The limiting behavior of the one-dimensional RM procedure is investigated when the prescribed $x$-levels of sequential experiments can be realized when random errors only. The errors of constant variance and of variance decreasing to zero are studied in Sections 2 and 3, respectively.
"Robbins-Monro Procedure with Both Variables Subject to Experimental Error." Ann. Math. Statist. 43 (4) 1089 - 1095, August, 1972. https://doi.org/10.1214/aoms/1177692462