IEMAX

One approach to experiment design is that we would like to search a particular region and be sure that we have not overlooked any settings in the region that are better than those we found. At the same time, we'd like to concentrate the experiments in promising areas to hone in on the best ones. IEMAX operates in a way similar to IESAFE, except that it chooses the best upper confidence interval rather than the best lower confidence interval when doing maximization. This gives exactly the effect we are looking for. Initially, when there is no data, the upper confidence interval is very high everywhere. As data is collected, the upper confidence interval gets pushed down near the data points. When there is enough data to give gross estimates throughout the region, IEMAX starts concentrating on the most promising areas since their upper confidence intervals will still be higher than the other areas.

To demonstrate this process, we'll show what IEMAX does on the trivial task of minimizing the function without noise. Note that when minimizing, IEMAX will be choosing the point with the lowest lower confidence interval, rather than the highest upper confidence interval.

Optex -> New
         Project name      experiment
         Use current data  OFF
         Number of inputs  1
         Number of outputs 1
         Continue
         OK
         Minimize expression
         OK
Edit -> Metacode -> L40:9
Optex -> Edit -> Settings -> opt_type  IEMAX
         Choose (chooses 0.5)
         Output  0.04
         Observe
         Choose (chooses 1.0)
         Output  0.09
         Observe
(continue repeating these three steps)

  
Figure 31: Experiment selections using IEMAX on a minimization problem

You may continue asking for new experiments and manually computing what the output will be ( ). Fig. 31 shows what the predictions and confidence intervals look like from the second data point to the seventh. Notice that in each graph, the data point is taken at the point where the lower confidence interval was lowest in the previous graph. If you continue asking for more experiment choices after the seventh point, Optex will continue honing in on the best setting in the region of 0.7.