A quantile-based nested partition algorithm for black-box functions on a continuous domain

摘要

Simulation models commonly describe complex systems with no closed-form analytical representation. This paper proposes an algorithm for functions on continuous domains that fits into the nested partition framework and uses quantile estimation to rank regions and identify the most promising region. Additionally, we apply the optimal computational budget allocation (OCBA) method for allocating sample points using the normality property of quantile estimators. We prove that, for functions satisfying the Lipschitz condition, the algorithm converges in probability to a region that contains the true global optimum. The paper concludes with some numerical results.