def inner_func_with_gradient(X_inner):
X_inner = np.atleast_2d(X_inner)
muX_inner = self.model.posterior_mean(X_inner)
dmu_dX_inner = self.model.posterior_mean_gradient(
X_inner)
a = np.matmul(utility_params_samples[l], muX_inner)
# a = support[t]*muX_inner
da_dX_inner = np.tensordot(
utility_params_samples[l],
dmu_dX_inner,
axes=1)
func_val = np.reshape(a, (len(X_inner), 1))
func_gradient = np.reshape(da_dX_inner,
X_inner.shape)
grad_c = gradients(x_new=x,
model=self.model_c,
Z=Z_samples_c[z],
aux=aux_c,
X_inner=X_inner,
precompute_grad=True)
Fz, grad_Fz = grad_c.compute_probability_feasibility_multi_gp(
x=X_inner, l=0, gradient_flag=True)
func_val_constrained = func_val * Fz
func_gradient_constrained = np.array(
func_val).reshape(-1) * grad_Fz.reshape(
-1) + Fz.reshape(
-1) * func_gradient.reshape(-1)
return func_val_constrained, func_gradient_constrained
def inner_func_with_gradient(X_inner):
X_inner = np.atleast_2d(X_inner)
muX_inner = self.model.posterior_mean(X_inner)
dmu_dX_inner = self.model.posterior_mean_gradient(
X_inner)
cov = self.model.posterior_covariance_between_points_partially_precomputed(
X_inner, x)[:, :, 0]
dcov_dX_inner = self.model.posterior_covariance_gradient_partially_precomputed(
X_inner, x)
a = np.matmul(utility_params_samples[l], muX_inner)
# a = support[t]*muX_inner
da_dX_inner = np.tensordot(
utility_params_samples[l],
dmu_dX_inner,
axes=1)
b = np.sqrt(np.matmul(aux, np.square(cov)))
for k in range(X_inner.shape[1]):
dcov_dX_inner[:, :, k] = np.multiply(
cov, dcov_dX_inner[:, :, k])
db_dX_inner = np.tensordot(aux,
dcov_dX_inner,
axes=1)
db_dX_inner = np.multiply(np.reciprocal(b),
db_dX_inner.T).T
func_val = np.reshape(a + b * Z_samples[z],
(len(X_inner), 1))
func_gradient = np.reshape(
da_dX_inner + db_dX_inner * Z_samples[z],
X_inner.shape)
grad_c = gradients(x_new=x,
model=self.model_c,
Z=Z_samples_c[z],
aux=aux_c,
X_inner=X_inner,
precompute_grad=True)
Fz, grad_Fz = grad_c.compute_probability_feasibility_multi_gp(
x=X_inner, l=0, gradient_flag=True)
func_val_constrained = func_val * Fz
func_gradient_constrained = np.array(
func_val).reshape(-1) * grad_Fz.reshape(
-1) + Fz.reshape(
-1) * func_gradient.reshape(-1)
return -func_val_constrained, -func_gradient_constrained
def inner_func(X_inner):
X_inner = np.atleast_2d(X_inner)
muX_inner = self.model.posterior_mean(X_inner)
cov = self.model.posterior_covariance_between_points_partially_precomputed(
X_inner, x)[:, :, 0]
a = np.matmul(utility_params_samples[l], muX_inner)
# a = support[t]*muX_inner
b = np.sqrt(np.matmul(aux, np.square(cov)))
func_val = np.reshape(a + b * Z_samples[z],
(len(X_inner), 1))
grad_c = gradients(
x_new=x,
model=self.model_c,
Z=Z_samples_c[z],
aux=aux_c,
X_inner=X_inner
) # , test_samples = initial_design('random', self.space, 1000))
Fz = grad_c.compute_probability_feasibility_multi_gp(
x=X_inner, l=0)
func_val_constrained = func_val * Fz
return -func_val_constrained
def inner_func(X_inner,
plots=False,
include_best=None,
include_val=None):
X_inner = np.atleast_2d(X_inner)
muX_inner = self.model.posterior_mean(X_inner)
a = np.matmul(utility_params_samples[l], muX_inner)
# a = support[t]*muX_inner
func_val = np.reshape(a, (len(X_inner), 1))
grad_c = gradients(
x_new=x,
model=self.model_c,
Z=Z_samples_c[z],
aux=aux_c,
X_inner=X_inner
) # , test_samples = initial_design('random', self.space, 1000))
