

In [ ]:

    
%matplotlib inline

Use different base estimators for optimization

Sigurd Carlen, September 2019. Reformatted by Holger Nahrstaedt 2020

.. currentmodule:: skopt

To use different base_estimator or create a regressor with different parameters, we can create a regressor object and set it as kernel.



In [ ]:

    
print(__doc__)

import numpy as np
np.random.seed(1234)
import matplotlib.pyplot as plt

Toy example

Let assume the following noisy function $f$:



In [ ]:

    
noise_level = 0.1

# Our 1D toy problem, this is the function we are trying to
# minimize

def objective(x, noise_level=noise_level):
    return np.sin(5 * x[0]) * (1 - np.tanh(x[0] ** 2))\
           + np.random.randn() * noise_level



In [ ]:

    
from skopt import Optimizer
opt_gp = Optimizer([(-2.0, 2.0)], base_estimator="GP", n_initial_points=5,
                acq_optimizer="sampling", random_state=42)



In [ ]:

    
x = np.linspace(-2, 2, 400).reshape(-1, 1)
fx = np.array([objective(x_i, noise_level=0.0) for x_i in x])



In [ ]:

    
from skopt.acquisition import gaussian_ei

def plot_optimizer(res, next_x, x, fx, n_iter, max_iters=5):
    x_gp = res.space.transform(x.tolist())
    gp = res.models[-1]
    curr_x_iters = res.x_iters
    curr_func_vals = res.func_vals

    # Plot true function.
    ax = plt.subplot(max_iters, 2, 2 * n_iter + 1)
    plt.plot(x, fx, "r--", label="True (unknown)")
    plt.fill(np.concatenate([x, x[::-1]]),
             np.concatenate([fx - 1.9600 * noise_level,
                             fx[::-1] + 1.9600 * noise_level]),
             alpha=.2, fc="r", ec="None")
    if n_iter < max_iters - 1:
        ax.get_xaxis().set_ticklabels([])
    # Plot GP(x) + contours
    y_pred, sigma = gp.predict(x_gp, return_std=True)
    plt.plot(x, y_pred, "g--", label=r"$\mu_{GP}(x)$")
    plt.fill(np.concatenate([x, x[::-1]]),
             np.concatenate([y_pred - 1.9600 * sigma,
                             (y_pred + 1.9600 * sigma)[::-1]]),
             alpha=.2, fc="g", ec="None")

    # Plot sampled points
    plt.plot(curr_x_iters, curr_func_vals,
             "r.", markersize=8, label="Observations")
    plt.title(r"x* = %.4f, f(x*) = %.4f" % (res.x[0], res.fun))
    # Adjust plot layout
    plt.grid()

    if n_iter == 0:
        plt.legend(loc="best", prop={'size': 6}, numpoints=1)

    if n_iter != 4:
        plt.tick_params(axis='x', which='both', bottom='off',
                        top='off', labelbottom='off')

    # Plot EI(x)
    ax = plt.subplot(max_iters, 2, 2 * n_iter + 2)
    acq = gaussian_ei(x_gp, gp, y_opt=np.min(curr_func_vals))
    plt.plot(x, acq, "b", label="EI(x)")
    plt.fill_between(x.ravel(), -2.0, acq.ravel(), alpha=0.3, color='blue')

    if n_iter < max_iters - 1:
        ax.get_xaxis().set_ticklabels([])

    next_acq = gaussian_ei(res.space.transform([next_x]), gp,
                           y_opt=np.min(curr_func_vals))
    plt.plot(next_x, next_acq, "bo", markersize=6, label="Next query point")

    # Adjust plot layout
    plt.ylim(0, 0.07)
    plt.grid()
    if n_iter == 0:
        plt.legend(loc="best", prop={'size': 6}, numpoints=1)

    if n_iter != 4:
        plt.tick_params(axis='x', which='both', bottom='off',
                        top='off', labelbottom='off')

GP kernel



In [ ]:

    
fig = plt.figure()
fig.suptitle("Standard GP kernel")
for i in range(10):
    next_x = opt_gp.ask()
    f_val = objective(next_x)
    res = opt_gp.tell(next_x, f_val)
    if i >= 5:
        plot_optimizer(res, opt_gp._next_x, x, fx, n_iter=i-5, max_iters=5)
plt.tight_layout(rect=[0, 0.03, 1, 0.95])
plt.plot()

Test different kernels



In [ ]:

    
from skopt.learning import GaussianProcessRegressor
from skopt.learning.gaussian_process.kernels import ConstantKernel, Matern
# Gaussian process with Matérn kernel as surrogate model

from sklearn.gaussian_process.kernels import (RBF, Matern, RationalQuadratic,
                                              ExpSineSquared, DotProduct,
                                              ConstantKernel)


kernels = [1.0 * RBF(length_scale=1.0, length_scale_bounds=(1e-1, 10.0)),
           1.0 * RationalQuadratic(length_scale=1.0, alpha=0.1),
           1.0 * ExpSineSquared(length_scale=1.0, periodicity=3.0,
                                length_scale_bounds=(0.1, 10.0),
                                periodicity_bounds=(1.0, 10.0)),
           ConstantKernel(0.1, (0.01, 10.0))
               * (DotProduct(sigma_0=1.0, sigma_0_bounds=(0.1, 10.0)) ** 2),
           1.0 * Matern(length_scale=1.0, length_scale_bounds=(1e-1, 10.0),
                        nu=2.5)]



In [ ]:

    
for kernel in kernels:
    gpr = GaussianProcessRegressor(kernel=kernel, alpha=noise_level ** 2,
                                   normalize_y=True, noise="gaussian",
                                   n_restarts_optimizer=2
                                   )
    opt = Optimizer([(-2.0, 2.0)], base_estimator=gpr, n_initial_points=5,
                    acq_optimizer="sampling", random_state=42)
    fig = plt.figure()
    fig.suptitle(repr(kernel))
    for i in range(10):
        next_x = opt.ask()
        f_val = objective(next_x)
        res = opt.tell(next_x, f_val)
        if i >= 5:
            plot_optimizer(res, opt._next_x, x, fx, n_iter=i - 5, max_iters=5)
    plt.tight_layout(rect=[0, 0.03, 1, 0.95])
    plt.show()