Sequential model based optimization with black-box constraints: Feasibility determination via machine learning

This paper presents a Sequential M odel Based Optimization framework for optimizing black-box expensive objective functions where feasibile search space is unknown a-priori. The framework is organized in two phases, the first uses M achine Learning (a Support Vector M achine classifier) to approximate the boundary of the feasible search space, the second uses standard Bayesian Optimization to perform efficient global optimization. With respect to the first phase, a specific acquisition function, to identify the next promising point to evaluate, has been proposed, dealing with the trade-off between improving the accuracy of the estimated feasible region and the possibility to discover possible disconnections of the actual feasible region. The main difference with standard Bayesian Optimization is that the optimization process is performed on the estimated feasibility region, only. Results on a set of 2D test functions proved that the proposed approach is more effective and efficient than standard Bayesian Optimization using a penalty for infeasibility.