IEMAX stands for interval estimation maximization, named after the interval estimation algorithm proposed by Leslie Kaelbling. Instead of using the expected cost, the algorithm is optimistic and uses the best cost that falls anywhere within a confidence interval on the expected value of Y. We use I(f(X)) to denote all the values of Y inside a confidence interval on the estimation of f(X). Then IEMAX is defined as:
Again, IEMAX will suggest the experiment with the highest (or lowest) value. In the case of minimization, the MAX operator is replaced with the MIN operator.