Adaptive experimental design using Bayesian optimization to improve the cost efficiency of small-plot field trials
In most agricultural experiments, factorial design is the standard choice of experimental design. It is intuitive, easy to use, and can be effective in some problems. However, what is hidden in these advantages is inefficiency in choosing factor levels to investigate. This is particularly problematic when the objective of experiments is to estimate the optimal value of some response function, rather than to estimate the overall shape of the response function. In the literature, this distinction is rarely made explicit, and factorial designs are used for both purposes. In this paper, we propose a novel approach, called Bayesian optimization, to adaptively designing agricultural experiments for optimization and demonstrate significant gain in the cost efficiency of small-plot field trials. Results show that the annual difference between two estimated profits by the factorial design and our approach can be as high as $272/ha despite the fact that our approach uses less than half of the plot numbers used in the factorial design. Considering the efficiency gain in both estimated profits and required number of plots, we think that Bayesian optimization can benefit many agricultural researchers in their own experiments.