# Doubly Robust Off-Policy Learning on Low-Dimensional Manifolds by Deep Neural Networks

arXiv: https://arxiv.org/abs/2011.01797 · HTML: https://mlsanity.com/paper/2011.01797/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Nov 2020.

## Built on by (most cited first, 7 of 7)

- [Deep Nonparametric Estimation of Operators between Infinite Dimensional Spaces](https://mlsanity.com/paper/2201.00217/) (2022)
- [Besov Function Approximation and Binary Classification on Low-Dimensional Manifolds Using Convolutional Residual Networks](https://mlsanity.com/paper/2109.02832/) (2021)
- [Robust Reinforcement Learning from Corrupted Human Feedback](https://mlsanity.com/paper/2406.15568/) (2024)
- [Deep Nonparametric Estimation of Intrinsic Data Structures by Chart Autoencoders: Generalization Error and Robustness](https://mlsanity.com/paper/2303.09863/) (2023)
- [Learning Interaction Kernels for Agent Systems on Riemannian Manifolds](https://mlsanity.com/paper/2102.00327/) (2021)
- [Convergence Guarantees for Deep Epsilon Greedy Policy Learning](https://mlsanity.com/paper/2112.03376/) (2021)
- [Benefits of Overparameterized Convolutional Residual Networks: Function Approximation under Smoothness Constraint](https://mlsanity.com/paper/2206.04569/) (2022)

## Abstract (arXiv)

Causal inference explores the causation between actions and the consequent rewards on a covariate set. Recently deep learning has achieved a remarkable performance in causal inference, but existing statistical theories cannot well explain such an empirical success, especially when the covariates are high-dimensional. Most theoretical results in causal inference are asymptotic, suffer from the curse of dimensionality, and only work for the finite-action scenario. To bridge such a gap between theory and practice, this paper studies doubly robust off-policy learning by deep neural networks. When the covariates lie on a low-dimensional manifold, we prove nonasymptotic regret bounds, which converge at a fast rate depending on the intrinsic dimension of the manifold. Our results cover both the finite- and continuous-action scenarios. Our theory shows that deep neural networks are adaptive to the low-dimensional geometric structures of the covariates, and partially explains the success of deep learning for causal inference.