Impact of exploration-exploitation trade-off on UCB-based Bayesian Optimization

Abstract

As an efficient global optimization method to deal with expensive black-box functions, Bayesian optimization (BO) has great potential in the field of turbomachinery component design. It can relieve the complexity, long cycle, and excessive dependence on experience of the design process. A core of Bayesian optimization is acquisition functions which aim to guide the search to efficiently find the optimum. An excellent acquisition function can greatly improve the performance of the algorithm. The well-known acquisition function, upper confidence bound (UCB), in Bayesian optimization achieves the balance between local exploitation and global exploration through an explicit trade-off coefficient. The trade-off coefficient is a key to the quality of UCB-based Bayesian optimization. Currently, this coefficient is either manually specified according to some criterion or sampled from a specific distribution. Due to the lack of a comparative study on existing trade-off strategies, this paper attempts to comprehensively analyse and highlight the impact of various trade-off strategies on the performance of UCB-based BO algorithm through eleven numerical examples and two turbomachinery design cases. The comparative results indicate that the proper trade-off is key for the optimization quality, and the strategy of looping through a trade-off set shows superiority in our numerical experiments.