def optimize_gp_hyperparameter(self,mygp=None,gp_params=None):
if mygp==None:
mygp=self.gp
if gp_params==None:
gp_params=self.gp_params
if self.optimize_gp=='maximize':
newlengthscale = mygp.optimize_lengthscale_SE_maximizing(gp_params['lengthscale'],gp_params['noise_delta'])
gp_params['lengthscale']=newlengthscale
if self.verbose==1:
print("MML estimated lengthscale =",newlengthscale)
elif self.optimize_gp=='loo':
newlengthscale = mygp.optimize_lengthscale_SE_loo(gp_params['lengthscale'],gp_params['noise_delta'])
gp_params['lengthscale']=newlengthscale
if self.verbose==1:
print("LOO estimated lengthscale =",newlengthscale)
elif self.optimize_gp=='marginal':
self.theta_vector = mygp.slice_sampling_lengthscale_SE(gp_params['lengthscale'],gp_params['noise_delta'])
gp_params['lengthscale']=self.theta_vector[0]
self.theta_vector =np.unique(self.theta_vector)
self.gp_params['newtheta_vector']=self.theta_vector
#print "estimated lengthscale ={:s}".format(self.theta_vector)
elif self.optimize_gp=="fstar":
fstar_scaled=(self.acq['fstar']-np.mean(self.Y_original))/np.std(self.Y_original)
newlengthscale = mygp.optimize_lengthscale_SE_fstar(gp_params['lengthscale'],gp_params['noise_delta'],fstar_scaled)
gp_params['lengthscale']=newlengthscale
print("estimated lengthscale =",newlengthscale)
tempX=mygp.X
tempY=mygp.Y
# init a new Gaussian Process after optimizing hyper-parameter
mygp=GaussianProcess(gp_params)
# Find unique rows of X to avoid GP from breaking
ur = unique_rows(tempX)
mygp.fit(tempX[ur], tempY[ur])
return mygp, gp_params
def maximize_pvrs(self):
"""
Main optimization method.
Input parameters
----------
gp_params: parameter for Gaussian Process
Returns
-------
x: recommented point for evaluation
"""
if self.stop_flag == 1:
return
if 'n_xstars' in self.acq:
numXstar = self.acq['n_xstars']
else:
numXstar = 10 * self.dim
# Set acquisition function
start_opt = time.time()
y_max = self.Y.max()
# run the acquisition function for the first time to get xstar
self.xstars = []
# finding the xt of UCB
numTheta = len(self.theta_vector)
temp = []
# finding the xt of Thompson Sampling
for ii in range(numXstar):
if self.theta_vector != []:
# since the numXstar > len(theta_vector)
index = np.random.randint(numTheta)
#print index
gp_params['theta'] = self.theta_vector[index]
# init a new Gaussian Process
self.gp = GaussianProcess(self.gp_params)
# Find unique rows of X to avoid GP from breaking
ur = unique_rows(self.X)
self.gp.fit(self.X[ur], self.Y[ur])
xt_TS, y_xt_TS = acq_max_with_name(gp=self.gp,
scalebounds=self.scalebounds,
acq_name="thompson",
IsReturnY=True)
temp.append(xt_TS)
# check if f* > y^max and ignore xt_TS otherwise
#if y_xt_TS>=y_max:
#self.xstars.append(xt_TS)
if self.xstars == []:
#print 'xt_suggestion is empty'
# again perform TS and take all of them
self.xstars = temp
# check predictive variance before adding a new data points
var_before = self.gp.compute_var(self.gp.X, self.xstars)
var_before = np.mean(var_before)
if self.xstar_accumulate == []:
self.xstar_accumulate = np.asarray(self.xstars)
else:
self.xstar_accumulate = np.vstack(
(self.xstar_accumulate, np.asarray(self.xstars)))
accum_var_before = [
self.gp.compute_var(self.gp.X, val)
for idx, val in enumerate(self.xstar_accumulate)
]
accum_var_before = np.mean(accum_var_before)
self.gp.lengthscale_vector = self.theta_vector
self.acq['xstars'] = self.xstars
self.acq_func = AcquisitionFunction(self.acq)
x_max = acq_max(ac=self.acq_func.acq_kind,
gp=self.gp,
bounds=self.scalebounds,
opt_toolbox=self.opt_toolbox,
seeds=self.xstars)
#xstars_array=np.asarray(self.acq_func.object.xstars)
val_acq = -self.acq_func.acq_kind(x_max, self.gp)
# check predictive variance after
temp = np.vstack((self.gp.X, x_max))
var_after = self.gp.compute_var(temp, self.xstars)
var_after = np.mean(var_after)
accum_var_after = [
self.gp.compute_var(temp, val)
for idx, val in enumerate(self.xstar_accumulate)
]
accum_var_after = np.mean(accum_var_after)
if self.PVRS_before_after == []:
self.PVRS_before_after = np.asarray([var_before, var_after])
self.accummulate_PVRS_before_after = np.asarray(
[accum_var_before, accum_var_after])
else:
self.PVRS_before_after = np.vstack(
(self.PVRS_before_after, np.asarray([var_before, var_after])))
self.accummulate_PVRS_before_after = np.vstack(
(self.accummulate_PVRS_before_after,
np.asarray([accum_var_before, accum_var_after])))
#print "predictive variance before={:.12f} after={:.12f} val_acq={:.12f}".format(var_before,var_after,np.asscalar(val_acq))
# check maximum variance
var_acq = {}
var_acq['name'] = 'pure_exploration'
var_acq['dim'] = self.dim
var_acq['scalebounds'] = self.scalebounds
acq_var = AcquisitionFunction(var_acq)
temp = acq_max(ac=acq_var.acq_kind,
gp=self.gp,
bounds=self.scalebounds,
opt_toolbox='scipy')
# get the value f*
#max_var_after=acq_var.acq_kind(temp,self.gp,y_max=y_max)
#print "max predictive variance ={:.8f}".format(np.asscalar(max_var_after))
if self.stopping_criteria != 0 and val_acq < self.stopping_criteria:
val_acq = self.acq_func.acq_kind(x_max, self.gp)
self.stop_flag = 1
print(
"Stopping Criteria is violated. Stopping Criteria is {:.15f}".
format(self.stopping_criteria))
#mean,var=self.gp.predict(x_max, eval_MSE=True)
#var.flags['WRITEABLE']=True
#var[var<1e-20]=0
#self.Tau_Xt= np.append(self.Tau_Xt,val_acq/var)
# record the optimization time
finished_opt = time.time()
elapse_opt = finished_opt - start_opt
self.time_opt = np.hstack((self.time_opt, elapse_opt))
super(BayesOpt, self).augment_the_new_data(x_max)
def maximize(self):
"""
Main optimization method.
Input parameters
----------
gp_params: parameter for Gaussian Process
Returns
-------
x: recommented point for evaluation
"""
if self.stop_flag == 1:
return
if self.acq['name'] == 'random':
super(BayesOpt, self).generate_random_point()
return
# init a new Gaussian Process
self.gp = GaussianProcess(self.gp_params)
if self.gp.KK_x_x_inv == []:
# Find unique rows of X to avoid GP from breaking
ur = unique_rows(self.X)
self.gp.fit(self.X[ur], self.Y[ur])
acq = self.acq
# optimize GP parameters after 10 iterations
if len(self.Y) % (2 * self.dim) == 0:
self.gp, self.gp_params = super(BayesOpt,
self).optimize_gp_hyperparameter()
if self.acq['name'] == 'mes':
self.maximize_mes()
return
if self.acq['name'] == 'pvrs':
self.maximize_pvrs()
return
if self.acq['name'] == 'e3i':
self.maximize_e3i()
return
if self.acq['name'] == 'ei_kov' or self.acq[
'name'] == 'poi_kov' or self.acq['name'] == 'ei_fstar':
self.acq['fstar_scaled'] = (self.acq['fstar'] - np.mean(
self.Y_original)) / np.std(self.Y_original)
# Set acquisition function
start_opt = time.time()
#y_max = self.Y.max()
if 'xstars' not in globals():
xstars = []
self.xstars = xstars
self.acq['xstars'] = xstars
self.acq_func = AcquisitionFunction(self.acq)
if acq['name'] == "ei_mu":
#find the maximum in the predictive mean
x_mu_max, y_max = acq_max_with_name(gp=self.gp,
scalebounds=self.scalebounds,
acq_name='mu',
IsReturnY=True)
x_max = acq_max(ac=self.acq_func.acq_kind,
gp=self.gp,
bounds=self.scalebounds,
opt_toolbox=self.opt_toolbox,
seeds=self.xstars)
val_acq = self.acq_func.acq_kind(x_max, self.gp)
if self.stopping_criteria != 0 and val_acq < self.stopping_criteria:
#val_acq=self.acq_func.acq_kind(x_max,self.gp)
self.stop_flag = 1
#print "Stopping Criteria is violated. Stopping Criteria is {:.15f}".format(self.stopping_criteria)
self.alpha_Xt = np.append(self.alpha_Xt, val_acq)
mean, var = self.gp.predict(x_max, eval_MSE=True)
var.flags['WRITEABLE'] = True
var[var < 1e-20] = 0
#self.Tau_Xt= np.append(self.Tau_Xt,val_acq/var)
# record the optimization time
finished_opt = time.time()
elapse_opt = finished_opt - start_opt
self.time_opt = np.hstack((self.time_opt, elapse_opt))
super(BayesOpt, self).augment_the_new_data(x_max)
class BayesOpt(BO_Sequential_Base):
def __init__(self, gp_params, func_params, acq_params, verbose=1):
"""
Input parameters
----------
gp_params: GP parameters
gp_params.theta: to compute the kernel
gp_params.delta: to compute the kernel
func_params: function to optimize
func_params.init bound: initial bounds for parameters
func_params.bounds: bounds on parameters
func_params.func: a function to be optimized
acq_params: acquisition function,
acq_params.acq_func['name']=['ei','ucb','poi','lei']
,acq['kappa'] for ucb, acq['k'] for lei
acq_params.opt_toolbox: optimization toolbox 'nlopt','direct','scipy'
Returns
-------
dim: dimension
bounds: bounds on original scale
scalebounds: bounds on normalized scale of 0-1
time_opt: will record the time spent on optimization
gp: Gaussian Process object
"""
# Find number of parameters
super(BayesOpt, self).__init__(gp_params, func_params, acq_params,
verbose)
"""
bounds=func_params['function'].bounds
self.dim = len(bounds)
# Create an array with parameters bounds
if isinstance(bounds,dict):
# Get the name of the parameters
self.keys = list(bounds.keys())
self.bounds = []
for key in list(bounds.keys()):
self.bounds.append(bounds[key])
self.bounds = np.asarray(self.bounds)
else:
self.bounds=np.asarray(bounds)
#print(self.bounds)
# create a scalebounds 0-1
scalebounds=np.array([np.zeros(self.dim), np.ones(self.dim)])
self.scalebounds=scalebounds.T
self.max_min_gap=self.bounds[:,1]-self.bounds[:,0]
# Some function to be optimized
self.f = func_params['function'].func
# optimization toolbox
if 'opt_toolbox' not in acq_params:
self.opt_toolbox='scipy'
else:
self.opt_toolbox=acq_params['opt_toolbox']
# acquisition function type
self.acq=acq_params['acq_func']
self.acq['scalebounds']=self.scalebounds
if 'debug' not in self.acq:
self.acq['debug']=0
if 'stopping' not in acq_params:
self.stopping_criteria=0
else:
self.stopping_criteria=acq_params['stopping']
if 'optimize_gp' not in acq_params:
self.optimize_gp=0
else:
self.optimize_gp=acq_params['optimize_gp']
if 'marginalize_gp' not in acq_params:
self.marginalize_gp=0
else:
self.marginalize_gp=acq_params['marginalize_gp']
# store X in original scale
self.X_original= None
# store X in 0-1 scale
self.X = None
# store y=f(x)
# (y - mean)/(max-min)
self.Y = None
# y original scale
self.Y_original = None
# performance evaluation at the maximum mean GP (for information theoretic)
self.Y_original_maxGP = None
self.X_original_maxGP = None
# value of the acquisition function at the selected point
self.alpha_Xt=None
self.Tau_Xt=None
self.time_opt=0
self.k_Neighbor=2
# Lipschitz constant
self.L=0
self.gp_params=gp_params
# Gaussian Process class
self.gp=GaussianProcess(gp_params)
# acquisition function
self.acq_func = None
# stop condition
self.stop_flag=0
self.logmarginal=0
# xt_suggestion, caching for Consensus
self.xstars=[]
self.xstar_accumulate=[]
# theta vector for marginalization GP
self.theta_vector =[]
# PVRS before and after
self.PVRS_before_after=[]
self.accummulate_PVRS_before_after=[]
# store ystars
#self.ystars=np.empty((0,100), float)
self.ystars=[]
"""
# will be later used for visualization
def posterior(self, Xnew):
self.gp.fit(self.X, self.Y)
mu, sigma2 = self.gp.predict(Xnew, eval_MSE=True)
return mu, np.sqrt(sigma2)
def init(self, gp_params, n_init_points=3, seed=1):
"""
Input parameters
----------
gp_params: Gaussian Process structure
n_init_points: # init points
"""
super(BayesOpt, self).init(gp_params, n_init_points, seed)
def init_with_data(self, init_X, init_Y):
"""
Input parameters
----------
gp_params: Gaussian Process structure
x,y: # init data observations (in original scale)
"""
super(BayesOpt, self).init_with_data(init_X, init_Y)
def estimate_L(self, bounds):
'''
Estimate the Lipschitz constant of f by taking maximizing the norm of the expectation of the gradient of *f*.
