def __init__(self, model, X_lower, X_upper, par=0.0, **kwargs):
r"""
Probability of Improvement solves the following equation
:math:`PI(X) := \mathbb{P}\left( f(\mathbf{X^+}) - f_{t+1}(\mathbf{X}) > \xi\right)`, where
:math:`f(X^+)` is the best input found so far.
Parameters
----------
model: Model object
A model that implements at least
- predict(X)
- getCurrentBestX().
If you want to calculate derivatives than it should also support
- predictive_gradients(X)
X_lower: np.ndarray (D)
Lower bounds of the input space
X_upper: np.ndarray (D)
Upper bounds of the input space
par: float
Controls the balance between exploration
and exploitation of the acquisition function. Default is 0.01
"""
super(PI, self).__init__(model, X_lower, X_upper)
self.par = par
self.rec = BestObservation(self.model, self.X_lower, self.X_upper)
def __init__(self, model, X_lower, X_upper, par=0.0, **kwargs):
r"""
Computes for a given x the expected improvement as
acquisition value.
:math:`EI(X) :=
\mathbb{E}\left[ \max\{0, f(\mathbf{X^+}) -
f_{t+1}(\mathbf{X}) - \xi\right] \} ]`, with
:math:`f(X^+)` as the incumbent.
Parameters
----------
model: Model object
A model that implements at least
- predict(X)
- getCurrentBestX().
If you want to calculate derivatives than it should also support
- predictive_gradients(X)
X_lower: np.ndarray (D)
Lower bounds of the input space
X_upper: np.ndarray (D)
Upper bounds of the input space
compute_incumbent: func
A python function that takes as input a model and returns
a np.array as incumbent
par: float
Controls the balance between exploration
and exploitation of the acquisition function. Default is 0.01
"""
super(EI, self).__init__(model, X_lower, X_upper)
self.par = par
self.rec = BestObservation(self.model, self.X_lower, self.X_upper)
def test(self):
X_lower = np.array([0])
X_upper = np.array([1])
X = init_random_uniform(X_lower, X_upper, 10)
Y = np.sin(X)
kernel = george.kernels.Matern52Kernel(np.ones([1]),
ndim=1)
prior = TophatPrior(-2, 2)
model = GaussianProcess(kernel, prior=prior)
model.train(X, Y)
rec = BestObservation(model, X_lower, X_upper)
startpoints = init_random_uniform(X_lower, X_upper, 10)
inc, inc_val = rec.estimate_incumbent(startpoints)
# Check shapes
assert len(inc.shape) == 2
assert inc.shape[0] == 1
assert inc.shape[1] == X_lower.shape[0]
assert len(inc_val.shape) == 2
assert inc_val.shape[0] == 1
assert inc_val.shape[1] == 1
# Check if incumbent is in the bounds
assert not np.any([np.any(inc[:, i] < X_lower[i])
for i in range(X_lower.shape[0])])
assert not np.any([np.any(inc[:, i] > X_upper[i])
for i in range(X_upper.shape[0])])
def test(self):
X_lower = np.array([0])
X_upper = np.array([1])
X = init_random_uniform(X_lower, X_upper, 10)
Y = np.sin(X)
kernel = george.kernels.Matern52Kernel(np.ones([1]),
ndim=1)
prior = TophatPrior(-2, 2)
model = GaussianProcess(kernel, prior=prior)
model.train(X, Y)
rec = BestObservation(model, X_lower, X_upper)
startpoints = init_random_uniform(X_lower, X_upper, 10)
inc, inc_val = rec.estimate_incumbent(startpoints)
# Check shapes
assert len(inc.shape) == 2
assert inc.shape[0] == 1
assert inc.shape[1] == X_lower.shape[0]
assert len(inc_val.shape) == 2
assert inc_val.shape[0] == 1
assert inc_val.shape[1] == 1
# Check if incumbent is in the bounds
assert not np.any([np.any(inc[:, i] < X_lower[i])
for i in range(X_lower.shape[0])])
assert not np.any([np.any(inc[:, i] > X_upper[i])
for i in range(X_upper.shape[0])])
def __init__(self, model, X_lower, X_upper, par=0.01, **kwargs):
r"""
Computes for a given x the logarithm expected improvement as
acquisition value.
Parameters
----------
model: Model object
A model that implements at least
- predict(X)
If you want to calculate derivatives than it should also support
- predictive_gradients(X)
X_lower: np.ndarray (D)
Lower bounds of the input space
X_upper: np.ndarray (D)
Upper bounds of the input space
par: float
Controls the balance between exploration
and exploitation of the acquisition function. Default is 0.01
"""
super(LogEI, self).__init__(model, X_lower, X_upper)
self.par = par
self.rec = BestObservation(self.model, self.X_lower, self.X_upper)
def update(self, model):
"""
This method will be called if the model is updated.
Parameters
----------
model : Model object
Models the objective function.
"""
super(PI, self).update(model)
self.rec = BestObservation(self.model, self.X_lower, self.X_upper)
def __init__(self, task=None, save_dir=None, num_save=1, rng=None):
"""
Random Search [1] that simply evaluates random points. We do not have
any priors thus we sample points uniformly at random.
[1] J. Bergstra and Y. Bengio.
Random search for hyper-parameter optimization.
JMLR, 2012.
Parameters
----------
task: TaskObject
Task object that contains the objective function and additional
meta information such as the lower and upper bound of the search
space.
num_save: int
Defines after how many iteration the output is saved.
save_dir: String
Output path
rng: numpy.random.RandomState
"""
if rng is None:
self.rng = np.random.RandomState(42)
else:
self.rng = rng
self.task = task
self.save_dir = save_dir
self.X = None
self.Y = None
self.estimator = BestObservation(self,
self.task.X_lower,
self.task.X_upper)
self.time_func_eval = None
self.time_overhead = None
self.num_save = num_save
self.model_untrained = True
self.incumbent = None
self.incumbents = []
self.incumbent_values = []
self.runtime = []
if self.save_dir is not None:
self.create_save_dir()
def __init__(self, model, X_lower, X_upper, par=0.0, **kwargs):
r"""
Probability of Improvement solves the following equation
:math:`PI(X) := \mathbb{P}\left( f(\mathbf{X^+}) - f_{t+1}(\mathbf{X}) > \xi\right)`, where
:math:`f(X^+)` is the best input found so far.
Parameters
----------
model: Model object
A model that implements at least
- predict(X)
- getCurrentBestX().
If you want to calculate derivatives than it should also support
- predictive_gradients(X)
X_lower: np.ndarray (D)
Lower bounds of the input space
X_upper: np.ndarray (D)
Upper bounds of the input space
par: float
Controls the balance between exploration
and exploitation of the acquisition function. Default is 0.01
"""
super(PI, self).__init__(model, X_lower, X_upper)
self.par = par
self.rec = BestObservation(self.model,
self.X_lower,
self.X_upper)
def __init__(self, model, X_lower, X_upper, par=0.0, **kwargs):
r"""
Computes for a given x the logarithm expected improvement as
acquisition value.
Parameters
----------
model: Model object
A model that implements at least
- predict(X)
If you want to calculate derivatives than it should also support
- predictive_gradients(X)
X_lower: np.ndarray (D)
Lower bounds of the input space
X_upper: np.ndarray (D)
Upper bounds of the input space
par: float
Controls the balance between exploration
and exploitation of the acquisition function. Default is 0.01
"""
super(LogEI, self).__init__(model, X_lower, X_upper)
self.par = par
self.rec = BestObservation(self.model, self.X_lower, self.X_upper)
def update(self, model):
"""
This method will be called if the model is updated.
Parameters
----------
model : Model object
Models the objective function.
"""
super(EI, self).update(model)
self.rec = BestObservation(self.model, self.X_lower, self.X_upper)
def __init__(self,
model,
X_lower,
X_upper,
par=0.0,
**kwargs):
r"""
Computes for a given x the expected improvement as
acquisition value.
:math:`EI(X) :=
\mathbb{E}\left[ \max\{0, f(\mathbf{X^+}) -
f_{t+1}(\mathbf{X}) - \xi\right] \} ]`, with
:math:`f(X^+)` as the incumbent.
