# Optimizing Sampled Function via Thompson SamplingΒΆ

This example is to optimize a function sampled from a Gaussian process prior via Thompson sampling. First of all, import the packages we need and bayeso.

import numpy as np

from bayeso import covariance
from bayeso.gp import gp
from bayeso.utils import utils_covariance
from bayeso.utils import utils_plotting


Declare some parameters to control this example, including zero-mean prior, and compute a covariance matrix.

num_points = 1000
str_cov = 'se'
num_iter = 50
num_ts = 10

list_Y_min = []

X = np.expand_dims(np.linspace(-5, 5, num_points), axis=1)
mu = np.zeros(num_points)
hyps = utils_covariance.get_hyps(str_cov, 1)
Sigma = covariance.cov_main(str_cov, X, X, hyps, True)


Optimize a function sampled from a Gaussian process prior. At each iteration, we sample a query point that outputs the mininum value of the function sampled from a Gaussian process posterior.

for ind_ts in range(0, num_ts):
print('TS:', ind_ts + 1, 'round')
Y = gp.sample_functions(mu, Sigma, num_samples=1)[0]

ind_init = np.argmin(Y)
bx_min = X[ind_init]
y_min = Y[ind_init]

ind_random = np.random.choice(num_points)

X_ = np.expand_dims(X[ind_random], axis=0)
Y_ = np.expand_dims(np.expand_dims(Y[ind_random], axis=0), axis=1)

for ind_iter in range(0, num_iter):
print(ind_iter + 1, 'iteration')

mu_, sigma_, Sigma_ = gp.predict_with_optimized_hyps(X_, Y_, X, str_cov=str_cov)
ind_ = np.argmin(gp.sample_functions(np.squeeze(mu_, axis=1), Sigma_, num_samples=1)[0])

X_ = np.concatenate([X_, [X[ind_]]], axis=0)
Y_ = np.concatenate([Y_, [[Y[ind_]]]], axis=0)

list_Y_min.append(Y_ - y_min)

Ys = np.array(list_Y_min)
Ys = np.squeeze(Ys, axis=2)
print(Ys.shape)


Plot the result obtained from the code block above.

utils_plotting.plot_minimum_vs_iter(
np.array([Ys]), ['TS'], 1, True,
str_x_axis=r'\textrm{Iteration}',
str_y_axis=r'\textrm{Minimum regret}'
)


Full code:

import numpy as np

from bayeso import covariance
from bayeso.gp import gp
from bayeso.utils import utils_covariance
from bayeso.utils import utils_plotting

num_points = 1000
str_cov = 'se'
num_iter = 50
num_ts = 10

list_Y_min = []

X = np.expand_dims(np.linspace(-5, 5, num_points), axis=1)
mu = np.zeros(num_points)
hyps = utils_covariance.get_hyps(str_cov, 1)
Sigma = covariance.cov_main(str_cov, X, X, hyps, True)

for ind_ts in range(0, num_ts):
print('TS:', ind_ts + 1, 'round')
Y = gp.sample_functions(mu, Sigma, num_samples=1)[0]

ind_init = np.argmin(Y)
bx_min = X[ind_init]
y_min = Y[ind_init]

ind_random = np.random.choice(num_points)

X_ = np.expand_dims(X[ind_random], axis=0)
Y_ = np.expand_dims(np.expand_dims(Y[ind_random], axis=0), axis=1)

for ind_iter in range(0, num_iter):
print(ind_iter + 1, 'iteration')

mu_, sigma_, Sigma_ = gp.predict_with_optimized_hyps(X_, Y_, X, str_cov=str_cov)
ind_ = np.argmin(gp.sample_functions(np.squeeze(mu_, axis=1), Sigma_, num_samples=1)[0])

X_ = np.concatenate([X_, [X[ind_]]], axis=0)
Y_ = np.concatenate([Y_, [[Y[ind_]]]], axis=0)

list_Y_min.append(Y_ - y_min)

Ys = np.array(list_Y_min)
Ys = np.squeeze(Ys, axis=2)
print(Ys.shape)

utils_plotting.plot_minimum_vs_iter(
np.array([Ys]), ['TS'], 1, True,