'''
def df(x, model, x0):
mean_derivative = gp_model.predictive_gradient(self.X, self.Y, x)
temp = mean_derivative * mean_derivative
if len(temp.shape) <= 1:
res = np.sqrt(temp)
else:
res = np.sqrt(
np.sum(temp, axis=1)
) # simply take the norm of the expectation of the gradient
return -res
gp_model = self.gp
dim = len(bounds)
num_data = 1000 * dim
samples = np.zeros(shape=(num_data, dim))
for k in range(0, dim):
samples[:, k] = np.random.uniform(low=bounds[k][0],
high=bounds[k][1],
size=num_data)
#samples = np.vstack([samples,gp_model.X])
pred_samples = df(samples, gp_model, 0)
x0 = samples[np.argmin(pred_samples)]
res = minimize(df,
x0,
method='L-BFGS-B',
bounds=bounds,
args=(gp_model, x0),
options={'maxiter': 100})
try:
minusL = res.fun[0][0]
except:
if len(res.fun.shape) == 1:
minusL = res.fun[0]
else:
minusL = res.fun
L = -minusL
if L < 1e-6:
L = 0.0001 ## to avoid problems in cases in which the model is flat.
return L
def maximize_with_lengthscale_derived_by_fstar(self, gp_params):
"""
Main optimization method.
Input parameters
----------
gp_params: parameter for Gaussian Process
Returns
-------
x: recommented point for evaluation
"""
if self.stop_flag == 1:
return
if self.acq['name'] == 'random':
x_max = [
np.random.uniform(x[0], x[1], size=1) for x in self.bounds
]
x_max = np.asarray(x_max)
x_max = x_max.T
self.X_original = np.vstack((self.X_original, x_max))
# evaluate Y using original X
#self.Y = np.append(self.Y, self.f(temp_X_new_original))
self.Y_original = np.append(self.Y_original, self.f(x_max))
# update Y after change Y_original
self.Y = (self.Y_original - np.mean(self.Y_original)) / np.std(
self.Y_original)
self.time_opt = np.hstack((self.time_opt, 0))
return
# init a new Gaussian Process
self.gp = GaussianProcess(gp_params)
if self.gp.KK_x_x_inv == []:
# Find unique rows of X to avoid GP from breaking
ur = unique_rows(self.X)
self.gp.fit(self.X[ur], self.Y[ur])
acq = self.acq
# optimize GP parameters after 10 iterations
if len(self.Y) % (3 * self.dim) == 0:
fstar_scaled = (self.acq['fstar'] -
np.mean(self.Y_original)) / np.std(self.Y_original)
newlengthscale = self.gp.optimize_lengthscale_SE_fstar(
self.gp_params['lengthscale'], self.gp_params['noise_delta'],
fstar_scaled)
self.gp_params['lengthscale'] = newlengthscale
print("estimated lengthscale =", newlengthscale)
# init a new Gaussian Process after optimizing hyper-parameter
self.gp = GaussianProcess(gp_params)
# Find unique rows of X to avoid GP from breaking
ur = unique_rows(self.X)
self.gp.fit(self.X[ur], self.Y[ur])
if self.acq['name'] == 'mes':
self.maximize_mes(gp_params)
return
if self.acq['name'] == 'pvrs':
self.maximize_pvrs(gp_params)
return
if self.acq['name'] == 'e3i':
self.maximize_e3i(gp_params)
return
if self.acq['name'] == 'ei_kov' or self.acq[
'name'] == 'poi_kov' or self.acq['name'] == 'ei_fstar':
self.acq['fstar_scaled'] = (self.acq['fstar'] - np.mean(
self.Y_original)) / np.std(self.Y_original)
# Set acquisition function
start_opt = time.time()
y_max = self.Y.max()
if 'xstars' not in globals():
xstars = []
self.xstars = xstars
self.acq['xstars'] = xstars
self.acq_func = AcquisitionFunction(self.acq)
if acq['name'] == "ei_mu":
#find the maximum in the predictive mean
x_mu_max, y_max = acq_max_with_name(gp=self.gp,
scalebounds=self.scalebounds,
acq_name='mu',
IsReturnY=True)
x_max = acq_max(ac=self.acq_func.acq_kind,
gp=self.gp,
bounds=self.scalebounds,
opt_toolbox=self.opt_toolbox,
seeds=self.xstars)
val_acq = self.acq_func.acq_kind(x_max, self.gp)
if self.stopping_criteria != 0 and val_acq < self.stopping_criteria:
val_acq = self.acq_func.acq_kind(x_max, self.gp)
self.stop_flag = 1
#print "Stopping Criteria is violated. Stopping Criteria is {:.15f}".format(self.stopping_criteria)
self.alpha_Xt = np.append(self.alpha_Xt, val_acq)
mean, var = self.gp.predict(x_max, eval_MSE=True)
var.flags['WRITEABLE'] = True
var[var < 1e-20] = 0
#self.Tau_Xt= np.append(self.Tau_Xt,val_acq/var)
# record the optimization time
finished_opt = time.time()
elapse_opt = finished_opt - start_opt
self.time_opt = np.hstack((self.time_opt, elapse_opt))
# store X
self.X = np.vstack((self.X, x_max.reshape((1, -1))))
# compute X in original scale
temp_X_new_original = x_max * self.max_min_gap + self.bounds[:, 0]
self.X_original = np.vstack((self.X_original, temp_X_new_original))
# evaluate Y using original X
#self.Y = np.append(self.Y, self.f(temp_X_new_original))
self.Y_original = np.append(self.Y_original,
self.f(temp_X_new_original))
# update Y after change Y_original
self.Y = (self.Y_original - np.mean(self.Y_original)) / np.std(
self.Y_original)
if self.gp.flagIncremental == 1:
self.gp.fit_incremental(x_max, self.Y[-1])
def maximize(self):
"""
Main optimization method.
Input parameters
----------
gp_params: parameter for Gaussian Process
Returns
-------
x: recommented point for evaluation
"""
if self.stop_flag == 1:
return
if self.acq['name'] == 'random':
super(BayesOpt, self).generate_random_point()
return
# init a new Gaussian Process
self.gp = GaussianProcess(self.gp_params)
if self.gp.KK_x_x_inv == []:
# Find unique rows of X to avoid GP from breaking
ur = unique_rows(self.X)
self.gp.fit(self.X[ur], self.Y[ur])
acq = self.acq
# optimize GP parameters after 10 iterations
if len(self.Y) % (2 * self.dim) == 0:
self.gp, self.gp_params = super(BayesOpt,
self).optimize_gp_hyperparameter()
if self.acq['name'] == 'mes':
self.maximize_mes()
return
if self.acq['name'] == 'pvrs':
self.maximize_pvrs()
return
if self.acq['name'] == 'e3i':
self.maximize_e3i()
return
if self.acq['name'] == 'ei_kov' or self.acq[
'name'] == 'poi_kov' or self.acq['name'] == 'ei_fstar':
self.acq['fstar_scaled'] = (self.acq['fstar'] - np.mean(
self.Y_original)) / np.std(self.Y_original)
# Set acquisition function
start_opt = time.time()
#y_max = self.Y.max()
if 'xstars' not in globals():
xstars = []
self.xstars = xstars
self.acq['xstars'] = xstars
self.acq_func = AcquisitionFunction(self.acq)
if acq['name'] == "ei_mu":
#find the maximum in the predictive mean
x_mu_max, y_max = acq_max_with_name(gp=self.gp,
scalebounds=self.scalebounds,
acq_name='mu',
IsReturnY=True)
x_max = acq_max(ac=self.acq_func.acq_kind,
gp=self.gp,
bounds=self.scalebounds,
opt_toolbox=self.opt_toolbox,
seeds=self.xstars)
val_acq = self.acq_func.acq_kind(x_max, self.gp)
if self.stopping_criteria != 0 and val_acq < self.stopping_criteria:
#val_acq=self.acq_func.acq_kind(x_max,self.gp)
self.stop_flag = 1
#print "Stopping Criteria is violated. Stopping Criteria is {:.15f}".format(self.stopping_criteria)
self.alpha_Xt = np.append(self.alpha_Xt, val_acq)
mean, var = self.gp.predict(x_max, eval_MSE=True)
var.flags['WRITEABLE'] = True
var[var < 1e-20] = 0
#self.Tau_Xt= np.append(self.Tau_Xt,val_acq/var)
# record the optimization time
finished_opt = time.time()
elapse_opt = finished_opt - start_opt
self.time_opt = np.hstack((self.time_opt, elapse_opt))
super(BayesOpt, self).augment_the_new_data(x_max)
def maximize_mes(self):
"""
Main optimization method.
Input parameters
----------
gp_params: parameter for Gaussian Process
Returns
-------
x: recommented point for evaluation
"""
if self.stop_flag == 1:
return
# Set acquisition function
start_opt = time.time()
y_max = self.Y.max()
# run the acquisition function for the first time to get xstar
self.xstars = []
# finding the xt of UCB
y_max = np.max(self.Y)
#numXtar=10*self.dim
numXtar = 30
y_stars = []
temp = []
# finding the xt of Thompson Sampling
for ii in range(numXtar):
xt_TS, y_xt_TS = acq_max_with_name(gp=self.gp,
scalebounds=self.scalebounds,
acq_name="thompson",
IsReturnY=True)
#if y_xt_TS>=y_max:
y_stars.append(y_xt_TS)
temp.append(xt_TS)
# check if f* > y^max and ignore xt_TS otherwise
if y_xt_TS >= y_max:
self.xstars.append(xt_TS)
if self.xstars == []:
#print 'xt_suggestion is empty'
# again perform TS and take all of them
self.xstars = temp
self.acq['xstars'] = self.xstars
self.acq['ystars'] = y_stars
self.acq_func = AcquisitionFunction(self.acq)
x_max = acq_max(ac=self.acq_func.acq_kind,
gp=self.gp,
bounds=self.scalebounds,
opt_toolbox=self.opt_toolbox,
seeds=self.xstars)
#xstars_array=np.asarray(self.acq_func.object.xstars)
val_acq = self.acq_func.acq_kind(x_max, self.gp)
if self.stopping_criteria != 0 and val_acq < self.stopping_criteria:
val_acq = self.acq_func.acq_kind(x_max, self.gp)
self.stop_flag = 1
print(
"Stopping Criteria is violated. Stopping Criteria is {:.15f}".
format(self.stopping_criteria))
# record the optimization time
finished_opt = time.time()
elapse_opt = finished_opt - start_opt
self.time_opt = np.hstack((self.time_opt, elapse_opt))
super(BayesOpt, self).augment_the_new_data(x_max)
# convert ystar to original scale
y_stars = [
val * np.std(self.Y_original) + np.mean(self.Y_original)
for idx, val in enumerate(y_stars)
]
self.ystars.append(np.ravel(y_stars))
def maximize_e3i(self):
"""
Main optimization method.