Parameters
----------
model: Model object
A model that implements at least
- predict(X)
- getCurrentBestX().
If you want to calculate derivatives than it should also support
- predictive_gradients(X)
X_lower: np.ndarray (D)
Lower bounds of the input space
X_upper: np.ndarray (D)
Upper bounds of the input space
compute_incumbent: func
A python function that takes as input a model and returns
a np.array as incumbent
par: float
Controls the balance between exploration
and exploitation of the acquisition function. Default is 0.01
"""
super(EI, self).__init__(model, X_lower, X_upper)
self.par = par
self.rec = BestObservation(self.model, self.X_lower, self.X_upper)
class EI(BaseAcquisitionFunction):
def __init__(self,
model,
X_lower,
X_upper,
par=0.0,
**kwargs):
r"""
Computes for a given x the expected improvement as
acquisition value.
:math:`EI(X) :=
\mathbb{E}\left[ \max\{0, f(\mathbf{X^+}) -
f_{t+1}(\mathbf{X}) - \xi\right] \} ]`, with
:math:`f(X^+)` as the incumbent.
Parameters
----------
model: Model object
A model that implements at least
- predict(X)
- getCurrentBestX().
If you want to calculate derivatives than it should also support
- predictive_gradients(X)
X_lower: np.ndarray (D)
Lower bounds of the input space
X_upper: np.ndarray (D)
Upper bounds of the input space
compute_incumbent: func
A python function that takes as input a model and returns
a np.array as incumbent
par: float
Controls the balance between exploration
and exploitation of the acquisition function. Default is 0.01
"""
super(EI, self).__init__(model, X_lower, X_upper)
self.par = par
self.rec = BestObservation(self.model, self.X_lower, self.X_upper)
def update(self, model):
"""
This method will be called if the model is updated.
Parameters
----------
model : Model object
Models the objective function.
"""
super(EI, self).update(model)
self.rec = BestObservation(self.model, self.X_lower, self.X_upper)
def compute(self, X, derivative=False, **kwargs):
"""
Computes the EI value and its derivatives.
Parameters
----------
X: np.ndarray(1, D), The input point where the acquisition function
should be evaluate. The dimensionality of X is (N, D), with N as
the number of points to evaluate at and D is the number of
dimensions of one X.
derivative: Boolean
If is set to true also the derivative of the acquisition
function at X is returned
Returns
-------
np.ndarray(1,1)
Expected Improvement of X
np.ndarray(1,D)
Derivative of Expected Improvement at X (only if derivative=True)
"""
if X.shape[0] > 1:
raise ValueError("EI is only for single test points")
if len(X.shape) == 1:
X = X[:, np.newaxis]
if np.any(X < self.X_lower) or np.any(X > self.X_upper):
if derivative:
f = 0
df = np.zeros((1, X.shape[1]))
return np.array([[f]]), np.array([df])
else:
return np.array([[0]])
m, v = self.model.predict(X)
# Use the best seen observation as incumbent
_, eta = self.rec.estimate_incumbent(None)
s = np.sqrt(v)
if (s == 0).any():
f = np.array([[0]])
df = np.zeros((1, X.shape[1]))
else:
z = (eta - m - self.par) / s
# f = (eta - m - self.par) * norm.cdf(z) + s * norm.pdf(z)
f = s * ( z * norm.cdf(z) + norm.pdf(z))
if derivative:
dmdx, ds2dx = self.model.predictive_gradients(X)
dmdx = dmdx[0]
ds2dx = ds2dx[0][:, None]
dsdx = ds2dx / (2 * s)
df = (-dmdx * norm.cdf(z) + (dsdx * norm.pdf(z))).T
if (f < 0).any():
logger.error("Expected Improvement is smaller than 0!")
raise ValueError
if derivative:
return f, df
else:
return f
def test(self):
X_lower = np.array([0])
X_upper = np.array([1])
X = init_random_uniform(X_lower, X_upper, 10)
Y = np.sin(X)
kernel = GPy.kern.Matern52(input_dim=1)
model = GPyModel(kernel)
model.train(X, Y)
x_test = init_random_uniform(X_lower, X_upper, 3)
# Shape matching predict
m, v = model.predict(x_test, full_cov=True)
assert len(m.shape) == 2
assert m.shape[0] == x_test.shape[0]
assert m.shape[1] == 1
assert len(v.shape) == 2
assert v.shape[0] == x_test.shape[0]
assert v.shape[1] == x_test.shape[0]
# Check gradients
dm, dv = model.predictive_gradients(x_test)
assert len(dm.shape) == 2
assert dm.shape[0] == x_test.shape[0]
assert dm.shape[1] == x_test.shape[1]
assert len(dv.shape) == 2
assert dv.shape[0] == x_test.shape[0]
assert dv.shape[1] == 1
# Shape matching function sampling
x_ = np.linspace(X_lower, X_upper, 10)
x_ = x_[:, np.newaxis]
funcs = model.sample_functions(x_, n_funcs=2)
assert len(funcs.shape) == 2
assert funcs.shape[0] == 2
assert funcs.shape[1] == x_.shape[0]
# Shape matching predict variance
x_test2 = np.array([np.random.rand(1)])
x_test1 = np.random.rand(10)[:, np.newaxis]
var = model.predict_variance(x_test1, x_test2)
assert len(var.shape) == 2
assert var.shape[0] == x_test1.shape[0]
assert var.shape[1] == 1
# Check compatibility with all acquisition functions
acq_func = EI(model,
X_upper=X_upper,
X_lower=X_lower)
acq_func.update(model)
acq_func(x_test)
acq_func = PI(model,
X_upper=X_upper,
X_lower=X_lower)
acq_func.update(model)
acq_func(x_test)
acq_func = LCB(model,
X_upper=X_upper,
X_lower=X_lower)
acq_func.update(model)
acq_func(x_test)
acq_func = InformationGain(model,
X_upper=X_upper,
X_lower=X_lower)
acq_func.update(model)
acq_func(x_test)
# Check compatibility with all incumbent estimation methods
rec = BestObservation(model, X_lower, X_upper)
inc, inc_val = rec.estimate_incumbent(None)
assert len(inc.shape) == 2
assert inc.shape[0] == 1
assert inc.shape[1] == X_upper.shape[0]
assert len(inc_val.shape) == 2
assert inc_val.shape[0] == 1
assert inc_val.shape[1] == 1
rec = PosteriorMeanOptimization(model, X_lower, X_upper)
startpoints = init_random_uniform(X_lower, X_upper, 4)
inc, inc_val = rec.estimate_incumbent(startpoints)
assert len(inc.shape) == 2
assert inc.shape[0] == 1
assert inc.shape[1] == X_upper.shape[0]
assert len(inc_val.shape) == 2
assert inc_val.shape[0] == 1
assert inc_val.shape[1] == 1
rec = PosteriorMeanAndStdOptimization(model, X_lower, X_upper)
startpoints = init_random_uniform(X_lower, X_upper, 4)
inc, inc_val = rec.estimate_incumbent(startpoints)
assert len(inc.shape) == 2
assert inc.shape[0] == 1
assert inc.shape[1] == X_upper.shape[0]
assert len(inc_val.shape) == 2
assert inc_val.shape[0] == 1
assert inc_val.shape[1] == 1
class PI(BaseAcquisitionFunction):
def __init__(self, model, X_lower, X_upper, par=0.0, **kwargs):
r"""
Probability of Improvement solves the following equation
:math:`PI(X) := \mathbb{P}\left( f(\mathbf{X^+}) - f_{t+1}(\mathbf{X}) > \xi\right)`, where
:math:`f(X^+)` is the best input found so far.
Parameters
----------
model: Model object
A model that implements at least
- predict(X)
- getCurrentBestX().
If you want to calculate derivatives than it should also support
- predictive_gradients(X)
X_lower: np.ndarray (D)
Lower bounds of the input space
X_upper: np.ndarray (D)
Upper bounds of the input space
par: float
Controls the balance between exploration
and exploitation of the acquisition function. Default is 0.01
"""
super(PI, self).__init__(model, X_lower, X_upper)
self.par = par
self.rec = BestObservation(self.model,
self.X_lower,
self.X_upper)
def update(self, model):
"""
This method will be called if the model is updated.
