Transfer Bayesian Optimization for Expensive Black-Box Optimization in Dynamic Environment

Expensive black-box optimization in dynamic environments is a challenging but important task since many real-world problems are changing over time and are computationally costly. Bayesian optimization has been widely recognized as an effective approach for tackling expensive black-box optimization in a static environment whereas it has rarely been studied for in dynamic environments. This paper proposes a simple but effective method to empower Bayesian optimization to solve dynamic optimization problems. It augments the covariance function with the measurement of the relationship between historical observations and the current ones. By doing so, the Bayesian optimization is able to leverage the observations from the previous time step to jump start the optimization in the new environment with a strictly limited computational budget. Experiments on synthetic benchmark test problems and a real-world case study demonstrate the effectiveness of our proposed algorithm.