Non-Gaussian Ensemble Optimization

Ensemble-based optimization (EnOpt), commonly used in reservoir management, can be seen as a special case of a natural evolution algorithm. Stein’s lemma gives a new interpretation of EnOpt. This interpretation enables us to study EnOpt in the context of general mutation distributions. In this paper, a non-Gaussian generalization of EnOpt (GenOpt) is proposed, where the control gradient is estimated using Stein’s lemma, and the mutation distribution is updated separately via natural evolution. For the multivariate case, a Gaussian copula is used to represent dependencies between the marginals. The correlation matrix is also iteratively optimized. It is shown that using beta distributions as marginals in the GenOpt algorithm addresses the truncation problem that sometimes arises when applying EnOpt on bounded optimization problems. The performance of the proposed optimization algorithm is evaluated on several test cases. The experiments indicate that GenOpt is less dependent on the chosen hyperparameters, and it is able to converge more quickly than EnOpt on a reservoir management test case.