Experimental Design via Generalized Mean Objective Cost of Uncertainty

The mean objective cost of uncertainty (MOCU) quantifies the performance cost of using an operator that is optimal across an uncertainty class of systems as opposed to using an operator that is optimal for a particular system. MOCU-based experimental design selects an experiment to maximally reduce MOCU, thereby gaining the greatest reduction of uncertainty impacting the operational objective. The original formulation applied to finding optimal system operators, where optimality is with respect to a cost function, such as mean-square error; and the prior distribution governing the uncertainty class relates directly to the underlying physical system. Here we provide a generalized MOCU and the corresponding experimental design. We then demonstrate how this new formulation includes as special cases MOCU-based experimental design methods developed for materials science and genomic networks when there is experimental error. Most importantly, we show that the classical Knowledge Gradient and Efficient Global Optimization experimental design procedures are actually implementations of MOCU-based experimental design under their modeling assumptions

Sequential Experimental Design for Optimal Structural Intervention in Gene Regulatory Networks Based on the Mean Objective Cost of Uncertainty

Scientists are attempting to use models of ever increasing complexity, especially in medicine, where gene-based diseases such as cancer require better modeling of cell regulation. Complex models suffer from uncertainty and experiments are needed to reduce this uncertainty. Because experiments can be costly and time-consuming it is desirable to determine experiments providing the most useful information. If a sequence of experiments is to be performed, experimental design is needed to determine the order. A classical approach is to maximally reduce the overall uncertainty in the model, meaning maximal entropy reduction. A recently proposed method takes into account both model uncertainty and the translational objective, for instance, optimal structural intervention in gene regulatory networks, where the aim is to alter the regulatory logic to maximally reduce the long-run likelihood of being in a cancerous state. The mean objective cost of uncertainty (MOCU) quantifies uncertainty based on the degree to which model uncertainty affects the objective. Experimental design involves choosing the experiment that yields the greatest reduction in MOCU. This paper introduces finite-horizon dynamic programming for MOCU-based sequential experimental design and compares it to the greedy approach, which selects one experiment at a time without consideration of the full horizon of experiments. A salient aspect of the paper is that it demonstrates the advantage of MOCU-based design over the widely used entropy-based design for both greedy and dynamic-programming strategies and investigates the effect of model conditions on the comparative performances