  There is an increasing need in solving high-dimensional optimization problems
under non-deterministic environment. The simultaneous perturbation stochastic
approximation (SPSA) algorithm has recently attracted considerable attention
for solving high-dimensional optimization problems where the analytical formula
cannot be attained. SPSA is designed to estimate the gradient by applying
perturbation on a random subset of dimensions at each iteration. SPSA can be
easily implemented and is highly efficient in that that it relies on
measurements of the objective function, not on measurements of the gradient of
the objective function. Since its invention, SPSA has been implemented in
various fields such as reinforcement learning, production optimization etc. The
paper briefly discuss the recent development of SPSA and its applications.
