Roulette Wheel Variable Selection for High Dimensional Bayesian Optimization

Bayesian optimization (BO) is a widely used method for expensive black-box optimization. The BO algorithm can effectively solve low-dimensional problems, but its performance of BO decreases sharply as the dimension increases. One of the main reasons is that the acquisition function is high-dimensional, therefore it is very challenging to find the global optimum of the acquisition function. This paper proposes a roulette wheel variable selection (RW-VS) approach to extend BO to high dimension. In each iteration, we measure the effectiveness of each variable, and then use the roulette wheel strategy to select the variables according to the important measurement. The algorithm optimizes the selected subspace to produce an acqui-sition point. The proposed roulette variable selection strategy in this paper can significantly improve the optimization efficiency of BO on high-dimensional optimization problems. Numerical experiments demonstrate the excellent performance of the RW-VS algorithm compared with the standard BO as well as five state-of-the-art high -dimensional BOs.