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When measuring the value of a function to be minimized is not only expensivebut also with noise, the popular simultaneous perturbation stochasticapproximation (SPSA) algorithm requires only two function values in eachiteration. In this paper, we propose a method requiring only one functionmeasurement value per iteration in the average sense. We prove the strongconvergence and asymptotic normality of the new algorithm. Experimental resultsshow the effectiveness and potential of our algorithm.

Simultaneous perturbation stochastic approximation: towards one-measurement per iteration