Fz = grad_c.compute_probability_feasibility_multi_gp(
x=X_inner, l=0)
func_val_constrained = func_val * Fz
if plots:
print("func_val", func_val, "Fz", Fz)
fig, axs = plt.subplots(2, 2)
true_func_values = self.true_func.evaluate(
X_inner)
best_scaled_val_idx = np.argmin(
func_val_constrained)
predicted_best_mu = self.model.posterior_mean(
include_best)
print("best_scaled_val",
np.min(func_val_constrained),
"optimised best", include_val)
print("utility_params_samples[l]",
utility_params_samples[l])
feasable_mu_index = np.array(
Fz > 0.51, dtype=bool).reshape(-1)
axs[0, 0].set_title("Inner_mu_plot")
axs[0,
0].scatter(muX_inner[0][feasable_mu_index],
muX_inner[1][feasable_mu_index],
c=np.array(a).reshape(-1)
[feasable_mu_index])
axs[0, 0].scatter(
muX_inner[0][best_scaled_val_idx],
muX_inner[1][best_scaled_val_idx],
color="red")
axs[0, 0].scatter(predicted_best_mu[0],
predicted_best_mu[1],
color="black")
axs[0, 0].legend()
axs[0, 1].set_title("predicted vs real f1")
axs[0, 1].scatter(
muX_inner[0],
np.array(
true_func_values[0][0]).reshape(-1))
axs[0, 1].legend()
axs[1, 0].set_title("predicted vs real f2")
axs[1, 0].scatter(
muX_inner[1],
np.array(
true_func_values[0][1]).reshape(-1))
axs[1, 0].legend()
plt.show()
return func_val_constrained
def _marginal_acq_with_gradient(self, X, utility_params_samples):
"""
"""
marginal_acqX = np.zeros((X.shape[0], len(utility_params_samples)))
marginal_dacq_dX = np.zeros(
(X.shape[0], X.shape[1], len(utility_params_samples)))
n_h = 1 # Number of GP hyperparameters samples.
# gp_hyperparameters_samples = self.model.get_hyperparameters_samples(n_h)
n_z = len(self.Z_samples_obj) #2 # Number of samples of Z.
Z_samples = self.Z_samples_obj #np.random.normal(size=n_z)
Z_samples_c = self.Z_samples_const
for h in range(n_h):
# self.model.set_hyperparameters(h)
varX = self.model.posterior_variance(X, noise=True)
dvar_dX = self.model.posterior_variance_gradient(X)
varX_c = self.model_c.posterior_variance(X, noise=True)
dvar_c_dX = self.model_c.posterior_variance_gradient(X)
for i in range(0, len(X)):
x = np.atleast_2d(X[i])
self.model.partial_precomputation_for_covariance(x)
self.model.partial_precomputation_for_covariance_gradient(x)
self.model_c.partial_precomputation_for_covariance(x)
self.model_c.partial_precomputation_for_covariance_gradient(x)
for l in range(0, len(utility_params_samples)):
# Precompute aux1 and aux2 for computational efficiency.
aux = np.multiply(np.square(utility_params_samples[l]),
np.reciprocal(varX[:, i]))
aux2 = np.multiply(np.square(utility_params_samples[l]),
np.square(np.reciprocal(varX[:, i])))
aux_c = np.reciprocal(varX_c[:, i])
aux2_c = np.square(np.reciprocal(varX_c[:, i]))
for z in range(len(Z_samples)):
# inner function of maKG acquisition function.
def inner_func(X_inner):
X_inner = np.atleast_2d(X_inner)
muX_inner = self.model.posterior_mean(X_inner)
cov = self.model.posterior_covariance_between_points_partially_precomputed(
X_inner, x)[:, :, 0]
a = np.matmul(utility_params_samples[l], muX_inner)
# a = support[t]*muX_inner
b = np.sqrt(np.matmul(aux, np.square(cov)))
func_val = np.reshape(a + b * Z_samples[z],
(len(X_inner), 1))
grad_c = gradients(
x_new=x,
model=self.model_c,
Z=Z_samples_c[z],
aux=aux_c,
X_inner=X_inner
) # , test_samples = initial_design('random', self.space, 1000))
Fz = grad_c.compute_probability_feasibility_multi_gp(
x=X_inner, l=0)
