You may be wondering what’s “Bayesian” about Bayesian Optimization if we’re just optimizing these acquisition functions. Use an acquisition function α ( x ) \alpha(x) α ( x ) , which is a function of the posterior, to decide the next sample point x t = argmax x α ( x ) x_t = \text{argmax}_x \alpha(x) x t ​ = argmax x ​ α ( x ) . Like the PI acquisition function, we can moderate the amount of exploration of the EI acquisition function by modifying ϵ \epsilon ϵ.