Built on by (most cited first, 3 of 3)

- [Fisher Decorator: Refining Flow Policy via a Local Transport Map](https://mlsanity.com/paper/2604.17919/) (2026)
- [Thinned Mean Field Langevin Dynamics](https://mlsanity.com/paper/2605.28589/) (2026)
- [Doubly Robust Proxy Causal Learning with Neural Mean Embeddings](https://mlsanity.com/paper/2605.09514/) (2026)

## Abstract (arXiv)

We establish the first global convergence result of neural networks for two stage least squares (2SLS) approach in nonparametric instrumental variable regression (NPIV). This is achieved by adopting a lifted perspective through mean-field Langevin dynamics (MFLD), unlike standard MFLD, however, our setting of 2SLS entails a bilevel optimization problem in the space of probability measures. To address this challenge, we leverage the penalty gradient approach recently developed for bilevel optimization which formulates bilevel optimization as a Lagrangian problem. This leads to a novel fully first-order algorithm, termed textttF2BMLD. Apart from the convergence bound, we further provide a generalization bound, revealing an inherent trade-off in the choice of the Lagrange multiplier between optimization and statistical guarantees. Finally, we empirically validate the effectiveness of the proposed method on an offline reinforcement learning benchmark.