Developments in stochastic optimization algorithms with gradient approximations based on function measurements

There has recently been much interest in recursive optimization algorithms that rely on measurements of only the objective function, not requiring measurements of the gradient (or higher derivatives) of the objective function. The algorithms are implemented by forming an approximation to the gradient at each iteration that is based on the function measurements. Such algorithms have the advantage of not requiring detailed modeling information describing the relationship between the parameters to be optimized and the objective function. To properly cope with the noise that generally occurs in the measurements, these algorithms are best placed within a stochastic approximation framework. This paper discusses some of the main contributions to this class of algorithms, beginning in the early 1950s and progressing until now.