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from __future__ import print_function, division, absolute_import

import GPy
import numpy as np
import matplotlib as mpl
import matplotlib.pyplot as plt
%matplotlib inline

import safeopt

mpl.rcParams['figure.figsize'] = (20.0, 10.0)
mpl.rcParams['font.size'] = 20
mpl.rcParams['lines.markersize'] = 20

Define a kernel and function

Here we define a kernel. The function is drawn at random from the GP and is corrupted my Gaussian noise



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# Measurement noise
noise_var = 0.05 ** 2
noise_var2 = 1e-5

# Bounds on the inputs variable
bounds = [(-10., 10.)]

# Define Kernel
kernel = GPy.kern.RBF(input_dim=len(bounds), variance=2., lengthscale=1.0, ARD=True)
kernel2 = kernel.copy()

# set of parameters
parameter_set = safeopt.linearly_spaced_combinations(bounds, 1000)

# Initial safe point
x0 = np.zeros((1, len(bounds)))

# Generate function with safe initial point at x=0
def sample_safe_fun():
    fun = safeopt.sample_gp_function(kernel, bounds, noise_var, 100)
    while True:
        fun2 = safeopt.sample_gp_function(kernel2, bounds, noise_var2, 100)
        if fun2(0, noise=False) > 1:
            break
            
    def combined_fun(x, noise=True):
        return np.hstack([fun(x, noise), fun2(x, noise)])
    return combined_fun

Interactive run of the algorithm



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# Define the objective function
fun = sample_safe_fun()

# The statistical model of our objective function and safety constraint
y0 = fun(x0)
gp = GPy.models.GPRegression(x0, y0[:, 0, None], kernel, noise_var=noise_var)
gp2 = GPy.models.GPRegression(x0, y0[:, 1, None], kernel2, noise_var=noise_var2)

# The optimization routine
# opt = safeopt.SafeOptSwarm([gp, gp2], [-np.inf, 0.], bounds=bounds, threshold=0.2)
opt = safeopt.SafeOpt([gp, gp2], parameter_set, [-np.inf, 0.], lipschitz=None, threshold=0.1)



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def plot():
    # Plot the GP
    opt.plot(100)
    # Plot the true function
    y = fun(parameter_set, noise=False)
    for manager, true_y in zip(mpl._pylab_helpers.Gcf.get_all_fig_managers(), y.T):
        figure = manager.canvas.figure
        figure.gca().plot(parameter_set, true_y, color='C2', alpha=0.3)
    
plot()



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# Obtain next query point
x_next = opt.optimize()
# Get a measurement from the real system
y_meas = fun(x_next)
# Add this to the GP model
opt.add_new_data_point(x_next, y_meas)

plot()



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