Parameters
----------
model : Model object
Models the objective function.
"""
super(PI, self).update(model)
self.rec = BestObservation(self.model, self.X_lower, self.X_upper)
def compute(self, X, derivative=False, **kwargs):
"""
Computes the PI value and its derivatives.
Parameters
----------
X: np.ndarray(1, D), The input point where the acquisition function
should be evaluate. The dimensionality of X is (N, D), with N as
the number of points to evaluate at and D is the number of
dimensions of one X.
derivative: Boolean
If is set to true also the derivative of the acquisition
function at X is returned
Returns
-------
np.ndarray(1,1)
Probability of Improvement of X
np.ndarray(1,D)
Derivative of Probability of Improvement at X
(only if derivative=True)
"""
if X.shape[0] > 1:
logger.error("PI is only for single x inputs")
return
if np.any(X < self.X_lower) or np.any(X > self.X_upper):
if derivative:
f = 0
df = np.zeros((1, X.shape[1]))
return np.array([[f]]), np.array([df])
else:
return np.array([[0]])
m, v = self.model.predict(X)
_, eta = self.rec.estimate_incumbent(None)
s = np.sqrt(v)
z = (eta - m - self.par) / s
f = norm.cdf(z)
if derivative:
dmdx, ds2dx = self.model.predictive_gradients(X)
dmdx = dmdx[0]
ds2dx = ds2dx[0][:, None]
dsdx = ds2dx / (2 * s)
df = (-(-norm.pdf(z) / s) * (dmdx + dsdx * z)).T
return f, df
else:
return f
class RandomSearch(BaseSolver):
def __init__(self, task=None, save_dir=None, num_save=1, rng=None):
"""
Random Search [1] that simply evaluates random points. We do not have
any priors thus we sample points uniformly at random.
[1] J. Bergstra and Y. Bengio.
Random search for hyper-parameter optimization.
JMLR, 2012.
Parameters
----------
task: TaskObject
Task object that contains the objective function and additional
meta information such as the lower and upper bound of the search
space.
num_save: int
Defines after how many iteration the output is saved.
save_dir: String
Output path
rng: numpy.random.RandomState
"""
if rng is None:
self.rng = np.random.RandomState(42)
else:
self.rng = rng
self.task = task
self.save_dir = save_dir
self.X = None
self.Y = None
self.estimator = BestObservation(self,
self.task.X_lower,
self.task.X_upper)
self.time_func_eval = None
self.time_overhead = None
self.num_save = num_save
self.model_untrained = True
self.incumbent = None
self.incumbents = []
self.incumbent_values = []
self.runtime = []
if self.save_dir is not None:
self.create_save_dir()
def run(self, num_iterations=10):
"""
The main optimization loop
Parameters
----------
num_iterations: int
The number of iterations
Returns
-------
np.ndarray(1,D)
Incumbent
np.ndarray(1,1)
(Estimated) function value of the incumbent
"""
self.time_start = time.time()
for it in range(num_iterations):
logger.info("Start iteration %d ... ", it)
start_time = time.time()
# Choose next point to evaluate
new_x = self.choose_next()
time_overhead = time.time() - start_time
self.time_overhead = np.append(self.time_overhead,
np.array([time_overhead]))
logger.info("Optimization overhead was %f seconds" %
(self.time_overhead[-1]))
logger.info("Evaluate candidate %s" % (str(new_x)))
start_time = time.time()
new_y = self.task.evaluate(new_x)
time_func_eval = time.time() - start_time
self.time_func_eval = np.append(self.time_func_eval,
np.array([time_func_eval]))
logger.info("Configuration achieved a performance of %f " %
(new_y[0, 0]))
logger.info("Evaluation of this configuration took %f seconds" %
(self.time_func_eval[-1]))
self.runtime.append(time.time() - self.time_start)
# Update the data
if self.X is None and self.Y is None:
self.X = new_x
self.Y = new_y
else:
self.X = np.append(self.X, new_x, axis=0)
self.Y = np.append(self.Y, new_y, axis=0)
# The incumbent is just the best observation we have seen so far
start_time_inc = time.time()
self.incumbent, self.incumbent_value = \
self.estimator.estimate_incumbent(None)
self.incumbents.append(self.incumbent)
self.incumbent_values.append(self.incumbent_value)
logger.info("New incumbent %s found in %f seconds with "
"estimated performance %f",
str(self.incumbent), time.time() - start_time_inc,
self.incumbent_value)
if self.save_dir is not None and (it) % self.num_save == 0:
self.save_iteration(it)
logger.info("Return %s as incumbent with predicted performance %f" %
(str(self.incumbent), self.incumbent_value))
return self.incumbent, self.incumbent_value
def choose_next(self):
"""
Sample a new point uniformly at random.
Returns
-------
np.ndarray(1,D)
Suggested point to evaluate
"""
return self.rng.uniform(self.task.X_lower,
self.task.X_upper)[np.newaxis, :]
def test(self):
X_lower = np.array([0])
X_upper = np.array([1])
X = init_random_uniform(X_lower, X_upper, 10)
Y = np.sin(X)
model = RandomForest(types=np.zeros([X_lower.shape[0]]))
model.train(X, Y)
x_test = init_random_uniform(X_lower, X_upper, 3)
# Shape matching predict
m, v = model.predict(x_test)
assert len(m.shape) == 2
assert m.shape[0] == x_test.shape[0]
assert m.shape[1] == 1
assert len(v.shape) == 2
assert v.shape[0] == x_test.shape[0]
assert v.shape[1] == 1
# Shape matching function sampling
x_ = np.linspace(X_lower, X_upper, 10)
x_ = x_[:, np.newaxis]
#funcs = model.sample_functions(x_, n_funcs=2)
#assert len(funcs.shape) == 2
#assert funcs.shape[0] == 2
#assert funcs.shape[1] == x_.shape[0]
# Check compatibility with all acquisition functions
acq_func = EI(model, X_upper=X_upper, X_lower=X_lower)
acq_func.update(model)
acq_func(x_test)
acq_func = PI(model, X_upper=X_upper, X_lower=X_lower)
acq_func.update(model)
acq_func(x_test)
acq_func = LCB(model, X_upper=X_upper, X_lower=X_lower)
acq_func.update(model)
acq_func(x_test)
# Check compatibility with all incumbent estimation methods
rec = BestObservation(model, X_lower, X_upper)
inc, inc_val = rec.estimate_incumbent(None)
assert len(inc.shape) == 2
assert inc.shape[0] == 1
assert inc.shape[1] == X_upper.shape[0]
assert len(inc_val.shape) == 2
assert inc_val.shape[0] == 1
assert inc_val.shape[1] == 1
rec = PosteriorMeanOptimization(model, X_lower, X_upper)
startpoints = init_random_uniform(X_lower, X_upper, 4)
inc, inc_val = rec.estimate_incumbent(startpoints)
assert len(inc.shape) == 2
assert inc.shape[0] == 1
assert inc.shape[1] == X_upper.shape[0]
assert len(inc_val.shape) == 2
assert inc_val.shape[0] == 1
assert inc_val.shape[1] == 1
rec = PosteriorMeanAndStdOptimization(model, X_lower, X_upper)
startpoints = init_random_uniform(X_lower, X_upper, 4)
inc, inc_val = rec.estimate_incumbent(startpoints)
assert len(inc.shape) == 2
assert inc.shape[0] == 1
assert inc.shape[1] == X_upper.shape[0]
assert len(inc_val.shape) == 2
assert inc_val.shape[0] == 1
assert inc_val.shape[1] == 1
def __init__(self,
acquisition_func,
model,
maximize_func,
task,
save_dir=None,
initial_design=None,
initial_points=3,
incumbent_estimation=None,
num_save=1,
train_intervall=1,
n_restarts=1):
"""
Implementation of the standard Bayesian optimization loop that uses
an acquisition function and a model to optimize a given task.