Input parameters
----------
gp_params: parameter for Gaussian Process
Returns
-------
x: recommented point for evaluation
"""
if self.stop_flag == 1:
return
# Set acquisition function
start_opt = time.time()
y_max = self.Y.max()
# run the acquisition function for the first time to get xstar
self.xstars = []
# finding the xt of UCB
y_max = np.max(self.Y)
numXtar = 50 * self.dim
#numXtar=20
y_stars = []
temp = []
# finding the xt of Thompson Sampling
for ii in range(numXtar):
xt_TS, y_xt_TS = acq_max_with_name(gp=self.gp,
scalebounds=self.scalebounds,
acq_name="thompson",
IsReturnY=True)
y_stars.append(y_xt_TS)
temp.append(xt_TS)
# check if f* > y^max and ignore xt_TS otherwise
#if y_xt_TS>=y_max:
self.xstars.append(xt_TS)
#y_stars=y_stars*np.std(self.Y_original)+np.mean(self.Y_original)
#print "{:.5f} {:.6f}".format(np.mean(y_stars),np.std(y_stars))
#print "ymax={:.5f}".format(np.max(self.Y))
if self.acq['debug'] == 1:
print('mean y*={:.4f}({:.8f}) y+={:.4f}'.format(
np.mean(y_xt_TS), np.std(y_xt_TS), y_max))
if self.xstars == []:
#print 'xt_suggestion is empty'
# again perform TS and take all of them
self.xstars = temp
self.acq['xstars'] = self.xstars
self.acq['ystars'] = y_stars
self.acq_func = AcquisitionFunction(self.acq)
x_max = acq_max(ac=self.acq_func.acq_kind,
gp=self.gp,
bounds=self.scalebounds,
opt_toolbox=self.opt_toolbox,
seeds=self.xstars)
#xstars_array=np.asarray(self.acq_func.object.xstars)
val_acq = self.acq_func.acq_kind(x_max, self.gp)
if self.stopping_criteria != 0 and val_acq < self.stopping_criteria:
val_acq = self.acq_func.acq_kind(x_max, self.gp)
self.stop_flag = 1
print(
"Stopping Criteria is violated. Stopping Criteria is {:.15f}".
format(self.stopping_criteria))
# record the optimization time
finished_opt = time.time()
elapse_opt = finished_opt - start_opt
self.time_opt = np.hstack((self.time_opt, elapse_opt))
super(BayesOpt, self).augment_the_new_data(x_max)
def maximize_pvrs(self):
"""
Main optimization method.
Input parameters
----------
gp_params: parameter for Gaussian Process
Returns
-------
x: recommented point for evaluation
"""
if self.stop_flag == 1:
return
if 'n_xstars' in self.acq:
numXstar = self.acq['n_xstars']
else:
numXstar = 10 * self.dim
# Set acquisition function
start_opt = time.time()
y_max = self.Y.max()
# run the acquisition function for the first time to get xstar
self.xstars = []
# finding the xt of UCB
numTheta = len(self.theta_vector)
temp = []
# finding the xt of Thompson Sampling
for ii in range(numXstar):
if self.theta_vector != []:
# since the numXstar > len(theta_vector)
index = np.random.randint(numTheta)
#print index
gp_params['theta'] = self.theta_vector[index]
# init a new Gaussian Process
self.gp = GaussianProcess(self.gp_params)
# Find unique rows of X to avoid GP from breaking
ur = unique_rows(self.X)
self.gp.fit(self.X[ur], self.Y[ur])
xt_TS, y_xt_TS = acq_max_with_name(gp=self.gp,
scalebounds=self.scalebounds,
acq_name="thompson",
IsReturnY=True)
temp.append(xt_TS)
# check if f* > y^max and ignore xt_TS otherwise
#if y_xt_TS>=y_max:
#self.xstars.append(xt_TS)
if self.xstars == []:
#print 'xt_suggestion is empty'
# again perform TS and take all of them
self.xstars = temp
# check predictive variance before adding a new data points
var_before = self.gp.compute_var(self.gp.X, self.xstars)
var_before = np.mean(var_before)
if self.xstar_accumulate == []:
self.xstar_accumulate = np.asarray(self.xstars)
else:
self.xstar_accumulate = np.vstack(
(self.xstar_accumulate, np.asarray(self.xstars)))
accum_var_before = [
self.gp.compute_var(self.gp.X, val)
for idx, val in enumerate(self.xstar_accumulate)
]
accum_var_before = np.mean(accum_var_before)
self.gp.lengthscale_vector = self.theta_vector
self.acq['xstars'] = self.xstars
self.acq_func = AcquisitionFunction(self.acq)
x_max = acq_max(ac=self.acq_func.acq_kind,
gp=self.gp,
bounds=self.scalebounds,
opt_toolbox=self.opt_toolbox,
seeds=self.xstars)
#xstars_array=np.asarray(self.acq_func.object.xstars)
val_acq = -self.acq_func.acq_kind(x_max, self.gp)
# check predictive variance after
temp = np.vstack((self.gp.X, x_max))
var_after = self.gp.compute_var(temp, self.xstars)
var_after = np.mean(var_after)
accum_var_after = [
self.gp.compute_var(temp, val)
for idx, val in enumerate(self.xstar_accumulate)
]
accum_var_after = np.mean(accum_var_after)
if self.PVRS_before_after == []:
self.PVRS_before_after = np.asarray([var_before, var_after])
self.accummulate_PVRS_before_after = np.asarray(
[accum_var_before, accum_var_after])
else:
self.PVRS_before_after = np.vstack(
(self.PVRS_before_after, np.asarray([var_before, var_after])))
self.accummulate_PVRS_before_after = np.vstack(
(self.accummulate_PVRS_before_after,
np.asarray([accum_var_before, accum_var_after])))
#print "predictive variance before={:.12f} after={:.12f} val_acq={:.12f}".format(var_before,var_after,np.asscalar(val_acq))
# check maximum variance
var_acq = {}
var_acq['name'] = 'pure_exploration'
var_acq['dim'] = self.dim
var_acq['scalebounds'] = self.scalebounds
acq_var = AcquisitionFunction(var_acq)
temp = acq_max(ac=acq_var.acq_kind,
gp=self.gp,
bounds=self.scalebounds,
opt_toolbox='scipy')
# get the value f*
#max_var_after=acq_var.acq_kind(temp,self.gp,y_max=y_max)
#print "max predictive variance ={:.8f}".format(np.asscalar(max_var_after))
if self.stopping_criteria != 0 and val_acq < self.stopping_criteria:
val_acq = self.acq_func.acq_kind(x_max, self.gp)
self.stop_flag = 1
print(
"Stopping Criteria is violated. Stopping Criteria is {:.15f}".
format(self.stopping_criteria))
#mean,var=self.gp.predict(x_max, eval_MSE=True)
#var.flags['WRITEABLE']=True
#var[var<1e-20]=0
#self.Tau_Xt= np.append(self.Tau_Xt,val_acq/var)
# record the optimization time
finished_opt = time.time()
elapse_opt = finished_opt - start_opt
self.time_opt = np.hstack((self.time_opt, elapse_opt))
super(BayesOpt, self).augment_the_new_data(x_max)
def maximize_with_lengthscale_derived_by_fstar(self, gp_params):
"""
Main optimization method.
Input parameters
----------
gp_params: parameter for Gaussian Process
Returns
-------
x: recommented point for evaluation
"""
if self.stop_flag == 1:
return
if self.acq['name'] == 'random':
x_max = [
np.random.uniform(x[0], x[1], size=1) for x in self.bounds
]
x_max = np.asarray(x_max)
x_max = x_max.T
self.X_original = np.vstack((self.X_original, x_max))
# evaluate Y using original X
#self.Y = np.append(self.Y, self.f(temp_X_new_original))
self.Y_original = np.append(self.Y_original, self.f(x_max))
# update Y after change Y_original
self.Y = (self.Y_original - np.mean(self.Y_original)) / np.std(
self.Y_original)
self.time_opt = np.hstack((self.time_opt, 0))
return
# init a new Gaussian Process
self.gp = GaussianProcess(gp_params)
if self.gp.KK_x_x_inv == []:
# Find unique rows of X to avoid GP from breaking
ur = unique_rows(self.X)
self.gp.fit(self.X[ur], self.Y[ur])
acq = self.acq
# optimize GP parameters after 10 iterations
if len(self.Y) % (3 * self.dim) == 0:
fstar_scaled = (self.acq['fstar'] -
np.mean(self.Y_original)) / np.std(self.Y_original)
newlengthscale = self.gp.optimize_lengthscale_SE_fstar(
self.gp_params['lengthscale'], self.gp_params['noise_delta'],
fstar_scaled)
self.gp_params['lengthscale'] = newlengthscale
print("estimated lengthscale =", newlengthscale)
# init a new Gaussian Process after optimizing hyper-parameter
self.gp = GaussianProcess(gp_params)
# Find unique rows of X to avoid GP from breaking
ur = unique_rows(self.X)
self.gp.fit(self.X[ur], self.Y[ur])
if self.acq['name'] == 'mes':
self.maximize_mes(gp_params)
return
if self.acq['name'] == 'pvrs':
self.maximize_pvrs(gp_params)
return
if self.acq['name'] == 'e3i':
self.maximize_e3i(gp_params)
return
if self.acq['name'] == 'ei_kov' or self.acq[
'name'] == 'poi_kov' or self.acq['name'] == 'ei_fstar':
self.acq['fstar_scaled'] = (self.acq['fstar'] - np.mean(
self.Y_original)) / np.std(self.Y_original)
# Set acquisition function
start_opt = time.time()
y_max = self.Y.max()
if 'xstars' not in globals():
xstars = []
self.xstars = xstars
self.acq['xstars'] = xstars
self.acq_func = AcquisitionFunction(self.acq)
if acq['name'] == "ei_mu":
#find the maximum in the predictive mean
x_mu_max, y_max = acq_max_with_name(gp=self.gp,
scalebounds=self.scalebounds,
acq_name='mu',
IsReturnY=True)
x_max = acq_max(ac=self.acq_func.acq_kind,
gp=self.gp,
bounds=self.scalebounds,
opt_toolbox=self.opt_toolbox,
seeds=self.xstars)
val_acq = self.acq_func.acq_kind(x_max, self.gp)
if self.stopping_criteria != 0 and val_acq < self.stopping_criteria:
val_acq = self.acq_func.acq_kind(x_max, self.gp)
self.stop_flag = 1
#print "Stopping Criteria is violated. Stopping Criteria is {:.15f}".format(self.stopping_criteria)
self.alpha_Xt = np.append(self.alpha_Xt, val_acq)
mean, var = self.gp.predict(x_max, eval_MSE=True)
var.flags['WRITEABLE'] = True
var[var < 1e-20] = 0
#self.Tau_Xt= np.append(self.Tau_Xt,val_acq/var)
# record the optimization time
finished_opt = time.time()
elapse_opt = finished_opt - start_opt
self.time_opt = np.hstack((self.time_opt, elapse_opt))
# store X
self.X = np.vstack((self.X, x_max.reshape((1, -1))))
# compute X in original scale
temp_X_new_original = x_max * self.max_min_gap + self.bounds[:, 0]
self.X_original = np.vstack((self.X_original, temp_X_new_original))
# evaluate Y using original X
#self.Y = np.append(self.Y, self.f(temp_X_new_original))
self.Y_original = np.append(self.Y_original,
self.f(temp_X_new_original))
# update Y after change Y_original
self.Y = (self.Y_original - np.mean(self.Y_original)) / np.std(
self.Y_original)
if self.gp.flagIncremental == 1:
self.gp.fit_incremental(x_max, self.Y[-1])
class BO_Sequential_Base(object):
def __init__(self, gp_params, func_params, acq_params, verbose=1):
"""
Input parameters
----------
gp_params: GP parameters
gp_params.theta: to compute the kernel
gp_params.delta: to compute the kernel
func_params: function to optimize
func_params.init bound: initial bounds for parameters
func_params.bounds: bounds on parameters
func_params.func: a function to be optimized
acq_params: acquisition function,
acq_params.acq_func['name']=['ei','ucb','poi','lei']
,acq['kappa'] for ucb, acq['k'] for lei
acq_params.opt_toolbox: optimization toolbox 'nlopt','direct','scipy'
Returns
-------
dim: dimension
bounds: bounds on original scale
scalebounds: bounds on normalized scale of 0-1
time_opt: will record the time spent on optimization
gp: Gaussian Process object
"""
# Find number of parameters
self.verbose=verbose
try:
bounds=func_params['function']['bounds']
except:
bounds=func_params['function'].bounds
self.dim = len(bounds)
# Create an array with parameters bounds
if isinstance(bounds,dict):
# Get the name of the parameters
self.keys = list(bounds.keys())
self.bounds = []
for key in list(bounds.keys()):
self.bounds.append(bounds[key])
self.bounds = np.asarray(self.bounds)
else:
self.bounds=np.asarray(bounds)
# create a scalebounds 0-1
scalebounds=np.array([np.zeros(self.dim), np.ones(self.dim)])
self.scalebounds=scalebounds.T
self.max_min_gap=self.bounds[:,1]-self.bounds[:,0]
# Some function to be optimized
self.function=func_params['function']
try:
self.f = func_params['function']['func']
except:
self.f = func_params['function'].func
# optimization toolbox
if 'opt_toolbox' not in acq_params:
self.opt_toolbox='scipy'
else:
self.opt_toolbox=acq_params['opt_toolbox']
# acquisition function type
self.acq=acq_params['acq_func']
self.acq['scalebounds']=self.scalebounds
if 'debug' not in self.acq:
self.acq['debug']=0
if 'stopping' not in acq_params:
self.stopping_criteria=0
else:
self.stopping_criteria=acq_params['stopping']
if 'optimize_gp' not in acq_params:
self.optimize_gp=0
else:
self.optimize_gp=acq_params['optimize_gp']
if 'marginalize_gp' not in acq_params:
self.marginalize_gp=0
else:
self.marginalize_gp=acq_params['marginalize_gp']
# store X in original scale
self.X_original= None
# store X in 0-1 scale
self.X = None
# store y=f(x)
# (y - mean)/(max-min)
self.Y = None
# y original scale
self.Y_original = None
# performance evaluation at the maximum mean GP (for information theoretic)
self.Y_original_maxGP = None
self.X_original_maxGP = None
# value of the acquisition function at the selected point
self.alpha_Xt=None
self.Tau_Xt=None
self.time_opt=0
self.k_Neighbor=2
# Lipschitz constant
self.L=0
self.gp_params=gp_params
# Gaussian Process class
self.gp=GaussianProcess(gp_params)
# acquisition function
self.acq_func = None
# stop condition
self.stop_flag=0
self.logmarginal=0
# xt_suggestion, caching for Consensus
self.xstars=[]
self.xstar_accumulate=[]
# theta vector for marginalization GP
self.theta_vector =[]
# PVRS before and after
self.PVRS_before_after=[]
self.accummulate_PVRS_before_after=[]
# store ystars
#self.ystars=np.empty((0,100), float)
self.ystars=[]
def init(self, gp_params, n_init_points=3,seed=1):
"""
Input parameters
----------
gp_params: Gaussian Process structure
n_init_points: # init points
"""
np.random.seed(seed)
# Generate random points
l = [np.random.uniform(x[0], x[1]) for _ in range(n_init_points) for x in self.bounds]
#l=[np.linspace(x[0],x[1],num=n_init_points) for x in self.init_bounds]
