Stochastic Approximation with Gaussian Process Regression
Yingcui Yan, Haihui Shen, Zhibin Jiang · 2021
Stochastic approximation (SA) is attractive due to its curse-of-dimensionality-free convergence rate, but its finite-sample performance is not always satisfying. In addition to improving SA solely, it is also a promising direction to combine SA with other simulation optimization methods together for better performance. In this paper we propose to integrate the original SA with Gaussian process (GP) regression, and call this algorithm SAwGP. The GP regression serves as a surrogate model and it uses all the past sampling information to guide the SA iteration, which tends to be beneficial especially in the early stage. We theoretically prove that integrating the surrogate model does not ruin the local convergence of SA, and numerically demonstrate that the finite-sample performance of SAwGP is better than the original SA while the rate of convergence does not deteriorate and is even enhanced.