Online Statistical Inference for Stochastic Optimization via Kiefer-Wolfowitz Methods

Xi Chen, Zehua Lai, He Li and Yichen Zhang

Journal of the American Statistical Association, 2024, vol. 119, issue 548, 2972-2982

Abstract: This article investigates the problem of online statistical inference of model parameters in stochastic optimization problems via the Kiefer-Wolfowitz algorithm with random search directions. We first present the asymptotic distribution for the Polyak-Ruppert-averaging type Kiefer-Wolfowitz (AKW) estimators, whose asymptotic covariance matrices depend on the distribution of search directions and the function-value query complexity. The distributional result reflects the tradeoff between statistical efficiency and function query complexity. We further analyze the choice of random search directions to minimize certain summary statistics of the asymptotic covariance matrix. Based on the asymptotic distribution, we conduct online statistical inference by providing two construction procedures of valid confidence intervals. Supplementary materials for this article are available online.

Date: 2024
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DOI: 10.1080/01621459.2023.2296703

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