# Concatenate new random points to possible existing
# points from self.explore method.
temp=np.asarray(l)
temp=temp.T
init_X=list(temp.reshape((n_init_points,-1)))
self.X_original = np.asarray(init_X)
self.X_original_maxGP= np.asarray(init_X)
# Evaluate target function at all initialization
y_init=self.f(init_X)
y_init=np.reshape(y_init,(n_init_points,1))
self.Y_original = np.asarray(y_init)
self.Y_original_maxGP=np.asarray(y_init)
self.Y=(self.Y_original-np.mean(self.Y_original))/np.std(self.Y_original)
# convert it to scaleX
temp_init_point=np.divide((init_X-self.bounds[:,0]),self.max_min_gap)
self.X = np.asarray(temp_init_point)
def init_with_data(self, init_X,init_Y):
"""
Input parameters
----------
gp_params: Gaussian Process structure
x,y: # init data observations (in original scale)
"""
# Turn it into np array and store.
self.X_original=np.asarray(init_X)
temp_init_point=np.divide((init_X-self.bounds[:,0]),self.max_min_gap)
self.X_original = np.asarray(init_X)
self.X = np.asarray(temp_init_point)
self.Y_original = np.asarray(init_Y)
#self.Y=(self.Y_original-np.mean(self.Y_original))/np.std(self.Y_original)
self.Y=(self.Y_original-np.mean(self.Y_original))/np.std(self.Y_original)
# Set acquisition function
self.acq_func = AcquisitionFunction(self.acq)
# Find unique rows of X to avoid GP from breaking
ur = unique_rows(self.X)
self.gp.fit(self.X[ur], self.Y[ur])
def optimize_gp_hyperparameter(self,mygp=None,gp_params=None):
if mygp==None:
mygp=self.gp
if gp_params==None:
gp_params=self.gp_params
if self.optimize_gp=='maximize':
newlengthscale = mygp.optimize_lengthscale_SE_maximizing(gp_params['lengthscale'],gp_params['noise_delta'])
gp_params['lengthscale']=newlengthscale
if self.verbose==1:
print("MML estimated lengthscale =",newlengthscale)
elif self.optimize_gp=='loo':
newlengthscale = mygp.optimize_lengthscale_SE_loo(gp_params['lengthscale'],gp_params['noise_delta'])
gp_params['lengthscale']=newlengthscale
if self.verbose==1:
print("LOO estimated lengthscale =",newlengthscale)
elif self.optimize_gp=='marginal':
self.theta_vector = mygp.slice_sampling_lengthscale_SE(gp_params['lengthscale'],gp_params['noise_delta'])
gp_params['lengthscale']=self.theta_vector[0]
self.theta_vector =np.unique(self.theta_vector)
self.gp_params['newtheta_vector']=self.theta_vector
#print "estimated lengthscale ={:s}".format(self.theta_vector)
elif self.optimize_gp=="fstar":
fstar_scaled=(self.acq['fstar']-np.mean(self.Y_original))/np.std(self.Y_original)
newlengthscale = mygp.optimize_lengthscale_SE_fstar(gp_params['lengthscale'],gp_params['noise_delta'],fstar_scaled)
gp_params['lengthscale']=newlengthscale
print("estimated lengthscale =",newlengthscale)
tempX=mygp.X
tempY=mygp.Y
# init a new Gaussian Process after optimizing hyper-parameter
mygp=GaussianProcess(gp_params)
# Find unique rows of X to avoid GP from breaking
ur = unique_rows(tempX)
mygp.fit(tempX[ur], tempY[ur])
return mygp, gp_params
def generate_random_point(self):
x_max = [np.random.uniform(x[0], x[1], size=1) for x in self.bounds]
x_max=np.asarray(x_max)
x_max=x_max.T
self.X_original=np.vstack((self.X_original, x_max))
# evaluate Y using original X
#self.Y = np.append(self.Y, self.f(temp_X_new_original))
self.Y_original = np.append(self.Y_original, self.f(x_max))
# update Y after change Y_original
self.Y=(self.Y_original-np.mean(self.Y_original))/np.std(self.Y_original)
self.time_opt=np.hstack((self.time_opt,0))
def augment_the_new_data(self,x_max):
# store X
self.X = np.vstack((self.X, x_max.reshape((1, -1))))
# compute X in original scale
temp_X_new_original=x_max*self.max_min_gap+self.bounds[:,0]
self.X_original=np.vstack((self.X_original, temp_X_new_original))
# evaluate Y using original X
#self.Y = np.append(self.Y, self.f(temp_X_new_original))
self.Y_original = np.append(self.Y_original, self.f(temp_X_new_original))
# update Y after change Y_original
self.Y=(self.Y_original-np.mean(self.Y_original))/np.std(self.Y_original)
# find the maximizer in the GP mean function
try:
len(self.gp)
x_mu_max=[]
for j in range(self.J):
x_mu_max_temp=acq_max_with_name(gp=self.gp[j],scalebounds=self.scalebounds[self.featIdx[j]],acq_name="mu")
x_mu_max=np.hstack((x_mu_max,x_mu_max_temp))
except:
x_mu_max=acq_max_with_name(gp=self.gp,scalebounds=self.scalebounds,acq_name="mu")
x_mu_max_original=x_mu_max*self.max_min_gap+self.bounds[:,0]
# set y_max = mu_max
#mu_max=acq_mu.acq_kind(x_mu_max,gp=self.gp)
self.Y_original_maxGP = np.append(self.Y_original_maxGP, self.f(x_mu_max_original))
self.X_original_maxGP = np.vstack((self.X_original_maxGP, x_mu_max_original))
def __init__(self, gp_params, func_params, acq_params, verbose=1):
"""
Input parameters
----------
gp_params: GP parameters
gp_params.theta: to compute the kernel
gp_params.delta: to compute the kernel
func_params: function to optimize
func_params.init bound: initial bounds for parameters
func_params.bounds: bounds on parameters
func_params.func: a function to be optimized
acq_params: acquisition function,
acq_params.acq_func['name']=['ei','ucb','poi','lei']
,acq['kappa'] for ucb, acq['k'] for lei
acq_params.opt_toolbox: optimization toolbox 'nlopt','direct','scipy'
Returns
-------
dim: dimension
bounds: bounds on original scale
scalebounds: bounds on normalized scale of 0-1
time_opt: will record the time spent on optimization
gp: Gaussian Process object
"""
# Find number of parameters
self.verbose=verbose
try:
bounds=func_params['function']['bounds']
except:
bounds=func_params['function'].bounds
self.dim = len(bounds)
# Create an array with parameters bounds
if isinstance(bounds,dict):
# Get the name of the parameters
self.keys = list(bounds.keys())
self.bounds = []
for key in list(bounds.keys()):
self.bounds.append(bounds[key])
self.bounds = np.asarray(self.bounds)
else:
self.bounds=np.asarray(bounds)
# create a scalebounds 0-1
scalebounds=np.array([np.zeros(self.dim), np.ones(self.dim)])
self.scalebounds=scalebounds.T
self.max_min_gap=self.bounds[:,1]-self.bounds[:,0]
# Some function to be optimized
self.function=func_params['function']
try:
self.f = func_params['function']['func']
except:
self.f = func_params['function'].func
# optimization toolbox
if 'opt_toolbox' not in acq_params:
self.opt_toolbox='scipy'
else:
self.opt_toolbox=acq_params['opt_toolbox']
# acquisition function type
self.acq=acq_params['acq_func']
self.acq['scalebounds']=self.scalebounds
if 'debug' not in self.acq:
self.acq['debug']=0
if 'stopping' not in acq_params:
self.stopping_criteria=0
else:
self.stopping_criteria=acq_params['stopping']
if 'optimize_gp' not in acq_params:
self.optimize_gp=0
else:
self.optimize_gp=acq_params['optimize_gp']
if 'marginalize_gp' not in acq_params:
self.marginalize_gp=0
else:
self.marginalize_gp=acq_params['marginalize_gp']
# store X in original scale
self.X_original= None
# store X in 0-1 scale
self.X = None
# store y=f(x)
# (y - mean)/(max-min)
self.Y = None
# y original scale
self.Y_original = None
# performance evaluation at the maximum mean GP (for information theoretic)
self.Y_original_maxGP = None
self.X_original_maxGP = None
# value of the acquisition function at the selected point
self.alpha_Xt=None
self.Tau_Xt=None
self.time_opt=0
self.k_Neighbor=2
# Lipschitz constant
self.L=0
self.gp_params=gp_params
# Gaussian Process class
self.gp=GaussianProcess(gp_params)
# acquisition function
self.acq_func = None
# stop condition
self.stop_flag=0
self.logmarginal=0
# xt_suggestion, caching for Consensus
self.xstars=[]
self.xstar_accumulate=[]
# theta vector for marginalization GP
self.theta_vector =[]
# PVRS before and after
self.PVRS_before_after=[]
self.accummulate_PVRS_before_after=[]
# store ystars
#self.ystars=np.empty((0,100), float)
self.ystars=[]
def __init__(self,gp_params, func_params, acq_params):
"""
Input parameters
----------
gp_params: GP parameters
gp_params.thete: to compute the kernel
gp_params.delta: to compute the kernel
func_params: function to optimize
func_params.init bound: initial bounds for parameters
func_params.bounds: bounds on parameters
func_params.func: a function to be optimized
acq_params: acquisition function,
acq_params.acq_func['name']=['ei','ucb','poi','lei']
,acq['kappa'] for ucb, acq['k'] for lei
acq_params.opt_toolbox: optimization toolbox 'nlopt','direct','scipy'
Returns
-------
dim: dimension
bounds: bounds on original scale
scalebounds: bounds on normalized scale of 0-1
time_opt: will record the time spent on optimization
gp: Gaussian Process object
"""
try:
bounds=func_params['bounds']
except:
bounds=func_params['function'].bounds
