BayesianOptimizer_get_ei.py

    def _get_expected_improvement(self, x_new):

        # Using estimate from Gaussian surrogate instead of actual function for 
        # a new trial data point to avoid cost 
 
        mean_y_new, sigma_y_new = self.gauss_pr.predict(np.array([x_new]), return_std=True)
        sigma_y_new = sigma_y_new.reshape(-1,1)
        if sigma_y_new == 0.0:
            return 0.0
        
        # Using estimates from Gaussian surrogate instead of actual function for 
        # entire prior distribution to avoid cost
        
        mean_y = self.gauss_pr.predict(self.x_init)
        max_mean_y = np.max(mean_y)
        z = (mean_y_new - max_mean_y) / sigma_y_new
        exp_imp = (mean_y_new - max_mean_y) * norm.cdf(z) + sigma_y_new * norm.pdf(z)
        
        return exp_imp