Online Statistical Inference for Stochastic Optimization via Kiefer-Wolfowitz Methods
研究了通过Kiefer-Wolfowitz算法对随机优化问题中的模型参数进行在线统计推断，给出了渐近分布并构建了有效的置信区间。
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.