self.dim = len(bounds)
# Create an array with parameters bounds
if isinstance(bounds,dict):
# Get the name of the parameters
self.keys = list(bounds.keys())
self.bounds = []
for key in list(bounds.keys()):
self.bounds.append(bounds[key])
self.bounds = np.asarray(self.bounds)
else:
self.bounds=np.asarray(bounds)
scalebounds=np.array([np.zeros(self.dim), np.ones(self.dim)])
self.scalebounds=scalebounds.T
self.max_min_gap=self.bounds[:,1]-self.bounds[:,0]
# acquisition function type
self.acq=acq_params['acq_func']
if 'debug' not in self.acq:
self.acq['debug']=0
if 'optimize_gp' not in acq_params:
self.optimize_gp=0
else:
self.optimize_gp=acq_params['optimize_gp']
if 'marginalize_gp' not in acq_params:
self.marginalize_gp=0
else:
self.marginalize_gp=acq_params['marginalize_gp']
# Some function to be optimized
self.function=func_params['function']
try:
self.f = func_params['function']['func']
except:
self.f = func_params['function'].func
# optimization toolbox
if 'opt_toolbox' not in acq_params:
self.opt_toolbox='scipy'
else:
self.opt_toolbox=acq_params['opt_toolbox']
# store the batch size for each iteration
self.NumPoints=[]
# Numpy array place holders
self.X_original= None
# scale the data to 0-1 fit GP better
self.X = None # X=( X_original - min(bounds) / (max(bounds) - min(bounds))
self.Y = None # Y=( Y_original - mean(bounds) / (max(bounds) - min(bounds))
self.Y_original = None
self.opt_time=0
self.L=0 # lipschitz
self.gp=GaussianProcess(gp_params)
self.gp_params=gp_params
# Acquisition Function
#self.acq_func = None
self.acq_func = AcquisitionFunction(acq=self.acq)
self.accum_dist=[]
# theta vector for marginalization GP
self.theta_vector =[]
if 'xstars' not in self.acq:
self.xstars=[]
else:
self.xstars=self.acq['xstars']
# PVRS before and after
self.PVRS_before_after=[]
self.xstars=[]
self.Y_original_maxGP=None
self.X_original_maxGP=None
def maximize_batch_greedy_PVRS(self,B=5):
"""
Finding a batch of points using Peak Suppression / Constant Liar approach
Input Parameters
----------
gp_params: Parameters to be passed to the Gaussian Process class
kappa: constant value in UCB
Returns
-------
X: a batch of [x_1..x_Nt]
"""
y_max = self.Y.max()
# Set parameters if any was passed
self.gp=GaussianProcess(self.gp_params)
# Find unique rows of X to avoid GP from breaking
ur = unique_rows(self.X)
self.gp.fit(self.X[ur], self.Y[ur])
start_opt=time.time()
if 'n_xstars' in self.acq:
numXtar=self.acq['n_xstars']
else:
numXtar=30*self.dim
#temp=[]
# finding the xt of Thompson Sampling
xstars=[]
for ii in range(numXtar):
mu_acq={}
mu_acq['name']='thompson'
mu_acq['dim']=self.dim
mu_acq['scalebounds']=self.scalebounds
acq_mu=AcquisitionFunction(mu_acq)
xt_TS = acq_max(ac=acq_mu.acq_kind,gp=self.gp,bounds=self.scalebounds,opt_toolbox='scipy')
#temp.append(xt_TS)
xstars.append(xt_TS)
self.xstars=xstars
# Set acquisition function
myacq={}
myacq['name']='pvrs'
myacq['dim']=self.acq['dim']
myacq['xstars']=xstars
acq_func = AcquisitionFunction(myacq)
# copy GP, X and Y
temp_gp=copy.deepcopy(self.gp)
temp_X=copy.deepcopy(self.X)
temp_Y=copy.deepcopy(self.Y)
#temp_Y_original=self.Y_original
start_batch=time.time()
# check predictive variance before adding a new data points
var_before=self.gp.compute_var(temp_X,xstars)
var_before=np.mean(var_before)
#store new_x
new_X=np.empty((0,self.dim),float)
for ii in range(B):
# Finding argmax of the acquisition function.
x_max = acq_max(ac=acq_func.acq_kind,gp=temp_gp, bounds=self.scalebounds)
new_X= np.vstack((new_X, x_max.reshape((1, -1))))
temp_X = np.vstack((temp_X, x_max.reshape((1, -1))))
# check predictive variance after
var_after=self.gp.compute_var(temp_X,xstars)
var_after=np.mean(var_after)
if self.PVRS_before_after==[]:
self.PVRS_before_after=np.asarray([var_before,var_after])
else:
temp_var=np.asarray([var_before,var_after])
self.PVRS_before_after=np.vstack((self.PVRS_before_after, temp_var))
var_before=var_after
const_liar,const_liar_variance=temp_gp.predict(x_max,eval_MSE=1)
const_liar=np.random.rand()
temp_Y = np.append(temp_Y, const_liar )
temp_gp.fit(temp_X,temp_Y)
# for debug
finish_batch=time.time()-start_batch
#return new_X,new_X_original
self.NumPoints=np.append(self.NumPoints,new_X.shape[0])
self.X=np.vstack((self.X,new_X))
# convert back to original scale
temp_X_new_original=[val*self.max_min_gap+self.bounds[:,0] for idx, val in enumerate(new_X)]
temp_X_new_original=np.asarray(temp_X_new_original)
self.X_original=np.vstack((self.X_original, temp_X_new_original))
# evaluate y=f(x)
temp=self.f(temp_X_new_original)
temp=np.reshape(temp,(-1,1))
self.Y_original=np.append(self.Y_original,temp)
self.Y=(self.Y_original-np.mean(self.Y_original))/(np.max(self.Y_original)-np.min(self.Y_original))
# find the maximizer in the GP mean function
try:
len(self.gp)
x_mu_max=[]
for j in range(self.J):
x_mu_max_temp=acq_max_with_name(gp=self.gp[j],scalebounds=self.scalebounds[self.featIdx[j]],acq_name="mu")
x_mu_max=np.hstack((x_mu_max,x_mu_max_temp))
except:
x_mu_max=acq_max_with_name(gp=self.gp,scalebounds=self.scalebounds,acq_name="mu")
x_mu_max_original=x_mu_max*self.max_min_gap+self.bounds[:,0]
# set y_max = mu_max
#mu_max=acq_mu.acq_kind(x_mu_max,gp=self.gp)
self.Y_original_maxGP = np.append(self.Y_original_maxGP, self.f(x_mu_max_original))
self.X_original_maxGP = np.vstack((self.X_original_maxGP, x_mu_max_original))
return new_X
class BatchPVRS(object):
def __init__(self,gp_params, func_params, acq_params):
"""
Input parameters
----------
gp_params: GP parameters
gp_params.thete: to compute the kernel
gp_params.delta: to compute the kernel
func_params: function to optimize
func_params.init bound: initial bounds for parameters
func_params.bounds: bounds on parameters
func_params.func: a function to be optimized
acq_params: acquisition function,
acq_params.acq_func['name']=['ei','ucb','poi','lei']
,acq['kappa'] for ucb, acq['k'] for lei
acq_params.opt_toolbox: optimization toolbox 'nlopt','direct','scipy'
Returns
-------
dim: dimension
bounds: bounds on original scale
scalebounds: bounds on normalized scale of 0-1
time_opt: will record the time spent on optimization
gp: Gaussian Process object
"""
try:
bounds=func_params['bounds']
except:
bounds=func_params['function'].bounds
self.dim = len(bounds)
# Create an array with parameters bounds
if isinstance(bounds,dict):
# Get the name of the parameters
self.keys = list(bounds.keys())
self.bounds = []
for key in list(bounds.keys()):
self.bounds.append(bounds[key])
self.bounds = np.asarray(self.bounds)
else:
self.bounds=np.asarray(bounds)
scalebounds=np.array([np.zeros(self.dim), np.ones(self.dim)])
self.scalebounds=scalebounds.T
self.max_min_gap=self.bounds[:,1]-self.bounds[:,0]
# acquisition function type
self.acq=acq_params['acq_func']
if 'debug' not in self.acq:
self.acq['debug']=0
if 'optimize_gp' not in acq_params:
self.optimize_gp=0
else:
self.optimize_gp=acq_params['optimize_gp']
if 'marginalize_gp' not in acq_params:
self.marginalize_gp=0
else:
self.marginalize_gp=acq_params['marginalize_gp']
# Some function to be optimized
self.function=func_params['function']
try:
self.f = func_params['function']['func']
except:
self.f = func_params['function'].func
# optimization toolbox
if 'opt_toolbox' not in acq_params:
self.opt_toolbox='scipy'
else:
self.opt_toolbox=acq_params['opt_toolbox']
# store the batch size for each iteration
self.NumPoints=[]
# Numpy array place holders
self.X_original= None
# scale the data to 0-1 fit GP better
self.X = None # X=( X_original - min(bounds) / (max(bounds) - min(bounds))
self.Y = None # Y=( Y_original - mean(bounds) / (max(bounds) - min(bounds))
self.Y_original = None
self.opt_time=0
self.L=0 # lipschitz
self.gp=GaussianProcess(gp_params)
self.gp_params=gp_params
# Acquisition Function
#self.acq_func = None
self.acq_func = AcquisitionFunction(acq=self.acq)
self.accum_dist=[]
# theta vector for marginalization GP
self.theta_vector =[]
if 'xstars' not in self.acq:
self.xstars=[]
else:
self.xstars=self.acq['xstars']
# PVRS before and after
self.PVRS_before_after=[]
self.xstars=[]
self.Y_original_maxGP=None
self.X_original_maxGP=None
def posterior(self, Xnew):
#xmin, xmax = -2, 10
ur = unique_rows(self.X)
self.gp.fit(self.X[ur], self.Y[ur])
mu, sigma2 = self.gp.predict(Xnew, eval_MSE=True)
return mu, np.sqrt(sigma2)
def init(self, n_init_points):
"""
Input parameters
----------
gp_params: Gaussian Process structure
n_init_points: # init points
"""
# Generate random points
l = [np.random.uniform(x[0], x[1], size=n_init_points) for x in self.bounds]