This module keeps track of additional information such as runtime,
optimization overhead, evaluated points and saves the output
in a csv file.
Parameters
----------
acquisition_func: BaseAcquisitionFunctionObject
The acquisition function which will be maximized.
model: ModelObject
Model (i.e. GaussianProcess, RandomForest) that models our current
believe of the objective function.
task: TaskObject
Task object that contains the objective function and additional
meta information such as the lower and upper bound of the search
space.
save_dir: String
Output path
initial_design: function
Function that returns some points which will be evaluated before
the Bayesian optimization loop is started. This allows to
initialize the model.
initial_points: int
Defines the number of initial points that are evaluated before the
actual Bayesian optimization.
incumbent_estimation: IncumbentEstimationObject,
Object to estimate the incumbent based on the current model. The
incumbent is the current best guess of the global optimum and is
estimated in each iteration.
num_save: int
Defines after how many iteration the output is saved.
train_intervall: int
Specifies after how many iterations the model is retrained.
n_restarts: int
How often the incumbent estimation is repeated.
"""
super(BayesianOptimization,
self).__init__(acquisition_func, model, maximize_func, task,
save_dir)
self.start_time = time.time()
if initial_design == None:
self.initial_design = init_random_uniform
else:
self.initial_design = initial_design
self.X = None
self.Y = None
self.time_func_eval = None
self.time_overhead = None
self.train_intervall = train_intervall
self.num_save = num_save
self.time_start = None
self.model_untrained = True
if incumbent_estimation is None:
self.estimator = BestObservation(self.model, self.task.X_lower,
self.task.X_upper)
else:
self.estimator = incumbent_estimation
self.incumbent = None
self.incumbents = []
self.incumbent_values = []
self.n_restarts = n_restarts
self.init_points = initial_points
self.runtime = []
class RandomSearch(BaseSolver):
def __init__(self, task=None, save_dir=None, num_save=1, rng=None):
"""
Random Search [1] that simply evaluates random points. We do not have
any priors thus we sample points uniformly at random.
[1] J. Bergstra and Y. Bengio.
Random search for hyper-parameter optimization.
JMLR, 2012.
Parameters
----------
task: TaskObject
Task object that contains the objective function and additional
meta information such as the lower and upper bound of the search
space.
num_save: int
Defines after how many iteration the output is saved.
save_dir: String
Output path
rng: numpy.random.RandomState
"""
if rng is None:
self.rng = np.random.RandomState(np.random.randint(0, 10000))
else:
self.rng = rng
self.task = task
self.save_dir = save_dir
self.X = None
self.Y = None
self.estimator = BestObservation(self, self.task.X_lower,
self.task.X_upper)
self.time_func_eval = []
self.time_overhead = []
self.num_save = num_save
self.model_untrained = True
self.incumbent = None
self.incumbents = []
self.incumbent_values = []
self.runtime = []
if self.save_dir is not None:
self.create_save_dir()
def run(self, num_iterations=10):
"""
The main optimization loop
Parameters
----------
num_iterations: int
The number of iterations
Returns
-------
np.ndarray(1,D)
Incumbent
np.ndarray(1,1)
(Estimated) function value of the incumbent
"""
self.time_start = time.time()
for it in range(num_iterations):
logger.info("Start iteration %d ... ", it)
start_time = time.time()
# Choose next point to evaluate
new_x = self.choose_next()
time_overhead = time.time() - start_time
self.time_overhead.append(time_overhead)
logger.info("Optimization overhead was %f seconds" %
(self.time_overhead[-1]))
logger.info("Evaluate candidate %s" % (str(new_x)))
start_time = time.time()
new_y = self.task.evaluate(new_x)
time_func_eval = time.time() - start_time
self.time_func_eval.append(time_func_eval)
logger.info("Configuration achieved a performance of %f " %
(new_y[0, 0]))
logger.info("Evaluation of this configuration took %f seconds" %
(self.time_func_eval[-1]))
self.runtime.append(time.time() - self.time_start)
# Update the data
if self.X is None and self.Y is None:
self.X = new_x
self.Y = new_y
else:
self.X = np.append(self.X, new_x, axis=0)
self.Y = np.append(self.Y, new_y, axis=0)
# The incumbent is just the best observation we have seen so far
start_time_inc = time.time()
self.incumbent, self.incumbent_value = \
self.estimator.estimate_incumbent(None)
self.incumbents.append(self.incumbent)
self.incumbent_values.append(self.incumbent_value)
logger.info(
"New incumbent %s found in %f seconds with "
"estimated performance %f", str(self.incumbent),
time.time() - start_time_inc, self.incumbent_value)
if self.save_dir is not None and (it) % self.num_save == 0:
self.save_iteration(it)
logger.info("Return %s as incumbent with predicted performance %f" %
(str(self.incumbent), self.incumbent_value))
return self.incumbent, self.incumbent_value
def choose_next(self):
"""
Sample a new point uniformly at random.
Returns
-------
np.ndarray(1,D)
Suggested point to evaluate
"""
x = self.rng.uniform(self.task.X_lower, self.task.X_upper)
if type(x) == np.float:
return np.array([[x]])
else:
return x[np.newaxis, :]
class BayesianOptimization(BaseSolver):
def __init__(self,
acquisition_func,
model,
maximize_func,
task,
save_dir=None,
initial_design=None,
initial_points=3,
incumbent_estimation=None,
num_save=1,
train_intervall=1,
n_restarts=1):
"""
Implementation of the standard Bayesian optimization loop that uses
an acquisition function and a model to optimize a given task.
This module keeps track of additional information such as runtime,
optimization overhead, evaluated points and saves the output
in a csv file.
Parameters
----------
acquisition_func: AcquisitionFunctionObject
The acquisition function which will be maximized.
model: ModelObject
Model (i.e. GaussianProcess, RandomForest) that models our current
believe of the objective function.
task: TaskObject
Task object that contains the objective function and additional
meta information such as the lower and upper bound of the search
space.
save_dir: String
Output path
initial_design: function
Function that returns some points which will be evaluated before
the Bayesian optimization loop is started. This allows to
initialize the model.
initial_points: int
Defines the number of initial points that are evaluated before the
actual Bayesian optimization.
incumbent_estimation: IncumbentEstimationObject,
Object to estimate the incumbent based on the current model. The
incumbent is the current best guess of the global optimum and is
estimated in each iteration.
num_save: int
Defines after how many iteration the output is saved.
train_intervall: int
Specifies after how many iterations the model is retrained.
n_restarts: int
How often the incumbent estimation is repeated.
