Efficient global optimization using SPSA

A desire with iterative optimization techniques is that the algorithm reach the global optimum rather than get stranded at a local optimum value. One method used to try to assure global convergence is the injection of extra noise terms into the recursion, which may allow the algorithm to escape local optimum points. The amplitude of the injected noise is decreased over time (a process called "annealing"), so that the algorithm can finally converge when it reaches the global optimum point. In this context, we examine a certain gradient-free method, simultaneous perturbation stochastic approximation (SPSA), that has performed well in complex optimization problems. We develop a proof of conditions under which SPSA will converge globally. We argue that, in some cases, the naturally occurring error in the SPSA gradient approximation effectively introduces injected noise that promotes convergence of the algorithm to a global optimum (obviating the necessity for injecting extra noise). The discussion is supported by a numerical study.