# Concatenate new random points to possible existing
# points from self.explore method.
#self.init_points += list(map(list, zip(*l)))
temp=np.asarray(l)
temp=temp.T
init_X=list(temp.reshape((n_init_points,-1)))
# Evaluate target function at all initialization
y_init=self.f(init_X)
# Turn it into np array and store.
self.X_original=np.asarray(init_X)
temp_init_point=np.divide((init_X-self.bounds[:,0]),self.max_min_gap)
self.X_original_maxGP= np.asarray(init_X)
self.X_original = np.asarray(init_X)
self.X = np.asarray(temp_init_point)
y_init=np.reshape(y_init,(n_init_points,1))
self.Y_original = np.asarray(y_init)
self.Y_original_maxGP=np.asarray(y_init)
self.Y=(self.Y_original-np.mean(self.Y_original))/(np.max(self.Y_original)-np.min(self.Y_original))
self.NumPoints=np.append(self.NumPoints,n_init_points)
# Set parameters if any was passed
#self.gp=GaussianProcess(gp_params)
# Find unique rows of X to avoid GP from breaking
#ur = unique_rows(self.X)
#self.gp.fit(self.X[ur], self.Y[ur])
#print "#Batch={:d} f_max={:.4f}".format(n_init_points,self.Y.max())
def init_with_data(self, init_X,init_Y):
"""
Input parameters
----------
gp_params: Gaussian Process structure
x,y: # init data observations (in original scale)
"""
# Turn it into np array and store.
self.X_original=np.asarray(init_X)
temp_init_point=np.divide((init_X-self.bounds[:,0]),self.max_min_gap)
self.X_original = np.asarray(init_X)
self.X_original_maxGP= np.asarray(init_X)
self.X = np.asarray(temp_init_point)
self.Y_original = np.asarray(init_Y)
self.Y_original_maxGP=np.asarray(init_Y)
self.Y=(self.Y_original-np.mean(self.Y_original))/(np.max(self.Y_original)-np.min(self.Y_original))
self.NumPoints=np.append(self.NumPoints,len(init_Y))
# Set acquisition function
self.acq_func = AcquisitionFunction(self.acq)
# Find unique rows of X to avoid GP from breaking
ur = unique_rows(self.X)
self.gp.fit(self.X[ur], self.Y[ur])
def compute_PredictiveVariance(self,Xstars,X_t):
"""
Xstars: locations of global optimums
X: existing observations
X_t: suggested_batch
"""
# for robustness, remove empty X_t
X_t=np.atleast_2d(X_t)
mask = ~np.any(np.isnan(X_t), axis=1)
X_t = X_t[mask]
X=np.vstack((self.X,X_t))
var=self.gp.compute_var(X,Xstars)
mean_variance=np.mean(var)
return np.asarray(mean_variance)
def maximize_batch_PVRS_iterative_greedy(self,B=5,first_batch=[]):
"""
Finding a batch of points using Peak Suppression / Constant Liar approach
Input Parameters
----------
gp_params: Parameters to be passed to the Gaussian Process class
kappa: constant value in UCB
Returns
-------
X: a batch of [x_1..x_Nt]
"""
y_max = self.Y.max()
# Set parameters if any was passed
gp=GaussianProcess(self.gp_params)
# Find unique rows of X to avoid GP from breaking
ur = unique_rows(self.X)
gp.fit(self.X[ur], self.Y[ur])
# define the number of Thompson sample M
if 'n_xstars' in self.acq:
numXtar=self.acq['n_xstars']
else:
numXtar=20*self.dim
if self.xstars==[]:
xstars=[]
for ii in range(numXtar):
mu_acq={}
mu_acq['name']='thompson'
mu_acq['dim']=self.dim
mu_acq['scalebounds']=self.scalebounds
acq_mu=AcquisitionFunction(mu_acq)
xt_TS = acq_max(ac=acq_mu.acq_kind,gp=gp,bounds=self.scalebounds,opt_toolbox='scipy')
#temp.append(xt_TS)
xstars.append(xt_TS)
else:
xstars=self.xstars
# Set acquisition function
myacq={}
myacq['name']='pvrs'
myacq['dim']=self.acq['dim']
myacq['xstars']=xstars
acq_func = AcquisitionFunction(myacq)
nRepeat=8
pred_var=[0]*nRepeat
bestBatch=[0]*nRepeat
for tt in range(nRepeat):
# copy GP, X and Y
temp_gp=copy.deepcopy(gp)
temp_X=copy.deepcopy(self.X)
temp_Y=copy.deepcopy(self.Y)
start_batch=time.time()
#store new_x
if tt==0: # first iteration (repeat) use Greedy approach to fill a batch
if first_batch==[]: # if the first batch is not initialized by greedy
new_X=[]
for ii in range(B):
# Finding argmax of the acquisition function.
x_max = acq_max(ac=acq_func.acq_kind,gp=temp_gp, bounds=self.scalebounds)
if ii==0:
new_X=x_max
else:
new_X= np.vstack((new_X, x_max.reshape((1, -1))))
temp_X = np.vstack((temp_X, x_max.reshape((1, -1))))
const_liar,const_liar_variance=temp_gp.predict(x_max,eval_MSE=1)
const_liar=np.random.rand()
temp_Y = np.append(temp_Y, const_liar )
temp_gp.fit(temp_X,temp_Y)
else:
new_X=first_batch
#temp_X = np.vstack((temp_X, new_X.reshape((B, -1))))
#const_liar,const_liar_variance=temp_gp.predict(new_X,eval_MSE=1)
#const_liar=np.random.rand()
#temp_Y = np.append(temp_Y, const_liar )
#temp_gp.fit(temp_X,temp_Y)
else:# >=1 iteration
for ii in range(B):
#new_X=new_X.pop(0)
temp_X=copy.deepcopy(self.X)
if ii==0: # first element
temp_X = np.vstack((temp_X, new_X[ii+1:])) # remove item ii
else:
if ii==B-1: # last element
temp_X = np.vstack((temp_X, new_X[0:ii-1])) # remove item ii
else:
#temp_X = np.vstack((temp_X, new_X[0:ii]+new_X[ii+1:])) # remove item ii
temp_X = np.vstack((temp_X, np.vstack((new_X[0:ii],new_X[ii+1:])))) # remove item ii
temp_Y,const_liar_variance=temp_gp.predict(temp_X,eval_MSE=1)
#temp_Y=np.random.random(size=(len(temp_X),1)) # constant liar
temp_gp.fit(temp_X,temp_Y)
# Finding argmax of the acquisition function.
x_max = acq_max_with_init(ac=acq_func.acq_kind,
gp=temp_gp, y_max=y_max,
bounds=self.scalebounds,
#init_location=np.asarray(new_X[ii]))
init_location=[])
previous_var=self.compute_PredictiveVariance(Xstars=xstars,X_t=np.asarray(new_X))
# back up old value
old_value=new_X[ii].copy()
new_X[ii]=x_max
new_var=self.compute_PredictiveVariance(Xstars=xstars,X_t=np.asarray(new_X))
if new_var>previous_var: # keep the previous value if the uncertainty does not reduce
new_X[ii]=old_value
#print "old value"
#new_var2=self.compute_PredictiveVariance(Xstars=xstars,X_t=np.asarray(new_X))
#print "prev var={:.6f}, newvar={:.6f}, newvar2={:.6f}".format(np.asscalar(previous_var),
#np.asscalar(new_var),np.asscalar(new_var2))
pred_var[tt]=self.compute_PredictiveVariance(Xstars=xstars,X_t=np.asarray(new_X))
#print pred_var
bestBatch[tt]=np.asarray(new_X)
#return new_X,new_X_original
idxBest=np.argmin(pred_var)
new_X=bestBatch[idxBest]
self.NumPoints=np.append(self.NumPoints,new_X.shape[0])
self.X=np.vstack((self.X,new_X))
# convert back to original scale
temp_X_new_original=[val*self.max_min_gap+self.bounds[:,0] for idx, val in enumerate(new_X)]
temp_X_new_original=np.asarray(temp_X_new_original)
self.X_original=np.vstack((self.X_original, temp_X_new_original))
# evaluate y=f(x)
temp=self.f(temp_X_new_original)
temp=np.reshape(temp,(-1,1))
self.Y_original=np.append(self.Y_original,temp)
self.Y=(self.Y_original-np.mean(self.Y_original))/(np.max(self.Y_original)-np.min(self.Y_original))
#return bestBatch[idxBest],pred_var[idxBest]
return bestBatch[idxBest],pred_var
def maximize_batch_greedy_PVRS(self,B=5):
"""
Finding a batch of points using Peak Suppression / Constant Liar approach
Input Parameters
----------
gp_params: Parameters to be passed to the Gaussian Process class
kappa: constant value in UCB
Returns
-------
X: a batch of [x_1..x_Nt]
"""
y_max = self.Y.max()
# Set parameters if any was passed
self.gp=GaussianProcess(self.gp_params)
# Find unique rows of X to avoid GP from breaking
ur = unique_rows(self.X)
self.gp.fit(self.X[ur], self.Y[ur])
start_opt=time.time()
if 'n_xstars' in self.acq:
numXtar=self.acq['n_xstars']
else:
numXtar=30*self.dim
#temp=[]
# finding the xt of Thompson Sampling
xstars=[]
for ii in range(numXtar):
mu_acq={}
mu_acq['name']='thompson'
mu_acq['dim']=self.dim
mu_acq['scalebounds']=self.scalebounds
acq_mu=AcquisitionFunction(mu_acq)
xt_TS = acq_max(ac=acq_mu.acq_kind,gp=self.gp,bounds=self.scalebounds,opt_toolbox='scipy')
#temp.append(xt_TS)
xstars.append(xt_TS)
self.xstars=xstars
# Set acquisition function
myacq={}
myacq['name']='pvrs'
myacq['dim']=self.acq['dim']
myacq['xstars']=xstars
acq_func = AcquisitionFunction(myacq)
# copy GP, X and Y
temp_gp=copy.deepcopy(self.gp)
temp_X=copy.deepcopy(self.X)
temp_Y=copy.deepcopy(self.Y)
#temp_Y_original=self.Y_original
start_batch=time.time()
# check predictive variance before adding a new data points
var_before=self.gp.compute_var(temp_X,xstars)
var_before=np.mean(var_before)
#store new_x
new_X=np.empty((0,self.dim),float)
for ii in range(B):
# Finding argmax of the acquisition function.
x_max = acq_max(ac=acq_func.acq_kind,gp=temp_gp, bounds=self.scalebounds)
new_X= np.vstack((new_X, x_max.reshape((1, -1))))
temp_X = np.vstack((temp_X, x_max.reshape((1, -1))))
# check predictive variance after
var_after=self.gp.compute_var(temp_X,xstars)
var_after=np.mean(var_after)
if self.PVRS_before_after==[]:
self.PVRS_before_after=np.asarray([var_before,var_after])
else:
temp_var=np.asarray([var_before,var_after])
self.PVRS_before_after=np.vstack((self.PVRS_before_after, temp_var))
var_before=var_after
const_liar,const_liar_variance=temp_gp.predict(x_max,eval_MSE=1)
const_liar=np.random.rand()
temp_Y = np.append(temp_Y, const_liar )
temp_gp.fit(temp_X,temp_Y)
# for debug
finish_batch=time.time()-start_batch
#return new_X,new_X_original
self.NumPoints=np.append(self.NumPoints,new_X.shape[0])
self.X=np.vstack((self.X,new_X))
# convert back to original scale
temp_X_new_original=[val*self.max_min_gap+self.bounds[:,0] for idx, val in enumerate(new_X)]
temp_X_new_original=np.asarray(temp_X_new_original)
self.X_original=np.vstack((self.X_original, temp_X_new_original))
# evaluate y=f(x)
temp=self.f(temp_X_new_original)
temp=np.reshape(temp,(-1,1))
self.Y_original=np.append(self.Y_original,temp)
self.Y=(self.Y_original-np.mean(self.Y_original))/(np.max(self.Y_original)-np.min(self.Y_original))
# find the maximizer in the GP mean function
try:
len(self.gp)
x_mu_max=[]
for j in range(self.J):
x_mu_max_temp=acq_max_with_name(gp=self.gp[j],scalebounds=self.scalebounds[self.featIdx[j]],acq_name="mu")
x_mu_max=np.hstack((x_mu_max,x_mu_max_temp))
except:
x_mu_max=acq_max_with_name(gp=self.gp,scalebounds=self.scalebounds,acq_name="mu")
x_mu_max_original=x_mu_max*self.max_min_gap+self.bounds[:,0]
# set y_max = mu_max
#mu_max=acq_mu.acq_kind(x_mu_max,gp=self.gp)
self.Y_original_maxGP = np.append(self.Y_original_maxGP, self.f(x_mu_max_original))
self.X_original_maxGP = np.vstack((self.X_original_maxGP, x_mu_max_original))
return new_X
def maximize_batch_PVRS_iterative_greedy(self,B=5,first_batch=[]):
"""
Finding a batch of points using Peak Suppression / Constant Liar approach
Input Parameters
----------
gp_params: Parameters to be passed to the Gaussian Process class
kappa: constant value in UCB
Returns
-------
X: a batch of [x_1..x_Nt]
"""
y_max = self.Y.max()
# Set parameters if any was passed
gp=GaussianProcess(self.gp_params)
# Find unique rows of X to avoid GP from breaking
ur = unique_rows(self.X)
gp.fit(self.X[ur], self.Y[ur])
# define the number of Thompson sample M
if 'n_xstars' in self.acq:
numXtar=self.acq['n_xstars']
else:
numXtar=20*self.dim
if self.xstars==[]:
xstars=[]
for ii in range(numXtar):
mu_acq={}
mu_acq['name']='thompson'
mu_acq['dim']=self.dim
mu_acq['scalebounds']=self.scalebounds
acq_mu=AcquisitionFunction(mu_acq)
xt_TS = acq_max(ac=acq_mu.acq_kind,gp=gp,bounds=self.scalebounds,opt_toolbox='scipy')
#temp.append(xt_TS)
xstars.append(xt_TS)
else:
xstars=self.xstars
# Set acquisition function
myacq={}
myacq['name']='pvrs'
myacq['dim']=self.acq['dim']
myacq['xstars']=xstars
acq_func = AcquisitionFunction(myacq)
nRepeat=8
pred_var=[0]*nRepeat
bestBatch=[0]*nRepeat
for tt in range(nRepeat):
# copy GP, X and Y
temp_gp=copy.deepcopy(gp)
temp_X=copy.deepcopy(self.X)
temp_Y=copy.deepcopy(self.Y)
start_batch=time.time()
#store new_x
if tt==0: # first iteration (repeat) use Greedy approach to fill a batch
if first_batch==[]: # if the first batch is not initialized by greedy
new_X=[]
for ii in range(B):
