On Bayesian Search for the Feasible Space Under Computationally Expensive Constraints
This work addresses the challenge of design exploration in engineering or optimization domains where simulations are costly, offering an incremental improvement in data-efficient search methods.
The paper tackles the problem of identifying feasible solutions under computationally expensive constraints by proposing a novel Bayesian acquisition function that balances exploitation and exploration, achieving effective prediction of feasibility with limited evaluations.
We are often interested in identifying the feasible subset of a decision space under multiple constraints to permit effective design exploration. If determining feasibility required computationally expensive simulations, the cost of exploration would be prohibitive. Bayesian search is data-efficient for such problems: starting from a small dataset, the central concept is to use Bayesian models of constraints with an acquisition function to locate promising solutions that may improve predictions of feasibility when the dataset is augmented. At the end of this sequential active learning approach with a limited number of expensive evaluations, the models can accurately predict the feasibility of any solution obviating the need for full simulations. In this paper, we propose a novel acquisition function that combines the probability that a solution lies at the boundary between feasible and infeasible spaces (representing exploitation) and the entropy in predictions (representing exploration). Experiments confirmed the efficacy of the proposed function.