A new acquisition function for robust Bayesian optimization of unconstrained problems

Sibghat Ullah, Hao Wang, Stefan Menzel, Bernhard Sendhoff, Thomas Bäck

Abstract: A new acquisition function is proposed for solving robust optimization problems via Bayesian Optimization. The proposed acquisition function reflects the need for the robust instead of the nominal optimum, and is based on the intuition of utilizing the higher moments of the improvement. The efficacy of Bayesian Optimization based on this acquisition function is demonstrated on four test problems, each affected by three different levels of noise. Our findings suggest the promising nature of the proposed acquisition function as it yields a better robust optimal value of the function in 6/12 test scenarios when compared with the baseline.