skopt.acquisition.gaussian_ei(X, model, y_opt=0.0, xi=0.01, return_grad=False)[source][source]

Use the expected improvement to calculate the acquisition values.

The conditional probability P(y=f(x) | x) form a gaussian with a certain mean and standard deviation approximated by the model.

The EI condition is derived by computing E[u(f(x))] where u(f(x)) = 0, if f(x) > y_opt and u(f(x)) = y_opt - f(x), if``f(x) < y_opt``.

This solves one of the issues of the PI condition by giving a reward proportional to the amount of improvement got.

Note that the value returned by this function should be maximized to obtain the X with maximum improvement.

Xarray-like, shape=(n_samples, n_features)

Values where the acquisition function should be computed.

modelsklearn estimator that implements predict with return_std

The fit estimator that approximates the function through the method predict. It should have a return_std parameter that returns the standard deviation.

y_optfloat, default 0

Previous minimum value which we would like to improve upon.

xifloat, default=0.01

Controls how much improvement one wants over the previous best values. Useful only when method is set to “EI”

return_gradboolean, optional

Whether or not to return the grad. Implemented only for the case where X is a single sample.

valuesarray-like, shape=(X.shape[0],)

Acquisition function values computed at X.