# Finding argmax of the acquisition function.
x_max = acq_max(ac=acq_func.acq_kind,gp=temp_gp, bounds=self.scalebounds)
if ii==0:
new_X=x_max
else:
new_X= np.vstack((new_X, x_max.reshape((1, -1))))
temp_X = np.vstack((temp_X, x_max.reshape((1, -1))))
const_liar,const_liar_variance=temp_gp.predict(x_max,eval_MSE=1)
const_liar=np.random.rand()
temp_Y = np.append(temp_Y, const_liar )
temp_gp.fit(temp_X,temp_Y)
else:
new_X=first_batch
#temp_X = np.vstack((temp_X, new_X.reshape((B, -1))))
#const_liar,const_liar_variance=temp_gp.predict(new_X,eval_MSE=1)
#const_liar=np.random.rand()
#temp_Y = np.append(temp_Y, const_liar )
#temp_gp.fit(temp_X,temp_Y)
else:# >=1 iteration
for ii in range(B):
#new_X=new_X.pop(0)
temp_X=copy.deepcopy(self.X)
if ii==0: # first element
temp_X = np.vstack((temp_X, new_X[ii+1:])) # remove item ii
else:
if ii==B-1: # last element
temp_X = np.vstack((temp_X, new_X[0:ii-1])) # remove item ii
else:
#temp_X = np.vstack((temp_X, new_X[0:ii]+new_X[ii+1:])) # remove item ii
temp_X = np.vstack((temp_X, np.vstack((new_X[0:ii],new_X[ii+1:])))) # remove item ii
temp_Y,const_liar_variance=temp_gp.predict(temp_X,eval_MSE=1)
#temp_Y=np.random.random(size=(len(temp_X),1)) # constant liar
temp_gp.fit(temp_X,temp_Y)
# Finding argmax of the acquisition function.
x_max = acq_max_with_init(ac=acq_func.acq_kind,
gp=temp_gp, y_max=y_max,
bounds=self.scalebounds,
#init_location=np.asarray(new_X[ii]))
init_location=[])
previous_var=self.compute_PredictiveVariance(Xstars=xstars,X_t=np.asarray(new_X))
# back up old value
old_value=new_X[ii].copy()
new_X[ii]=x_max
new_var=self.compute_PredictiveVariance(Xstars=xstars,X_t=np.asarray(new_X))
if new_var>previous_var: # keep the previous value if the uncertainty does not reduce
new_X[ii]=old_value
#print "old value"
#new_var2=self.compute_PredictiveVariance(Xstars=xstars,X_t=np.asarray(new_X))
#print "prev var={:.6f}, newvar={:.6f}, newvar2={:.6f}".format(np.asscalar(previous_var),
#np.asscalar(new_var),np.asscalar(new_var2))
pred_var[tt]=self.compute_PredictiveVariance(Xstars=xstars,X_t=np.asarray(new_X))
#print pred_var
bestBatch[tt]=np.asarray(new_X)
#return new_X,new_X_original
idxBest=np.argmin(pred_var)
new_X=bestBatch[idxBest]
self.NumPoints=np.append(self.NumPoints,new_X.shape[0])
self.X=np.vstack((self.X,new_X))
# convert back to original scale
temp_X_new_original=[val*self.max_min_gap+self.bounds[:,0] for idx, val in enumerate(new_X)]
temp_X_new_original=np.asarray(temp_X_new_original)
self.X_original=np.vstack((self.X_original, temp_X_new_original))
# evaluate y=f(x)
temp=self.f(temp_X_new_original)
temp=np.reshape(temp,(-1,1))
self.Y_original=np.append(self.Y_original,temp)
self.Y=(self.Y_original-np.mean(self.Y_original))/(np.max(self.Y_original)-np.min(self.Y_original))
#return bestBatch[idxBest],pred_var[idxBest]
return bestBatch[idxBest],pred_var
def maximize(self):
"""
Main optimization method.
Input parameters
----------
gp_params: parameter for Gaussian Process
Returns
-------
x: recommented point for evaluation
"""
if self.stop_flag == 1:
return
if self.acq['name'] == 'random':
x_max = generate_random_points(bounds=self.scalebounds, size=1)
self.X_original = np.vstack((self.X_original, x_max))
# evaluate Y using original X
#self.Y = np.append(self.Y, self.f(temp_X_new_original))
self.Y_original = np.append(self.Y_original, self.f(x_max))
# update Y after change Y_original
self.Y = (self.Y_original - np.mean(self.Y_original)) / np.std(
self.Y_original)
self.time_opt = np.hstack((self.time_opt, 0))
return
fstar_scaled = (self.fstar - np.mean(self.Y_original)) / np.std(
self.Y_original)
# init a new Gaussian Process
if self.isTGP == 1:
self.gp = TransformedGP(self.gp_params)
# Find unique rows of X to avoid GP from breaking
ur = unique_rows(self.X)
self.gp.fit(self.X[ur], self.Y[ur], fstar_scaled)
else:
self.gp = GaussianProcess(self.gp_params)
ur = unique_rows(self.X)
self.gp.fit(self.X[ur], self.Y[ur])
# optimize GP parameters after 10 iterations
newlengthscale = None
# we donot optimize lengthscale for the setting of gp_lengthscale
if len(self.Y) % (4 * self.dim) == 0:
if self.optimize_gp == 'maximize':
newlengthscale = self.gp.optimize_lengthscale_SE_maximizing(
self.gp_params['lengthscale'],
self.gp_params['noise_delta'])
self.gp_params['lengthscale'] = newlengthscale
elif self.optimize_gp == 'loo':
newlengthscale = self.gp.optimize_lengthscale_SE_loo(
self.gp_params['lengthscale'],
self.gp_params['noise_delta'])
self.gp_params['lengthscale'] = newlengthscale
if self.verbose == 1:
print("estimated lengthscale =", newlengthscale)
# init a new Gaussian Process after optimizing hyper-parameter
if self.isTGP == 1:
self.gp = TransformedGP(self.gp_params)
# Find unique rows of X to avoid GP from breaking
ur = unique_rows(self.X)
self.gp.fit(self.X[ur], self.Y[ur], fstar_scaled)
else:
self.gp = GaussianProcess(self.gp_params)
ur = unique_rows(self.X)
self.gp.fit(self.X[ur], self.Y[ur])
# Set acquisition function
start_opt = time.time()
# run the acquisition function for the first time to get xstar
self.xstars = []
fstar_scaled = (self.fstar - np.mean(self.Y_original)) / np.std(
self.Y_original)
fstar_scaled = (self.fstar - np.mean(self.Y_original)) / np.std(
self.Y_original)
self.acq['fstar_scaled'] = np.asarray([fstar_scaled])
x_max = acq_max_with_name(gp=self.gp,
scalebounds=self.scalebounds,
acq_name=self.acq['name'],
fstar_scaled=fstar_scaled)
"""
self.acq_func = AcquisitionFunction(self.acq)
x_max = acq_max(ac=self.acq_func.acq_kind,gp=self.gp,bounds=self.scalebounds,
opt_toolbox=self.opt_toolbox)
"""
# record the optimization time
finished_opt = time.time()
elapse_opt = finished_opt - start_opt
self.time_opt = np.hstack((self.time_opt, elapse_opt))
# store X
self.X = np.vstack((self.X, x_max.reshape((1, -1))))
# compute X in original scale
temp_X_new_original = x_max * self.max_min_gap + self.bounds[:, 0]
self.X_original = np.vstack((self.X_original, temp_X_new_original))
# evaluate Y using original X
#self.Y = np.append(self.Y, self.f(temp_X_new_original))
y_original = self.f(temp_X_new_original)
self.Y_original = np.append(self.Y_original, y_original)
# update Y after change Y_original
self.Y = (self.Y_original - np.mean(self.Y_original)) / np.std(
self.Y_original)
if self.gp.flagIncremental == 1:
self.gp.fit_incremental(x_max, self.Y[-1])
def __init__(self, gp_params, func_params, acq_params, verbose=1):
"""
Input parameters
----------
gp_params: GP parameters
gp_params.theta: to compute the kernel
gp_params.delta: to compute the kernel
func_params: function to optimize
func_params.init bound: initial bounds for parameters
func_params.bounds: bounds on parameters
func_params.func: a function to be optimized
acq_params: acquisition function,
acq_params.acq_func['name']=['ei','ucb','poi','lei']
,acq['kappa'] for ucb, acq['k'] for lei
acq_params.opt_toolbox: optimization toolbox 'nlopt','direct','scipy'
isTGP: using transformed Gaussian process
Returns
-------
dim: dimension
bounds: bounds on original scale
scalebounds: bounds on normalized scale of 0-1
time_opt: will record the time spent on optimization
gp: Gaussian Process object
"""
if verbose == 1:
self.verbose = 1
else:
self.verbose = 0
# Find number of parameters
bounds = func_params['function'].bounds
if 'init_bounds' not in func_params:
init_bounds = bounds
else:
init_bounds = func_params['init_bounds']
self.dim = len(bounds)
self.fstar = func_params['function'].fstar
#self.fstar_original==func_params['function'].fstar*func_params['function'].ismax
# Create an array with parameters bounds
if isinstance(bounds, dict):
# Get the name of the parameters
self.keys = list(bounds.keys())
self.bounds = []
for key in list(bounds.keys()):
self.bounds.append(bounds[key])
self.bounds = np.asarray(self.bounds)
else:
self.bounds = np.asarray(bounds)
if len(init_bounds) == 0:
self.init_bounds = self.bounds.copy()
else:
self.init_bounds = init_bounds
if isinstance(init_bounds, dict):
# Get the name of the parameters
self.keys = list(init_bounds.keys())
self.init_bounds = []
for key in list(init_bounds.keys()):
self.init_bounds.append(init_bounds[key])
self.init_bounds = np.asarray(self.init_bounds)
else:
self.init_bounds = np.asarray(init_bounds)
# create a scalebounds 0-1
scalebounds = np.array([np.zeros(self.dim), np.ones(self.dim)])
self.scalebounds = scalebounds.T
self.max_min_gap = self.bounds[:, 1] - self.bounds[:, 0]
# Some function to be optimized
self.f = func_params['function'].func
# optimization toolbox
if 'opt_toolbox' not in acq_params:
self.opt_toolbox = 'scipy'
else:
self.opt_toolbox = acq_params['opt_toolbox']
# acquisition function type
self.acq = acq_params['acq_func']
self.acq['scalebounds'] = self.scalebounds
if 'debug' not in self.acq:
self.acq['debug'] = 0
if 'stopping' not in acq_params:
self.stopping_criteria = 0
else:
self.stopping_criteria = acq_params['stopping']
if 'optimize_gp' not in acq_params:
self.optimize_gp = 'maximize'
else:
self.optimize_gp = acq_params['optimize_gp']
if 'marginalize_gp' not in acq_params:
self.marginalize_gp = 0
else:
self.marginalize_gp = acq_params['marginalize_gp']
# store X in original scale
self.X_original = None
# store X in 0-1 scale
self.X = None
# store y=f(x)
# (y - mean)/(max-min)
self.Y = None
# y original scale
self.Y_original = None
self.time_opt = 0
self.gp_params = gp_params
# Gaussian Process class
if 'surrogate' not in self.acq:
self.acq['surrogate'] = 'gp'
if self.acq['surrogate'] == 'tgp':
self.isTGP = 1
self.gp = TransformedGP(gp_params)
else:
self.isTGP = 0
self.gp = GaussianProcess(gp_params)
# acquisition function
self.acq_func = None
# stop condition
self.stop_flag = 0
self.logmarginal = 0
# xt_suggestion, caching for Consensus
self.xstars = []
self.xstar_accumulate = []
# theta vector for marginalization GP
self.theta_vector = []
if 'n_xstars' in self.acq:
self.numXstar = self.acq['n_xstars']
else:
#self.numXstar=self.dim*50
self.numXstar = 100
# store ystars
#self.ystars=np.empty((0,100), float)
