Random Search in the Presence of Noise, with Application to Machine Learning

A search for the global minimum of a function is proposed; the search is on the basis of sequential noisy measurements. Because no unimodality assumptions are made, stochastic approximation and other well-known methods are not directly applicable. The search plan is shown to be convergent in probability to a set of minimizers. This study was motivated by investigations into machine learning. This setting is explained, and the methodology is applied to create an adaptively improving strategy for 8-puzzle problems.