Doubly Robust Off-Policy Learning on Low-Dimensional Manifolds by Deep Neural Networks
This work provides theoretical justification for deep learning in causal inference, addressing a foundational problem for researchers in machine learning and statistics, though it is incremental in bridging theory and practice.
The paper tackles the gap between empirical success and theoretical understanding of deep learning in causal inference by proving nonasymptotic regret bounds for doubly robust off-policy learning with deep neural networks, showing convergence rates dependent on the intrinsic dimension of low-dimensional manifolds in covariates.
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.