"""
super(BayesianOptimization, self).__init__(acquisition_func,
model,
maximize_func,
task,
save_dir)
self.start_time = time.time()
if initial_design == None:
self.initial_design = init_random_uniform
else:
self.initial_design = initial_design
self.X = None
self.Y = None
self.time_func_eval = None
self.time_overhead = None
self.train_intervall = train_intervall
self.num_save = num_save
self.model_untrained = True
if incumbent_estimation is None:
self.estimator = BestObservation(self.model,
self.task.X_lower,
self.task.X_upper)
else:
self.estimator = incumbent_estimation
self.incumbent = None
self.incumbents = []
self.incumbent_values = []
self.n_restarts = n_restarts
self.init_points = initial_points
self.runtime = []
def run(self, num_iterations=10, X=None, Y=None):
"""
The main Bayesian optimization loop
Parameters
----------
num_iterations: int
The number of iterations
X: np.ndarray(N,D)
Initial points that are already evaluated
Y: np.ndarray(N,1)
Function values of the already evaluated points
Returns
-------
np.ndarray(1,D)
Incumbent
np.ndarray(1,1)
(Estimated) function value of the incumbent
"""
# Save the time where we start the Bayesian optimization procedure
self.time_start = time.time()
if X is None and Y is None:
self.time_func_eval = np.zeros([self.init_points])
self.time_overhead = np.zeros([self.init_points])
self.X = np.zeros([self.init_points, self.task.n_dims])
self.Y = np.zeros([self.init_points, 1])
init = self.initial_design(self.task.X_lower,
self.task.X_upper,
N=self.init_points)
for i, x in enumerate(init):
x = x[np.newaxis, :]
logger.info("Evaluate: %s" % x)
start_time = time.time()
y = self.task.evaluate(x)
self.X[i] = x[0, :]
self.Y[i] = y[0, :]
self.time_func_eval[i] = time.time() - start_time
self.time_overhead[i] = 0.0
logger.info("Configuration achieved a performance "
"of %f in %f seconds" %
(self.Y[i], self.time_func_eval[i]))
# Use best point seen so far as incumbent
best_idx = np.argmin(self.Y)
self.incumbent = np.array([self.X[best_idx]])
self.incumbent_value = np.array([self.Y[best_idx]])
self.incumbents.append(self.incumbent)
self.incumbent_values.append(self.incumbent_value)
self.runtime.append(time.time() - self.start_time)
if self.save_dir is not None and (i) % self.num_save == 0:
self.save_iteration(i, hyperparameters=None,
acquisition_value=0)
else:
self.X = X
self.Y = Y
self.time_func_eval = np.zeros([self.X.shape[0]])
self.time_overhead = np.zeros([self.X.shape[0]])
# best = np.argmin(Y)
# incumbent = X[best]
# incumbent_value = Y[best]
# self.incumbents.append(incumbent[np.newaxis, :])
# self.incumbent_values.append(incumbent_value[np.newaxis, :])
# self.runtime.append(time.time() - self.start_time)
for it in range(self.init_points, num_iterations):
logger.info("Start iteration %d ... ", it)
start_time = time.time()
# Choose next point to evaluate
if it % self.train_intervall == 0:
do_optimize = True
else:
do_optimize = False
new_x = self.choose_next(self.X, self.Y, do_optimize)
# Estimate current incumbent
start_time_inc = time.time()
startpoints = init_random_uniform(self.task.X_lower,
self.task.X_upper,
self.n_restarts)
self.incumbent, self.incumbent_value = \
self.estimator.estimate_incumbent(startpoints)
self.incumbents.append(self.incumbent)
self.incumbent_values.append(self.incumbent_value)
logger.info("New incumbent %s found in %f seconds with "
"estimated performance %f",
str(self.incumbent), time.time() - start_time_inc,
self.incumbent_value)
time_overhead = time.time() - start_time
self.time_overhead = np.append(self.time_overhead,
np.array([time_overhead]))
logger.info("Optimization overhead was %f seconds" %
(self.time_overhead[-1]))
logger.info("Evaluate candidate %s" % (str(new_x)))
start_time = time.time()
new_y = self.task.evaluate(new_x)
time_func_eval = time.time() - start_time
self.time_func_eval = np.append(self.time_func_eval,
np.array([time_func_eval]))
logger.info("Configuration achieved a performance of %f " %
(new_y[0, 0]))
logger.info("Evaluation of this configuration took %f seconds" %
(self.time_func_eval[-1]))
# Update the data
self.X = np.append(self.X, new_x, axis=0)
self.Y = np.append(self.Y, new_y, axis=0)
self.runtime.append(time.time() - self.start_time)
if self.save_dir is not None and (it) % self.num_save == 0:
hypers = self.model.hypers
self.save_iteration(
it,
hyperparameters=hypers,
acquisition_value=self.acquisition_func(new_x))
# TODO: Retrain model and then return the incumbent
logger.info("Return %s as incumbent with predicted performance %f" %
(str(self.incumbent), self.incumbent_value))
return self.incumbent, self.incumbent_value
def choose_next(self, X=None, Y=None, do_optimize=True):
"""
Suggests a new point to evaluate.
Parameters
----------
num_iterations: int
The number of iterations
X: np.ndarray(N,D)
Initial points that are already evaluated
Y: np.ndarray(N,1)
Function values of the already evaluated points
do_optimize: bool
If true the hyperparameters of the model are
optimized before the acquisition function is
maximized.
Returns
-------
np.ndarray(1,D)
Suggested point
"""
if X is None and Y is None:
x = self.initial_design(self.task.X_lower,
self.task.X_upper,
N=1)
elif X.shape[0] == 1:
# We need at least 2 data points to train a GP
x = self.initial_design(self.task.X_lower,
self.task.X_upper,
N=1)
else:
try:
logger.info("Train model...")
t = time.time()
self.model.train(X, Y, do_optimize=do_optimize)
logger.info("Time to train the model: %f", (time.time() - t))
except:
logger.error("Model could not be trained", X, Y)
raise
self.model_untrained = False
self.acquisition_func.update(self.model)
logger.info("Maximize acquisition function...")
t = time.time()
x = self.maximize_func.maximize()
logger.info("Time to maximize the acquisition function: %f", \
(time.time() - t))
return x
class PI(BaseAcquisitionFunction):
def __init__(self, model, X_lower, X_upper, par=0.0, **kwargs):
r"""
Probability of Improvement solves the following equation
:math:`PI(X) := \mathbb{P}\left( f(\mathbf{X^+}) - f_{t+1}(\mathbf{X}) > \xi\right)`, where
:math:`f(X^+)` is the best input found so far.
Parameters
----------
model: Model object
A model that implements at least
- predict(X)
- getCurrentBestX().
If you want to calculate derivatives than it should also support
- predictive_gradients(X)
X_lower: np.ndarray (D)
Lower bounds of the input space
X_upper: np.ndarray (D)
Upper bounds of the input space
par: float
Controls the balance between exploration
and exploitation of the acquisition function. Default is 0.01
"""
super(PI, self).__init__(model, X_lower, X_upper)
self.par = par
self.rec = BestObservation(self.model, self.X_lower, self.X_upper)
def update(self, model):
"""
This method will be called if the model is updated.
Parameters
----------
model : Model object
Models the objective function.
"""
super(PI, self).update(model)
self.rec = BestObservation(self.model, self.X_lower, self.X_upper)
def compute(self, X, derivative=False, **kwargs):
"""
Computes the PI value and its derivatives.
Parameters
----------
X: np.ndarray(1, D), The input point where the acquisition function
should be evaluate. The dimensionality of X is (N, D), with N as
the number of points to evaluate at and D is the number of
dimensions of one X.
derivative: Boolean
If is set to true also the derivative of the acquisition
function at X is returned
Returns
-------
np.ndarray(1,1)
Probability of Improvement of X
np.ndarray(1,D)
Derivative of Probability of Improvement at X
(only if derivative=True)
"""
if X.shape[0] > 1:
logger.error("PI is only for single x inputs")
return
if np.any(X < self.X_lower) or np.any(X > self.X_upper):
if derivative:
f = 0
df = np.zeros((1, X.shape[1]))
return np.array([[f]]), np.array([df])
else:
return np.array([[0]])
m, v = self.model.predict(X)
_, eta = self.rec.estimate_incumbent(None)
s = np.sqrt(v)
z = (eta - m - self.par) / s
f = norm.cdf(z)
if derivative:
dmdx, ds2dx = self.model.predictive_gradients(X)
dmdx = dmdx[0]
ds2dx = ds2dx[0][:, None]
dsdx = ds2dx / (2 * s)
df = (-(-norm.pdf(z) / s) * (dmdx + dsdx * z)).T
return f, df
else:
return f
def __init__(self,
acquisition_func,
model,
maximize_func,
task,
save_dir=None,
initial_design=None,
initial_points=3,
incumbent_estimation=None,
num_save=1,
train_intervall=1,
n_restarts=1):
"""
Implementation of the standard Bayesian optimization loop that uses
an acquisition function and a model to optimize a given task.
This module keeps track of additional information such as runtime,
optimization overhead, evaluated points and saves the output
in a csv file.
Parameters
----------
acquisition_func: AcquisitionFunctionObject
The acquisition function which will be maximized.
model: ModelObject
Model (i.e. GaussianProcess, RandomForest) that models our current
believe of the objective function.
task: TaskObject
Task object that contains the objective function and additional
meta information such as the lower and upper bound of the search
space.
save_dir: String
Output path
initial_design: function
Function that returns some points which will be evaluated before
the Bayesian optimization loop is started. This allows to
initialize the model.
initial_points: int
Defines the number of initial points that are evaluated before the
actual Bayesian optimization.
incumbent_estimation: IncumbentEstimationObject,
Object to estimate the incumbent based on the current model. The
incumbent is the current best guess of the global optimum and is
estimated in each iteration.
num_save: int
Defines after how many iteration the output is saved.
train_intervall: int
Specifies after how many iterations the model is retrained.
n_restarts: int
How often the incumbent estimation is repeated.
