利用expected improvement原理生成一段代码
时间: 2024-01-07 20:03:26 浏览: 31
以下是利用expected improvement原理生成一段Python代码的示例:
```
import numpy as np
from scipy.stats import norm
# Define the objective function
def objective(x):
return -np.sin(3*x) - x**2 + 0.7*x
# Define the acquisition function (expected improvement)
def acquisition(x, X_sample, Y_sample, xi=0.01):
mu, sigma = posterior(X_sample, Y_sample, x)
f_max = np.max(Y_sample)
with np.errstate(divide='warn'):
imp = mu - f_max - xi
Z = imp / sigma
ei = imp * norm.cdf(Z) + sigma * norm.pdf(Z)
ei[sigma == 0.0] = 0.0
return ei
# Define the posterior probability function
def posterior(X_sample, Y_sample, X_star, l=1.0, sigma_f=1.0, sigma_n=1e-4):
K = kernel(X_sample, X_sample, l, sigma_f) + sigma_n**2 * np.eye(len(X_sample))
K_star = kernel(X_sample, X_star, l, sigma_f)
K_star_star = kernel(X_star, X_star, l, sigma_f) + 1e-8 * np.eye(len(X_star))
K_inv = np.linalg.inv(K)
mu_star = K_star.T.dot(K_inv).dot(Y_sample)
sigma_star = K_star_star - K_star.T.dot(K_inv).dot(K_star)
return mu_star, sigma_star
# Define the kernel function (squared exponential)
def kernel(X1, X2, l=1.0, sigma_f=1.0):
sqdist = np.sum(X1**2, 1).reshape(-1, 1) + np.sum(X2**2, 1) - 2 * np.dot(X1, X2.T)
return sigma_f**2 * np.exp(-0.5 / l**2 * sqdist)
# Define the optimization loop
def optimize(objective, bounds, n_iter=50):
X_sample = np.array([])
Y_sample = np.array([])
for i in range(n_iter):
# Generate a random sample and evaluate the objective function
x = np.random.uniform(bounds[0], bounds[1], size=(1, 1))
y = objective(x)
# Add the sample to the data set
X_sample = np.vstack((X_sample, x)) if X_sample.size else x
Y_sample = np.vstack((Y_sample, y)) if Y_sample.size else y
# Update the model and compute the next sample
mu, sigma = posterior(X_sample, Y_sample, x)
next_x = np.argmax(acquisition(bounds, X_sample, Y_sample))
next_y = objective(next_x)
return next_x, next_y
```
上述代码实现了一个基于高斯过程的贝叶斯优化算法,其中用到了expected improvement原理来选择下一次采样的点。函数optimize()接受一个目标函数和变量的边界,返回下一个最优的点和该点的函数值。可以通过多次调用optimize()函数来逐步优化目标函数。