Myopic Policies for Budgeted Optimization with Constrained Experiments

Motivated by a real-world problem, we study a novel budgeted optimization problem where the goal is to optimize an unknown function f ( x ) given a budget. In our setting, it is not practical to request samples of  f ( x ) at precise input values due to the formidable cost of precise experimental setup. Rather, we may request a constrained experiment, which is a subset r of the input space for which the experimenter returns  x  in r and  f ( x ). Importantly, as the constraints become looser, the experimental cost decreases, but the uncertainty about the location  x  of the next observation increases. Our goal is to manage this trade-off by selecting a sequence of constrained experiments to best optimize f within the budget. We introduce cost-sensitive policies for selecting constrained experiments using both model-free and model-based approaches, inspired by policies for unconstrained settings. Experiments on synthetic functions and functions derived from real-world experimental data indicate that our policies outperform random selection, that the model-based policies are superior to model-free ones, and give insights into which policies are preferable overall.