"""
super(BayesianOptimization, self).__init__(acquisition_func,
model,
maximize_func,
task,
save_dir)
self.start_time = time.time()
if initial_design == None:
self.initial_design = init_random_uniform
else:
self.initial_design = initial_design
self.X = None
self.Y = None
self.time_func_eval = None
self.time_overhead = None
self.train_intervall = train_intervall
self.num_save = num_save
self.model_untrained = True
if incumbent_estimation is None:
self.estimator = BestObservation(self.model,
self.task.X_lower,
self.task.X_upper)
else:
self.estimator = incumbent_estimation
self.incumbent = None
self.incumbents = []
self.incumbent_values = []
self.n_restarts = n_restarts
self.init_points = initial_points
self.runtime = []
class LogEI(BaseAcquisitionFunction):
def __init__(self, model, X_lower, X_upper, par=0.0, **kwargs):
r"""
Computes for a given x the logarithm expected improvement as
acquisition value.
Parameters
----------
model: Model object
A model that implements at least
- predict(X)
If you want to calculate derivatives than it should also support
- predictive_gradients(X)
X_lower: np.ndarray (D)
Lower bounds of the input space
X_upper: np.ndarray (D)
Upper bounds of the input space
par: float
Controls the balance between exploration
and exploitation of the acquisition function. Default is 0.01
"""
super(LogEI, self).__init__(model, X_lower, X_upper)
self.par = par
self.rec = BestObservation(self.model, self.X_lower, self.X_upper)
def update(self, model):
"""
This method will be called if the model is updated.
Parameters
----------
model : Model object
Models the objective function.
"""
super(LogEI, self).update(model)
self.rec = BestObservation(self.model, self.X_lower, self.X_upper)
def compute(self, X, derivative=False, **kwargs):
"""
Computes the Log EI value and its derivatives.
Parameters
----------
X: np.ndarray(1, D), The input point where the acquisition function
should be evaluate. The dimensionality of X is (N, D), with N as
the number of points to evaluate at and D is the number of
dimensions of one X.
derivative: Boolean
If is set to true also the derivative of the acquisition
function at X is returned
Not implemented yet!
Returns
-------
np.ndarray(1,1)
Log Expected Improvement of X
np.ndarray(1,D)
Derivative of Log Expected Improvement at X
(only if derivative=True)
"""
if derivative:
logger.error("LogEI does not support derivative \
calculation until now")
return
if np.any(X < self.X_lower) or np.any(X > self.X_upper):
return np.array([[- np.finfo(np.float).max]])
m, v = self.model.predict(X)
_, eta = self.rec.estimate_incumbent(None)
f_min = eta - self.par
s = np.sqrt(v)
z = (f_min - m) / s
log_ei = np.zeros((m.size, 1))
for i in range(0, m.size):
mu, sigma = m[i], s[i]
# par_s = self.par * sigma
# Degenerate case 1: first term vanishes
if np.any(abs(f_min - mu)) == 0:
if sigma > 0:
log_ei[i] = np.log(sigma) + norm.logpdf(z[i])
else:
log_ei[i] = -np.Infinity
# Degenerate case 2: second term vanishes and first term
# has a special form.
elif sigma == 0:
if mu < np.any(f_min):
log_ei[i] = np.log(f_min - mu)
else:
log_ei[i] = -np.Infinity
# Normal case
else:
b = np.log(sigma) + norm.logpdf(z[i])
# log(y+z) is tricky, we distinguish two cases:
if np.any(f_min > mu):
# When y>0, z>0, we define a=ln(y), b=ln(z).
# Then y+z = exp[ max(a,b) + ln(1 + exp(-|b-a|)) ],
# and thus log(y+z) = max(a,b) + ln(1 + exp(-|b-a|))
a = np.log(f_min - mu) + norm.logcdf(z[i])
log_ei[i] = max(a, b) + np.log(1 + np.exp(-abs(b - a)))
else:
# When y<0, z>0, we define a=ln(-y), b=ln(z),
# and it has to be true that b >= a in
# order to satisfy y+z>=0.
# Then y+z = exp[ b + ln(exp(b-a) -1) ],
# and thus log(y+z) = a + ln(exp(b-a) -1)
a = np.log(mu - f_min) + norm.logcdf(z[i])
if a >= b:
# a>b can only happen due to numerical inaccuracies
# or approximation errors
log_ei[i] = -np.Infinity
else:
log_ei[i] = b + np.log(1 - np.exp(a - b))
return log_ei
def test(self):
X_lower = np.array([0])
X_upper = np.array([1])
X = init_random_uniform(X_lower, X_upper, 10)
Y = np.sin(X)
kernel = george.kernels.Matern52Kernel(np.ones([1]), ndim=1)
prior = TophatPrior(-2, 2)
model = GaussianProcess(kernel, prior=prior)
model.train(X, Y)
x_test = init_random_uniform(X_lower, X_upper, 3)
# Shape matching predict
m, v = model.predict(x_test)
assert len(m.shape) == 2
assert m.shape[0] == x_test.shape[0]
assert m.shape[1] == 1
assert len(v.shape) == 2
assert v.shape[0] == x_test.shape[0]
assert v.shape[1] == x_test.shape[0]
#TODO: check gradients
# Shape matching function sampling
x_ = np.linspace(X_lower, X_upper, 10)
x_ = x_[:, np.newaxis]
funcs = model.sample_functions(x_, n_funcs=2)
assert len(funcs.shape) == 2
assert funcs.shape[0] == 2
assert funcs.shape[1] == x_.shape[0]
# Shape matching predict variance
x_test1 = np.array([np.random.rand(1)])
x_test2 = np.random.rand(10)[:, np.newaxis]
var = model.predict_variance(x_test1, x_test2)
assert len(var.shape) == 2
assert var.shape[0] == x_test2.shape[0]
assert var.shape[1] == 1
# Check compatibility with all acquisition functions
acq_func = EI(model, X_upper=X_upper, X_lower=X_lower)
acq_func.update(model)
acq_func(x_test)
acq_func = PI(model, X_upper=X_upper, X_lower=X_lower)
acq_func.update(model)
acq_func(x_test)
acq_func = LCB(model, X_upper=X_upper, X_lower=X_lower)
acq_func.update(model)
acq_func(x_test)
acq_func = InformationGain(model, X_upper=X_upper, X_lower=X_lower)
acq_func.update(model)
acq_func(x_test)
# Check compatibility with all incumbent estimation methods
rec = BestObservation(model, X_lower, X_upper)
inc, inc_val = rec.estimate_incumbent(None)
assert len(inc.shape) == 2
assert inc.shape[0] == 1
assert inc.shape[1] == X_upper.shape[0]
assert len(inc_val.shape) == 2
assert inc_val.shape[0] == 1
assert inc_val.shape[1] == 1
rec = PosteriorMeanOptimization(model, X_lower, X_upper)
startpoints = init_random_uniform(X_lower, X_upper, 4)
inc, inc_val = rec.estimate_incumbent(startpoints)
assert len(inc.shape) == 2
assert inc.shape[0] == 1
assert inc.shape[1] == X_upper.shape[0]
assert len(inc_val.shape) == 2
assert inc_val.shape[0] == 1
assert inc_val.shape[1] == 1
rec = PosteriorMeanAndStdOptimization(model, X_lower, X_upper)
startpoints = init_random_uniform(X_lower, X_upper, 4)
inc, inc_val = rec.estimate_incumbent(startpoints)
assert len(inc.shape) == 2
assert inc.shape[0] == 1
assert inc.shape[1] == X_upper.shape[0]
assert len(inc_val.shape) == 2
assert inc_val.shape[0] == 1
assert inc_val.shape[1] == 1
def test(self):
X_lower = np.array([0])
X_upper = np.array([1])
X = init_random_uniform(X_lower, X_upper, 10)
Y = np.sin(X)
model = RandomForest(types=np.zeros([X_lower.shape[0]]))
model.train(X, Y)
x_test = init_random_uniform(X_lower, X_upper, 3)
# Shape matching predict
m, v = model.predict(x_test)
assert len(m.shape) == 2
assert m.shape[0] == x_test.shape[0]
assert m.shape[1] == 1
assert len(v.shape) == 2
assert v.shape[0] == x_test.shape[0]
assert v.shape[1] == 1
# Shape matching function sampling
x_ = np.linspace(X_lower, X_upper, 10)
x_ = x_[:, np.newaxis]
#funcs = model.sample_functions(x_, n_funcs=2)
#assert len(funcs.shape) == 2
#assert funcs.shape[0] == 2
#assert funcs.shape[1] == x_.shape[0]
# Check compatibility with all acquisition functions
acq_func = EI(model,
X_upper=X_upper,
X_lower=X_lower)
acq_func.update(model)
acq_func(x_test)
acq_func = PI(model,
X_upper=X_upper,
X_lower=X_lower)
acq_func.update(model)
acq_func(x_test)
acq_func = LCB(model,
X_upper=X_upper,
X_lower=X_lower)
acq_func.update(model)
acq_func(x_test)
# Check compatibility with all incumbent estimation methods
rec = BestObservation(model, X_lower, X_upper)
