Formal basis for algorithm comparisons in stochastic optimization

This paper establishes a framework for formal comparisons of several leading optimization algorithms, establishing guidance to practitioners for when to use or not use a particular method. The focus in this paper is four general algorithm forms: random search, simultaneous perturbation stochastic approximation, simulated annealing, and evolution strategies. We summarize the available theoretical results on rates of convergence for the four algorithm forms and then use the theoretical results to draw some preliminary conclusions on the relative efficiency. Our aim is to contribute towards sorting out some of the competing claims of efficiency and to suggest a structure for comparison that is more general and transferable than the usual problem-specific numerical studies.