Partition-Based Bayesian Optimization for Stochastic Simulations

Bayesian optimization (BO) is a popular simulation optimization approach. Despite its many successful applications, there remain several practical issues that have to be addressed. These includes the non-trivial optimization of the inner acquisition function (search criterion) to find the future evaluation points and the over-exploitative behavior of some BO algorithms. These issues can cause BO to select inferior points or get trapped in local optimal regions before exploring other more promising regions. This work proposes a new partition-based BO algorithm where the acquisition function is optimized over a representative set of finite points in each partition instead of the whole design space to reduce the computational complexity. Additionally, to overcome over-exploitation, the algorithm considers regions of different sizes simultaneously in each iteration, providing focus on exploration in larger regions especially at the start of the algorithm. Numerical experiments show that these features help in faster convergence to the optimal point.