inc, inc_val = rec.estimate_incumbent(None)
assert len(inc.shape) == 2
assert inc.shape[0] == 1
assert inc.shape[1] == X_upper.shape[0]
assert len(inc_val.shape) == 2
assert inc_val.shape[0] == 1
assert inc_val.shape[1] == 1
rec = PosteriorMeanOptimization(model, X_lower, X_upper)
startpoints = init_random_uniform(X_lower, X_upper, 4)
inc, inc_val = rec.estimate_incumbent(startpoints)
assert len(inc.shape) == 2
assert inc.shape[0] == 1
assert inc.shape[1] == X_upper.shape[0]
assert len(inc_val.shape) == 2
assert inc_val.shape[0] == 1
assert inc_val.shape[1] == 1
rec = PosteriorMeanAndStdOptimization(model, X_lower, X_upper)
startpoints = init_random_uniform(X_lower, X_upper, 4)
inc, inc_val = rec.estimate_incumbent(startpoints)
assert len(inc.shape) == 2
assert inc.shape[0] == 1
assert inc.shape[1] == X_upper.shape[0]
assert len(inc_val.shape) == 2
assert inc_val.shape[0] == 1
assert inc_val.shape[1] == 1
class BayesianOptimization(BaseSolver):
def __init__(self,
acquisition_func,
model,
maximize_func,
task,
save_dir=None,
initial_design=None,
initial_points=3,
incumbent_estimation=None,
num_save=1,
train_intervall=1,
n_restarts=1):
"""
Implementation of the standard Bayesian optimization loop that uses
an acquisition function and a model to optimize a given task.
This module keeps track of additional information such as runtime,
optimization overhead, evaluated points and saves the output
in a csv file.
Parameters
----------
acquisition_func: BaseAcquisitionFunctionObject
The acquisition function which will be maximized.
model: ModelObject
Model (i.e. GaussianProcess, RandomForest) that models our current
believe of the objective function.
task: TaskObject
Task object that contains the objective function and additional
meta information such as the lower and upper bound of the search
space.
save_dir: String
Output path
initial_design: function
Function that returns some points which will be evaluated before
the Bayesian optimization loop is started. This allows to
initialize the model.
initial_points: int
Defines the number of initial points that are evaluated before the
actual Bayesian optimization.
incumbent_estimation: IncumbentEstimationObject,
Object to estimate the incumbent based on the current model. The
incumbent is the current best guess of the global optimum and is
estimated in each iteration.
num_save: int
Defines after how many iteration the output is saved.
train_intervall: int
Specifies after how many iterations the model is retrained.
n_restarts: int
How often the incumbent estimation is repeated.
"""
super(BayesianOptimization,
self).__init__(acquisition_func, model, maximize_func, task,
save_dir)
self.start_time = time.time()
if initial_design == None:
self.initial_design = init_random_uniform
else:
self.initial_design = initial_design
self.X = None
self.Y = None
self.time_func_eval = None
self.time_overhead = None
self.train_intervall = train_intervall
self.num_save = num_save
self.time_start = None
self.model_untrained = True
if incumbent_estimation is None:
self.estimator = BestObservation(self.model, self.task.X_lower,
self.task.X_upper)
else:
self.estimator = incumbent_estimation
self.incumbent = None
self.incumbents = []
self.incumbent_values = []
self.n_restarts = n_restarts
self.init_points = initial_points
self.runtime = []
def run(self, num_iterations=10, X=None, Y=None):
"""
The main Bayesian optimization loop
Parameters
----------
num_iterations: int
The number of iterations
X: np.ndarray(N,D)
Initial points that are already evaluated
Y: np.ndarray(N,1)
Function values of the already evaluated points
Returns
-------
np.ndarray(1,D)
Incumbent
np.ndarray(1,1)
(Estimated) function value of the incumbent
"""
# Save the time where we start the Bayesian optimization procedure
self.time_start = time.time()
if X is None and Y is None:
self.time_func_eval = np.zeros([self.init_points])
self.time_overhead = np.zeros([self.init_points])
self.X = np.zeros([self.init_points, self.task.n_dims])
self.Y = np.zeros([self.init_points, 1])
init = self.initial_design(self.task.X_lower,
self.task.X_upper,
N=self.init_points)
for i, x in enumerate(init):
x = x[np.newaxis, :]
logger.info("Evaluate: %s" % x)
start_time = time.time()
y = self.task.evaluate(x)
self.X[i] = x[0, :]
self.Y[i] = y[0, :]
self.time_func_eval[i] = time.time() - start_time
self.time_overhead[i] = 0.0
logger.info("Configuration achieved a performance "
"of %f in %f seconds" %
(self.Y[i], self.time_func_eval[i]))
# Use best point seen so far as incumbent
best_idx = np.argmin(self.Y)
self.incumbent = np.array([self.X[best_idx]])
self.incumbent_value = np.array([self.Y[best_idx]])
self.incumbents.append(self.incumbent)
self.incumbent_values.append(self.incumbent_value)
self.runtime.append(time.time() - self.start_time)
if self.save_dir is not None and (i) % self.num_save == 0:
self.save_iteration(i,
hyperparameters=None,
acquisition_value=0)
self.save_json(i)
#print self.X
#print self.Y
else:
self.X = X
self.Y = Y
self.time_func_eval = np.zeros([self.X.shape[0]])
self.time_overhead = np.zeros([self.X.shape[0]])
self.init_points = X.shape[0]
print X.shape, Y.shape
for i in range(Y.shape[0]):
print "Score:", Y[i][0], X[i]
# best = np.argmin(Y)
# incumbent = X[best]
# incumbent_value = Y[best]
# self.incumbents.append(incumbent[np.newaxis, :])
# self.incumbent_values.append(incumbent_value[np.newaxis, :])
# self.runtime.append(time.time() - self.start_time)
it = self.init_points
while it < num_iterations:
self.acquisition_func.update_time(it)
logger.info("Start iteration %d ... ", it)
start_time = time.time()
# Choose next point to evaluate
if it % self.train_intervall == 0:
do_optimize = True
else:
do_optimize = False
try:
new_x = self.choose_next(self.X, self.Y, do_optimize)
# Estimate current incumbent
start_time_inc = time.time()
startpoints = init_random_uniform(self.task.X_lower,
self.task.X_upper,
self.n_restarts)
self.incumbent, self.incumbent_value = \
self.estimator.estimate_incumbent(startpoints)
self.incumbents.append(self.incumbent)
self.incumbent_values.append(self.incumbent_value)
logger.info(
"New incumbent %s found in %f seconds with "
"estimated performance %f", str(self.incumbent),
time.time() - start_time_inc, self.incumbent_value)
time_overhead = time.time() - start_time
self.time_overhead = np.append(self.time_overhead,
np.array([time_overhead]))
logger.info("Optimization overhead was %f seconds" %
(self.time_overhead[-1]))
logger.info("Evaluate candidate %s" % (str(new_x)))
start_time = time.time()
new_y = self.task.evaluate(new_x)
time_func_eval = time.time() - start_time
self.time_func_eval = np.append(self.time_func_eval,
np.array([time_func_eval]))
logger.info("Configuration achieved a performance of %f " %
(new_y[0, 0]))
logger.info(
"Evaluation of this configuration took %f seconds" %
(self.time_func_eval[-1]))
# Update the data
self.X = np.append(self.X, new_x, axis=0)
self.Y = np.append(self.Y, new_y, axis=0)
self.runtime.append(time.time() - self.start_time)
if self.save_dir is not None and (it) % self.num_save == 0:
hypers = self.model.hypers
self.save_iteration(
it,
hyperparameters=hypers,
acquisition_value=self.acquisition_func(new_x))
self.save_json(it)
it += 1
except KeyboardInterrupt:
raise Exception
except:
print "experiment failed, retrying"
# TODO: Retrain model and then return the incumbent
logger.info("Return %s as incumbent with predicted performance %f" %
(str(self.incumbent), self.incumbent_value))
return self.incumbent, self.incumbent_value
def choose_next(self, X=None, Y=None, do_optimize=True):
"""
Suggests a new point to evaluate.
