def optimize(self, num_iter=10):
if not self.initialised:
self._init_model(num_initial_evaluations=self.num_initial_evaluations)
logger.info("Optimising %d iterations" % num_iter)
for _ in range(num_iter):
index = policies.EI(self.model, self.bounds, self.X)
xnext, _ = solvers.solve_lbfgs(index, self.bounds)
# observe and update model
ynext = self._eval(xnext)
self.model.add_data(xnext, ynext)
self.X.append(xnext)
self.Y.append(ynext)
# best point so far
self.xbest = recommenders.best_incumbent(self.model, self.bounds, self.X)
return self._search_domain_to_param_dict(self.xbest)
ell = [1.] * len(bounds) # Lengthscales
mean = 1. # Mean
model = make_gp(sn2, rho, ell, mean) # Create GP surrogate
model.add_data(X, Y[:, 1]) # Add data
#model.optimize() # Optimise hyperparameters
"""
Multi-objective optimisation
"""
exp_iter = 20
for n in range(exp_iter):
print('Additional experiment {:d}/{:d}'.format(n + 1, exp_iter))
# Acquisition function
acqfunc = EHVI(P, r, model, detf)
# Choose next point to evaluate
xnext, _ = solvers.solve_lbfgs(acqfunc, bounds)
# Make 'observation'
ycnext = func.f1(xnext) # Deterministic
yfnext = func.f2(xnext) # Black-box
# record data
X = np.vstack((X, xnext))
Y = np.vstack((Y, np.array([ycnext, yfnext])))
P = pareto2d(np.array(Y), maxX=False, maxY=False)
# Update the model
model.add_data(xnext, yfnext)
#model.optimize()
plt.scatter(P[:, 0], P[:, 1], c='b', marker='o')
def main():
"""Run the demo."""
# define the bounds over which we'll optimize, the optimal x for comparison,
# and a sequence of test points
bounds = np.array([[-5, 10.], [0, 15]])
xopt = np.array([np.pi, 2.275])
x1, x2 = np.meshgrid(np.linspace(*bounds[0], num=100),
np.linspace(*bounds[1], num=100))
xx = np.c_[x1.flatten(), x2.flatten()]
# get initial data and some test points.
X = list(inits.init_latin(bounds, 6))
Y = [f(x_) for x_ in X]
F = list()
# initialize the model
model = make_gp(0.01, 10, [1., 1.], 0)
model.add_data(X, Y)
# set a prior on the parameters
model.params['like.sn2'].set_prior('uniform', 0.005, 0.015)
model.params['kern.rho'].set_prior('lognormal', 0, 3)
model.params['kern.ell'].set_prior('lognormal', 0, 3)
model.params['mean.bias'].set_prior('normal', 0, 20)
# make a model which samples parameters
model = MCMC(model, n=10, rng=None)
# create a new figure
fig = figure(figsize=(10, 6))
while True:
# get index to solve it and plot it
index = policies.EI(model, bounds, X, xi=0.1)
# get the recommendation and the next query
xbest = recommenders.best_incumbent(model, bounds, X)
xnext, _ = solvers.solve_lbfgs(index, bounds)
# observe and update model
ynext = f(xnext)
model.add_data(xnext, ynext)
# evaluate the posterior and the acquisition function
mu, s2 = model.predict(xx)
# record our data and update the model
X.append(xnext)
Y.append(ynext)
F.append(f(xbest))
fig.clear()
ax1 = fig.add_subplotspec((2, 2), (0, 0), hidex=True)
ax2 = fig.add_subplotspec((2, 2), (1, 0), hidey=True, sharex=ax1)
ax3 = fig.add_subplotspec((2, 2), (0, 1), rowspan=2)
# plot the posterior and data
ax1.contourf(x1, x2, mu.reshape(x1.shape), alpha=0.4)
X_ = np.array(X)
ax1.scatter(X_[:-1, 0], X_[:-1, 1], marker='.')
ax1.scatter(xbest[0], xbest[1], linewidths=3, marker='o', color='r')
ax1.scatter(xnext[0], xnext[1], linewidths=3, marker='o', color='g')
ax1.set_xlim(*bounds[0])
ax1.set_ylim(*bounds[1])
ax1.set_title('current model (xbest and xnext)')
# plot the acquisition function
ax2.contourf(x1, x2, index(xx).reshape(x1.shape), alpha=0.5)
ax2.scatter(xbest[0], xbest[1], linewidths=3, marker='o', color='r')
ax2.scatter(xnext[0], xnext[1], linewidths=3, marker='o', color='g')
ax2.set_xlim(*bounds[0])
ax2.set_ylim(*bounds[1])
ax2.set_title('current policy (xnext)')
# plot the latent function at recomended points
ax3.axhline(f(xopt))
ax3.plot(F)
ax3.set_ylim(-1., 0.)
ax3.set_title('value of recommendation')
# draw
fig.canvas.draw()
show(block=False)
def main():
"""Run the demo."""
