A framework for optimization under limited information

In many real world problems, optimisation decisions have to be made with limited information. The decision maker may have no a priori or posteriori data about the often nonconvex objective function except from on a limited number of data points. The scarcity of data may be due to high cost of observation or fast‐changing nature of the underlying system. This paper presents a ‘black‐box’ optimisation framework that takes into account the information collection, estimation, and optimisation aspects in a holistic and structured manner. Explicitly quantifying the observations at each optimisation step using the entropy measure from information theory, the often nonconvex‐objective function to be optimised is modelled and estimated by adopting a Bayesian approach and using Gaussian processes as a state‐of‐the‐art regression method. The resulting iterative scheme allows the decision maker to address the problem by expressing preferences for each aspect quantitatively and concurrently.