A one-measurement form of simultaneous perturbation stochastic approximation

The simultaneous perturbation stochastic approximation (SPSA) algorithm has proven very effective for difficult multivariate optimization problems where it is not possible to obtain direct gradient information. As discussed to date, SPSA is based on a highly efficient gradient approximation requiring only two measurements of the loss function independent of the number of parameters being estimated. This note presents a form of SPSA that requires only one function measurement (for any dimension). Theory is presented that identifies the class of problems for which this one-measurement form will be asymptotically superior to the standard two-measurement form.