A ONE-MEASUREMENT FORM OF SIMULTANEOUS PERTURBATION STOCHASTIC-APPROXIMATION

The simultaneous perturbation stochastic approximation (SPSA) algorith m has proven very effective for difficult multivariate optimization pr oblems where it is not possible to obtain direct gradient information. As discussed to date, SPSA is based on a highly efficient gradient ap proximation requiring only two measurements of the loss function indep endent of the number of parameters being estimated. This note presents a form of SPSA that requires only one function measurement (for any d imension). Theory is presented that identifies the class of problems f or which this one-measurement form will be asymptotically superior to the standard two-measurement form. (C) 1997 Elsevier Science Ltd.