Memory-based Stochastic Optimization

In this paper we introduce new algorithms for optimizing noisy plants in which each experiment is very expensive. The algorithms build a global nonlinear model of the expected output at the same time as using Bayesian linear regression analysis of locally weighted polynomial models. The local model answers queries about confidence, noise,gradient and Hessians, and use them to make automated decisions similar to those made by a practitioner of Response Surface Methodology. The global and local models are combined naturally as a locally weighted regression. We examine the question ofwhether the global model can really help optimization, and we extend it to the case of time-varying functions. We compare the new algorithms with a highly tuned higher-order stochastic optimization algorithmon randomly-generated functions and a simulated manufacturing task. We note significant improvements in total regret, time to converge, and final solution quality. 1 INTRODUCTION In a stochastic optimization problem, noisy samples are taken from a plant. A sample consists of a chosen control u (a vector ofreal numbers) and a noisy observed response y.