A Stochastic Approximation Method

Let M (x) denote the expected value at level x of the response to a certain experiment. M (x) is assumed to be a monotone function of x but is unknown to the experimenter, and it is desired to find the solution x = of the equation M (x) =, where is a given constant. We give a method for making successive experiments at levels x₁, x₂, in such a way that xₙ will tend to in probability.