func_val_constrained = func_val * Fz
return -func_val_constrained
# inner function of maKG acquisition function with its gradient.
def inner_func_with_gradient(X_inner):
X_inner = np.atleast_2d(X_inner)
muX_inner = self.model.posterior_mean(X_inner)
dmu_dX_inner = self.model.posterior_mean_gradient(
X_inner)
cov = self.model.posterior_covariance_between_points_partially_precomputed(
X_inner, x)[:, :, 0]
dcov_dX_inner = self.model.posterior_covariance_gradient_partially_precomputed(
X_inner, x)
a = np.matmul(utility_params_samples[l], muX_inner)
# a = support[t]*muX_inner
da_dX_inner = np.tensordot(
utility_params_samples[l],
dmu_dX_inner,
axes=1)
b = np.sqrt(np.matmul(aux, np.square(cov)))
for k in range(X_inner.shape[1]):
dcov_dX_inner[:, :, k] = np.multiply(
cov, dcov_dX_inner[:, :, k])
db_dX_inner = np.tensordot(aux,
dcov_dX_inner,
axes=1)
db_dX_inner = np.multiply(np.reciprocal(b),
db_dX_inner.T).T
func_val = np.reshape(a + b * Z_samples[z],
(len(X_inner), 1))
func_gradient = np.reshape(
da_dX_inner + db_dX_inner * Z_samples[z],
X_inner.shape)
grad_c = gradients(x_new=x,
model=self.model_c,
Z=Z_samples_c[z],
aux=aux_c,
X_inner=X_inner,
precompute_grad=True)
Fz, grad_Fz = grad_c.compute_probability_feasibility_multi_gp(
x=X_inner, l=0, gradient_flag=True)
func_val_constrained = func_val * Fz
func_gradient_constrained = np.array(
func_val).reshape(-1) * grad_Fz.reshape(
-1) + Fz.reshape(
-1) * func_gradient.reshape(-1)
return -func_val_constrained, -func_gradient_constrained
x_opt, opt_val = self.optimizer.optimize_inner_func(
f=inner_func, f_df=inner_func_with_gradient)
marginal_acqX[i, l] -= opt_val
x_opt = np.atleast_2d(x_opt)
#mu x opt calculations
muX_inner = self.model.posterior_mean(x_opt)
cov = self.model.posterior_covariance_between_points_partially_precomputed(
x_opt, x)[:, :, 0]
a = np.matmul(utility_params_samples[l], muX_inner)
b = np.sqrt(np.matmul(aux, np.square(cov)))
mu_xopt = np.reshape(a + b * Z_samples[z],
(len(x_opt), 1))
#grad x opt calculations
cov_opt = self.model.posterior_covariance_between_points_partially_precomputed(
x_opt, x)[:, 0, 0]
dcov_opt_dx = self.model.posterior_covariance_gradient(
x, x_opt)[:, 0, :]
b = np.sqrt(np.dot(aux, np.square(cov_opt)))
grad_mu_xopt = 0.5 * Z_samples[z] * np.reciprocal(
b) * np.matmul(
aux2, (2 * np.multiply(varX[:, i] * cov_opt,
dcov_opt_dx.T) -
np.multiply(np.square(cov_opt),
dvar_dX[:, i, :].T)).T)
grad_c = gradients(x_new=x,
model=self.model_c,
Z=Z_samples_c[z],
xopt=x_opt,
aux=aux_c,
aux2=aux2_c,
varX=varX_c[:, i],
dvar_dX=dvar_c_dX[:, i, :],
test_samples=initial_design(
'random', self.space, 1000))
Fz_xopt, grad_Fz_xopt = grad_c.compute_probability_feasibility_multi_gp_xopt(
xopt=x_opt, gradient_flag=True)
grad_f_val_xopt = np.array(mu_xopt).reshape(
-1) * np.array(grad_Fz_xopt).reshape(
-1) + np.array(Fz_xopt).reshape(-1) * np.array(
grad_mu_xopt).reshape(-1)
marginal_dacq_dX[i, :,
l] = grad_f_val_xopt # grad_f_val
marginal_acqX = marginal_acqX / (n_h * n_z)
marginal_dacq_dX = marginal_dacq_dX / (n_h * n_z)
return marginal_acqX, marginal_dacq_dX
