Optimal learning with local nonlinear parametric models over continuous designs

We consider the problem of optimizing an unknown function over a multidimensional continuous domain, where function evaluation is noisy and expensive. We assume that a globally accurate model of the function is not available, but there exist some parametric models that can well approximate the function in local regions. In this paper, we propose an algorithm in the optimal learning framework that learns the shape of the function and finds the optimal design with a limited number of measurements. We construct belief functions using a radial basis function-based local approximation technique, and use the knowledge gradient policy to decide where to measure, aiming at maximizing the value of information from each measurement. Experiments on both synthetic test problems and a real materials science application show the strong performance of our algorithm.