# define the bounds over which we'll optimize, the optimal x for comparison,
# and a sequence of test points
bounds = np.array([[-5, 10.], [0, 15]])
xopt = np.array([np.pi, 2.275])
x1, x2 = np.meshgrid(np.linspace(*bounds[0], num=100),
np.linspace(*bounds[1], num=100))
xx = np.c_[x1.flatten(), x2.flatten()]
# get initial data and some test points.
X = list(inits.init_latin(bounds, 6))
Y = [f(x_) for x_ in X]
F = list()
# initialize the model
model = make_gp(0.01, 10, [1., 1.], 0)
model.add_data(X, Y)
# set a prior on the parameters
model.params['like.sn2'].set_prior('uniform', 0.005, 0.015)
model.params['kern.rho'].set_prior('lognormal', 0, 3)
model.params['kern.ell'].set_prior('lognormal', 0, 3)
model.params['mean.bias'].set_prior('normal', 0, 20)
# make a model which samples parameters
model = MCMC(model, n=10, rng=None)
# create a new figure
fig = figure(figsize=(10, 6))
while True:
# get index to solve it and plot it
index = policies.EI(model, bounds, X, xi=0.1)
# get the recommendation and the next query
xbest = recommenders.best_incumbent(model, bounds, X)
xnext, _ = solvers.solve_lbfgs(index, bounds)
# observe and update model
ynext = f(xnext)
model.add_data(xnext, ynext)
# evaluate the posterior and the acquisition function
mu, s2 = model.predict(xx)
# record our data and update the model
X.append(xnext)
Y.append(ynext)
F.append(f(xbest))
fig.clear()
ax1 = fig.add_subplotspec((2, 2), (0, 0), hidex=True)
ax2 = fig.add_subplotspec((2, 2), (1, 0), hidey=True, sharex=ax1)
ax3 = fig.add_subplotspec((2, 2), (0, 1), rowspan=2)
# plot the posterior and data
ax1.contourf(x1, x2, mu.reshape(x1.shape), alpha=0.4)
X_ = np.array(X)
ax1.scatter(X_[:-1, 0], X_[:-1, 1], marker='.')
ax1.scatter(xbest[0], xbest[1], linewidths=3, marker='o', color='r')
ax1.scatter(xnext[0], xnext[1], linewidths=3, marker='o', color='g')
ax1.set_xlim(*bounds[0])
ax1.set_ylim(*bounds[1])
ax1.set_title('current model (xbest and xnext)')
# plot the acquisition function
ax2.contourf(x1, x2, index(xx).reshape(x1.shape), alpha=0.5)
ax2.scatter(xbest[0], xbest[1], linewidths=3, marker='o', color='r')
ax2.scatter(xnext[0], xnext[1], linewidths=3, marker='o', color='g')
ax2.set_xlim(*bounds[0])
ax2.set_ylim(*bounds[1])
ax2.set_title('current policy (xnext)')
# plot the latent function at recomended points
ax3.axhline(f(xopt))
ax3.plot(F)
ax3.set_ylim(-1., 0.)
ax3.set_title('value of recommendation')
# draw
fig.canvas.draw()
show(block=False)
def main():
"""Run the demo."""
# define the bounds over which we'll optimize, the optimal x for
# comparison, and a sequence of test points
bounds = np.array([[0.5, 2.5]])
xopt = 0.54856343
fopt = f(xopt)
x = np.linspace(bounds[0][0], bounds[0][1], 500)
# get initial data and some test points.
X = list(inits.init_latin(bounds, 3))
Y = [f(x_) for x_ in X]
F = []
# initialize the model
model = make_gp(0.01, 1.9, 0.1, 0)
model.add_data(X, Y)
# set a prior on the parameters
model.params['like.sn2'].set_prior('uniform', 0.005, 0.015)
model.params['kern.rho'].set_prior('lognormal', 0, 100)
model.params['kern.ell'].set_prior('lognormal', 0, 10)
model.params['mean.bias'].set_prior('normal', 0, 20)
# make a model which samples parameters
model = MCMC(model, n=20, rng=None)
# create a new figure
fig = figure(figsize=(10, 6))
while True:
# get acquisition function (or index)
index = policies.EI(model, bounds, X, xi=0.1)
# get the recommendation and the next query
xbest = recommenders.best_incumbent(model, bounds, X)
xnext, _ = solvers.solve_lbfgs(index, bounds)
ynext = f(xnext)
# evaluate the posterior before updating the model for plotting
mu, s2 = model.predict(x[:, None])
# record our data and update the model
X.append(xnext)
Y.append(ynext)
F.append(f(xbest))
model.add_data(xnext, ynext)
# PLOT EVERYTHING
fig.clear()
ax1 = fig.add_subplotspec((2, 2), (0, 0), hidex=True)
ax2 = fig.add_subplotspec((2, 2), (1, 0), hidey=True, sharex=ax1)
ax3 = fig.add_subplotspec((2, 2), (0, 1), rowspan=2)
# plot the posterior and data
ax1.plot_banded(x, mu, 2*np.sqrt(s2))
ax1.scatter(np.ravel(X), Y)
ax1.axvline(xbest)
ax1.axvline(xnext, color='g')
ax1.set_ylim(-6, 3)
ax1.set_title('current model (xbest and xnext)')
# plot the acquisition function
ax2.plot_banded(x, index(x[:, None]))
ax2.axvline(xnext, color='g')
ax2.set_xlim(*bounds)
ax2.set_title('current policy (xnext)')
# plot the latent function at recomended points
ax3.plot(F)
ax3.axhline(fopt)
ax3.set_ylim(0.4, 0.9)
ax3.set_title('value of recommendation')
# draw
fig.canvas.draw()
show(block=False)
