PINN-BO: A Black-box Optimization Algorithm using Physics-Informed Neural Networks
This addresses the problem of optimizing noisy and expensive black-box functions in real-world scenarios, representing an incremental improvement by incorporating domain knowledge.
The paper tackles black-box optimization by integrating knowledge from Partial Differential Equations (PDEs) using Physics-Informed Neural Networks to improve sample efficiency, achieving a tighter regret bound and demonstrating better performance in experiments compared to existing methods.
Black-box optimization is a powerful approach for discovering global optima in noisy and expensive black-box functions, a problem widely encountered in real-world scenarios. Recently, there has been a growing interest in leveraging domain knowledge to enhance the efficacy of machine learning methods. Partial Differential Equations (PDEs) often provide an effective means for elucidating the fundamental principles governing the black-box functions. In this paper, we propose PINN-BO, a black-box optimization algorithm employing Physics-Informed Neural Networks that integrates the knowledge from Partial Differential Equations (PDEs) to improve the sample efficiency of the optimization. We analyze the theoretical behavior of our algorithm in terms of regret bound using advances in NTK theory and prove that the use of the PDE alongside the black-box function evaluations, PINN-BO leads to a tighter regret bound. We perform several experiments on a variety of optimization tasks and show that our algorithm is more sample-efficient compared to existing methods.