Comparing Techniques for Selecting Successive Values of the Treatment Variable in Sequential Experimentation

Results are given on an investigation of stochastic approximation procedures of the Robbins-Monro type. Attention is focused on formal methods for selecting successive values of a single treatment variable for a specific case in sequential experimentation. Empirical results obtained by means of Monte Carlo methods are used to compare several formal stochastic approximation techniques and stopping rules. Marked differences were found between the five approximation procedures studied. A procedure using afinite memory performed most effectively. Two procedures suggested in the literature were judged to be inefficient under various conditions.