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

• URL: http://arxiv.org/abs/2011.01797v1
• Date: Tue, 3 Nov 2020 15:44:42 GMT
• Title: Doubly Robust Off-Policy Learning on Low-Dimensional Manifolds by Deep Neural Networks
• Abstract summary: This paper studies doubly robust off-policy learning by deep neural networks. We prove nonasymptotic regret bounds, which converge at a fast rate depending on the dimension of the manifold.
• Score: 45.75839193177168
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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