4 research outputs found
Online Statistical Inference for Stochastic Optimization via Kiefer-Wolfowitz Methods
This paper 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 function-value
query complexity and the distribution of search directions. The distributional
result reflects the trade-off between statistical efficiency and function query
complexity. We further analyze the choices of random search directions to
minimize the asymptotic covariance matrix, and conclude that the optimal search
direction depends on the optimality criteria with respect to different summary
statistics of the Fisher information matrix. Based on the asymptotic
distribution result, we conduct online statistical inference by providing two
construction procedures of valid confidence intervals. We provide numerical
experiments verifying our theoretical results with the practical effectiveness
of the procedures