self.gstars = np.empty((0, self.numXstar), float)
self.gap_gstar_fstar = np.empty((0, self.numXstar), float)
# store all selection of AF for algorithm with confidence bound
self.marker = []
self.flagTheta_TS = 0
self.mean_theta_TS = None
class BayesOpt_KnownOptimumValue(object):
def __init__(self, gp_params, func_params, acq_params, verbose=1):
"""
Input parameters
----------
gp_params: GP parameters
gp_params.theta: to compute the kernel
gp_params.delta: to compute the kernel
func_params: function to optimize
func_params.init bound: initial bounds for parameters
func_params.bounds: bounds on parameters
func_params.func: a function to be optimized
acq_params: acquisition function,
acq_params.acq_func['name']=['ei','ucb','poi','lei']
,acq['kappa'] for ucb, acq['k'] for lei
acq_params.opt_toolbox: optimization toolbox 'nlopt','direct','scipy'
isTGP: using transformed Gaussian process
Returns
-------
dim: dimension
bounds: bounds on original scale
scalebounds: bounds on normalized scale of 0-1
time_opt: will record the time spent on optimization
gp: Gaussian Process object
"""
if verbose == 1:
self.verbose = 1
else:
self.verbose = 0
# Find number of parameters
bounds = func_params['function'].bounds
if 'init_bounds' not in func_params:
init_bounds = bounds
else:
init_bounds = func_params['init_bounds']
self.dim = len(bounds)
self.fstar = func_params['function'].fstar
#self.fstar_original==func_params['function'].fstar*func_params['function'].ismax
# Create an array with parameters bounds
if isinstance(bounds, dict):
# Get the name of the parameters
self.keys = list(bounds.keys())
self.bounds = []
for key in list(bounds.keys()):
self.bounds.append(bounds[key])
self.bounds = np.asarray(self.bounds)
else:
self.bounds = np.asarray(bounds)
if len(init_bounds) == 0:
self.init_bounds = self.bounds.copy()
else:
self.init_bounds = init_bounds
if isinstance(init_bounds, dict):
# Get the name of the parameters
self.keys = list(init_bounds.keys())
self.init_bounds = []
for key in list(init_bounds.keys()):
self.init_bounds.append(init_bounds[key])
self.init_bounds = np.asarray(self.init_bounds)
else:
self.init_bounds = np.asarray(init_bounds)
# create a scalebounds 0-1
scalebounds = np.array([np.zeros(self.dim), np.ones(self.dim)])
self.scalebounds = scalebounds.T
self.max_min_gap = self.bounds[:, 1] - self.bounds[:, 0]
# Some function to be optimized
self.f = func_params['function'].func
# optimization toolbox
if 'opt_toolbox' not in acq_params:
self.opt_toolbox = 'scipy'
else:
self.opt_toolbox = acq_params['opt_toolbox']
# acquisition function type
self.acq = acq_params['acq_func']
self.acq['scalebounds'] = self.scalebounds
if 'debug' not in self.acq:
self.acq['debug'] = 0
if 'stopping' not in acq_params:
self.stopping_criteria = 0
else:
self.stopping_criteria = acq_params['stopping']
if 'optimize_gp' not in acq_params:
self.optimize_gp = 'maximize'
else:
self.optimize_gp = acq_params['optimize_gp']
if 'marginalize_gp' not in acq_params:
self.marginalize_gp = 0
else:
self.marginalize_gp = acq_params['marginalize_gp']
# store X in original scale
self.X_original = None
# store X in 0-1 scale
self.X = None
# store y=f(x)
# (y - mean)/(max-min)
self.Y = None
# y original scale
self.Y_original = None
self.time_opt = 0
self.gp_params = gp_params
# Gaussian Process class
if 'surrogate' not in self.acq:
self.acq['surrogate'] = 'gp'
if self.acq['surrogate'] == 'tgp':
self.isTGP = 1
self.gp = TransformedGP(gp_params)
else:
self.isTGP = 0
self.gp = GaussianProcess(gp_params)
# acquisition function
self.acq_func = None
# stop condition
self.stop_flag = 0
self.logmarginal = 0
# xt_suggestion, caching for Consensus
self.xstars = []
self.xstar_accumulate = []
# theta vector for marginalization GP
self.theta_vector = []
if 'n_xstars' in self.acq:
self.numXstar = self.acq['n_xstars']
else:
#self.numXstar=self.dim*50
self.numXstar = 100
# store ystars
#self.ystars=np.empty((0,100), float)
self.gstars = np.empty((0, self.numXstar), float)
self.gap_gstar_fstar = np.empty((0, self.numXstar), float)
# store all selection of AF for algorithm with confidence bound
self.marker = []
self.flagTheta_TS = 0
self.mean_theta_TS = None
# will be later used for visualization
def posterior(self, Xnew):
self.gp.fit(self.X, self.Y)
mu, sigma2 = self.gp.predict(Xnew, eval_MSE=True)
return mu, np.sqrt(sigma2)
def posterior_tgp(self, Xnew):
fstar_scaled = (self.fstar - np.mean(self.Y_original)) / np.std(
self.Y_original)
self.gp.fit(self.X, self.Y, fstar_scaled)
mu, sigma2 = self.gp.predict(Xnew, eval_MSE=True)
return mu, np.sqrt(sigma2)
def posterior_tgp_g(self, Xnew):
fstar_scaled = (self.fstar - np.mean(self.Y_original)) / np.std(
self.Y_original)
self.tgp.fit(self.X, self.Y, fstar_scaled)
mu, sigma2 = self.tgp.predict_G(Xnew, eval_MSE=True)
return mu, np.sqrt(sigma2)
def init_with_data(self, init_X, init_Y):
"""
Input parameters
----------
gp_params: Gaussian Process structure
x,y: # init data observations (in original scale)
"""
# Turn it into np array and store.
self.X_original = np.asarray(init_X)
temp_init_point = np.divide((init_X - self.bounds[:, 0]),
self.max_min_gap)
self.X_original = np.asarray(init_X)
self.X = np.asarray(temp_init_point)
self.Y_original = np.asarray(init_Y)
#self.Y=(self.Y_original-np.mean(self.Y_original))/np.std(self.Y_original)
# add y_optimum into Y set
#Y_temp=[self.Y_original,self.fstar]
#self.Y=(self.Y_original-np.mean(Y_temp))/np.std(Y_temp)
self.Y = (self.Y_original - np.mean(self.Y_original)) / np.std(
self.Y_original)
def init(self, gp_params, n_init_points=3, seed=1):
"""
Input parameters
----------
gp_params: Gaussian Process structure
n_init_points: # init points
"""
np.random.seed(seed)
# Generate random points
l = [
np.random.uniform(x[0], x[1]) for _ in range(n_init_points)
for x in self.init_bounds
]
#l=[np.linspace(x[0],x[1],num=n_init_points) for x in self.init_bounds]
# Concatenate new random points to possible existing
# points from self.explore method.
temp = np.asarray(l)
temp = temp.T
init_X = list(temp.reshape((n_init_points, -1)))
self.X_original = np.asarray(init_X)
# Evaluate target function at all initialization
y_init = self.f(init_X)
y_init = np.reshape(y_init, (n_init_points, 1))
self.Y_original = np.asarray(y_init)
self.Y = (self.Y_original - np.mean(self.Y_original)) / np.std(
self.Y_original)
# convert it to scaleX
temp_init_point = np.divide((init_X - self.bounds[:, 0]),
self.max_min_gap)
self.X = np.asarray(temp_init_point)
def maximize(self):
"""
Main optimization method.
Input parameters
----------
gp_params: parameter for Gaussian Process
Returns
-------
x: recommented point for evaluation
"""
if self.stop_flag == 1:
return
if self.acq['name'] == 'random':
x_max = generate_random_points(bounds=self.scalebounds, size=1)
self.X_original = np.vstack((self.X_original, x_max))
# evaluate Y using original X
#self.Y = np.append(self.Y, self.f(temp_X_new_original))
self.Y_original = np.append(self.Y_original, self.f(x_max))
# update Y after change Y_original
self.Y = (self.Y_original - np.mean(self.Y_original)) / np.std(
self.Y_original)
self.time_opt = np.hstack((self.time_opt, 0))
return
fstar_scaled = (self.fstar - np.mean(self.Y_original)) / np.std(
self.Y_original)
# init a new Gaussian Process
if self.isTGP == 1:
self.gp = TransformedGP(self.gp_params)
# Find unique rows of X to avoid GP from breaking
ur = unique_rows(self.X)
self.gp.fit(self.X[ur], self.Y[ur], fstar_scaled)
else:
self.gp = GaussianProcess(self.gp_params)
ur = unique_rows(self.X)
self.gp.fit(self.X[ur], self.Y[ur])
# optimize GP parameters after 10 iterations
newlengthscale = None
# we donot optimize lengthscale for the setting of gp_lengthscale
if len(self.Y) % (4 * self.dim) == 0:
if self.optimize_gp == 'maximize':
newlengthscale = self.gp.optimize_lengthscale_SE_maximizing(
self.gp_params['lengthscale'],
self.gp_params['noise_delta'])
self.gp_params['lengthscale'] = newlengthscale
elif self.optimize_gp == 'loo':
newlengthscale = self.gp.optimize_lengthscale_SE_loo(
self.gp_params['lengthscale'],
self.gp_params['noise_delta'])
self.gp_params['lengthscale'] = newlengthscale
if self.verbose == 1:
print("estimated lengthscale =", newlengthscale)
# init a new Gaussian Process after optimizing hyper-parameter
if self.isTGP == 1:
self.gp = TransformedGP(self.gp_params)
# Find unique rows of X to avoid GP from breaking
ur = unique_rows(self.X)
self.gp.fit(self.X[ur], self.Y[ur], fstar_scaled)
else:
self.gp = GaussianProcess(self.gp_params)
ur = unique_rows(self.X)
self.gp.fit(self.X[ur], self.Y[ur])
# Set acquisition function
start_opt = time.time()
# run the acquisition function for the first time to get xstar
self.xstars = []
fstar_scaled = (self.fstar - np.mean(self.Y_original)) / np.std(
self.Y_original)
fstar_scaled = (self.fstar - np.mean(self.Y_original)) / np.std(
self.Y_original)
self.acq['fstar_scaled'] = np.asarray([fstar_scaled])
x_max = acq_max_with_name(gp=self.gp,
scalebounds=self.scalebounds,
acq_name=self.acq['name'],
fstar_scaled=fstar_scaled)
"""
self.acq_func = AcquisitionFunction(self.acq)
x_max = acq_max(ac=self.acq_func.acq_kind,gp=self.gp,bounds=self.scalebounds,
opt_toolbox=self.opt_toolbox)
"""
# record the optimization time
finished_opt = time.time()
elapse_opt = finished_opt - start_opt
self.time_opt = np.hstack((self.time_opt, elapse_opt))
# store X
self.X = np.vstack((self.X, x_max.reshape((1, -1))))
# compute X in original scale
temp_X_new_original = x_max * self.max_min_gap + self.bounds[:, 0]
self.X_original = np.vstack((self.X_original, temp_X_new_original))
# evaluate Y using original X
#self.Y = np.append(self.Y, self.f(temp_X_new_original))
y_original = self.f(temp_X_new_original)
self.Y_original = np.append(self.Y_original, y_original)
# update Y after change Y_original
self.Y = (self.Y_original - np.mean(self.Y_original)) / np.std(
self.Y_original)
if self.gp.flagIncremental == 1:
self.gp.fit_incremental(x_max, self.Y[-1])