Generalization Bounds for Contextual Stochastic Optimization using Kernel Regression

Yijie Wang; Grani A. Hanasusanto; Chin Pang Ho

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arXiv · 2407.10764

Generalization Bounds for Contextual Stochastic Optimization using Kernel Regression

Yijie Wang·Grani A. Hanasusanto·Chin Pang Ho

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Abstract

In this paper, we consider contextual stochastic optimization using Nadaraya-Watson kernel regression, which is one of the most common approaches in nonparametric regression. Recent studies have explored the asymptotic convergence behavior of using Nadaraya-Watson kernel regression in contextual stochastic optimization; however, the performance guarantee under finite samples remains an open question. This paper derives a finite-sample generalization bound of the Nadaraya-Watson estimator with a spherical kernel under a generic loss function. Based on the generalization bound, we further establish a suboptimality bound for the solution of the Nadaraya-Watson approximation problem relative to the optimal solution. Finally, we derive the optimal kernel bandwidth and provide a sample complexity analysis of the Nadaraya-Watson approximation problem.

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Yijie Wang, Grani A. Hanasusanto, Chin Pang Ho. 2024-07-15. Generalization Bounds for Contextual Stochastic Optimization using Kernel Regression. https://arxiv.org/abs/2407.10764

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