from skopt import gp_minimize
from sklearn.gaussian_process import GaussianProcessRegressor
from sklearn.gaussian_process.kernels import ConstantKernel, RBF

# Define your observed data (replace with your own data)
observed_X = np.array([0.5, 1.5, 2.0])
observed_y = np.array([2.0, 1.0, 0.5])

# Reshape the observed_X to have shape (n_samples, n_features)
observed_X = observed_X.reshape(-1, 1)

# Define the surrogate model
kernel = ConstantKernel(1.0, constant_value_bounds="fixed") * RBF(length_scale=1.0, length_scale_bounds="fixed")
surrogate_model = GaussianProcessRegressor(kernel=kernel)

# Define the optimization function using the surrogate model's prediction
def optimization_function(x):
    return surrogate_model.predict(np.array([[x]]))

# Perform Bayesian optimization using Gaussian Process with observed data
result = gp_minimize(optimization_function,
                     dimensions=[(0., 5.0)],
                     n_calls=20,
                     n_random_starts=5,
                     x0=observed_X,
                     y0=observed_y)