Acquisition functions help determine which points in the search space should be evaluated, ideally providing information on the optimum value of f . A good acquisition function has to balance exploration against exploitation, with the trade-off based on the estimated uncertainty from a GP model. Exploration in this context involves seeking locations with high posterior variance (i.e., sampling uncertain areas), while exploitation focuses on seeking locations with low posterior mean (i.e., finding a local optimum). Three acquisition functions are commonly used, namely: probability of improvement (PI), expected improvement (EI), and GP lower confidence bound (GP-LCB), as shown in Equations 4, 5, and 6. The GP-LCB is also sometimes referred as upper confidence bound (UCB), when the optimization involves function maximization rather than minimization .