Parameters
----------
num_iterations: int
The number of iterations
X: np.ndarray(N,D)
Initial points that are already evaluated
Y: np.ndarray(N,1)
Function values of the already evaluated points
do_optimize: bool
If true the hyperparameters of the model are
optimized before the acquisition function is
maximized.
Returns
-------
np.ndarray(1,D)
Suggested point
"""
if X is None and Y is None:
x = self.initial_design(self.task.X_lower, self.task.X_upper, N=1)
elif X.shape[0] == 1:
# We need at least 2 data points to train a GP
x = self.initial_design(self.task.X_lower, self.task.X_upper, N=1)
else:
try:
logger.info("Train model...")
t = time.time()
self.model.train(X, Y, do_optimize=do_optimize)
logger.info("Time to train the model: %f", (time.time() - t))
except:
logger.error("Model could not be trained", X, Y)
raise
self.model_untrained = False
self.acquisition_func.update(self.model)
logger.info("Maximize acquisition function...")
t = time.time()
x = self.maximize_func.maximize()
logger.info("Time to maximize the acquisition function: %f", \
(time.time() - t))
return x
def get_json_data(self, it):
'''
Overrides method in BaseSolver.
'''
jsonData = dict()
jsonData = {
"optimization_overhead":
None if self.time_overhead is None else self.time_overhead[it],
"runtime":
None if self.time_start is None else time.time() - self.time_start,
"incumbent":
None if self.incumbent is None else self.incumbent.tolist(),
"incumbent_fval":
None
if self.incumbent_value is None else self.incumbent_value.tolist(),
"time_func_eval":
self.time_func_eval[it],
"iteration":
it
}
return jsonData
class LogEI(AcquisitionFunction):
def __init__(self, model, X_lower, X_upper, par=0.01, **kwargs):
r"""
Computes for a given x the logarithm expected improvement as
acquisition value.
Parameters
----------
model: Model object
A model that implements at least
- predict(X)
If you want to calculate derivatives than it should also support
- predictive_gradients(X)
X_lower: np.ndarray (D)
Lower bounds of the input space
X_upper: np.ndarray (D)
Upper bounds of the input space
par: float
Controls the balance between exploration
and exploitation of the acquisition function. Default is 0.01
"""
super(LogEI, self).__init__(model, X_lower, X_upper)
self.par = par
self.rec = BestObservation(self.model, self.X_lower, self.X_upper)
def update(self, model):
"""
This method will be called if the model is updated.
Parameters
----------
model : Model object
Models the objective function.
"""
super(LogEI, self).update(model)
self.rec = BestObservation(self.model, self.X_lower, self.X_upper)
def compute(self, X, derivative=False, **kwargs):
"""
Computes the Log EI value and its derivatives.
Parameters
----------
X: np.ndarray(1, D), The input point where the acquisition function
should be evaluate. The dimensionality of X is (N, D), with N as
the number of points to evaluate at and D is the number of
dimensions of one X.
derivative: Boolean
If is set to true also the derivative of the acquisition
function at X is returned
Not implemented yet!
Returns
-------
np.ndarray(1,1)
Log Expected Improvement of X
np.ndarray(1,D)
Derivative of Log Expected Improvement at X
(only if derivative=True)
"""
if derivative:
logger.error("LogEI does not support derivative \
calculation until now")
return
if np.any(X < self.X_lower) or np.any(X > self.X_upper):
return np.array([[-np.finfo(np.float).max]])
m, v = self.model.predict(X)
_, eta = self.rec.estimate_incumbent(None)
f_min = eta - self.par
s = np.sqrt(v)
z = (f_min - m) / s
log_ei = np.zeros((m.size, 1))
for i in range(0, m.size):
mu, sigma = m[i], s[i]
# par_s = self.par * sigma
# Degenerate case 1: first term vanishes
if np.any(abs(f_min - mu)) == 0:
if sigma > 0:
log_ei[i] = np.log(sigma) + norm.logpdf(z[i])
else:
log_ei[i] = -np.Infinity
# Degenerate case 2: second term vanishes and first term
# has a special form.
elif sigma == 0:
if mu < np.any(f_min):
log_ei[i] = np.log(f_min - mu)
else:
log_ei[i] = -np.Infinity
# Normal case
else:
b = np.log(sigma) + norm.logpdf(z[i])
# log(y+z) is tricky, we distinguish two cases:
if np.any(f_min > mu):
# When y>0, z>0, we define a=ln(y), b=ln(z).
# Then y+z = exp[ max(a,b) + ln(1 + exp(-|b-a|)) ],
# and thus log(y+z) = max(a,b) + ln(1 + exp(-|b-a|))
a = np.log(f_min - mu) + norm.logcdf(z[i])
log_ei[i] = max(a, b) + np.log(1 + np.exp(-abs(b - a)))
else:
# When y<0, z>0, we define a=ln(-y), b=ln(z),
# and it has to be true that b >= a in
# order to satisfy y+z>=0.
# Then y+z = exp[ b + ln(exp(b-a) -1) ],
# and thus log(y+z) = a + ln(exp(b-a) -1)
a = np.log(mu - f_min) + norm.logcdf(z[i])
if a >= b:
# a>b can only happen due to numerical inaccuracies
# or approximation errors
log_ei[i] = -np.Infinity
else:
log_ei[i] = b + np.log(1 - np.exp(a - b))
return log_ei
def test(self):
X_lower = np.array([0])
X_upper = np.array([1])
X = init_random_uniform(X_lower, X_upper, 10)
Y = np.sin(X)
kernel = george.kernels.Matern52Kernel(np.ones([1]),
ndim=1)
prior = TophatPrior(-2, 2)
model = GaussianProcess(kernel, prior=prior)
model.train(X, Y)
x_test = init_random_uniform(X_lower, X_upper, 3)
# Shape matching predict
m, v = model.predict(x_test)
assert len(m.shape) == 2
assert m.shape[0] == x_test.shape[0]
assert m.shape[1] == 1
assert len(v.shape) == 2
assert v.shape[0] == x_test.shape[0]
assert v.shape[1] == x_test.shape[0]
#TODO: check gradients
# Shape matching function sampling
x_ = np.linspace(X_lower, X_upper, 10)
x_ = x_[:, np.newaxis]
funcs = model.sample_functions(x_, n_funcs=2)
assert len(funcs.shape) == 2
assert funcs.shape[0] == 2
assert funcs.shape[1] == x_.shape[0]
# Shape matching predict variance
x_test1 = np.array([np.random.rand(1)])
x_test2 = np.random.rand(10)[:, np.newaxis]
var = model.predict_variance(x_test1, x_test2)
assert len(var.shape) == 2
assert var.shape[0] == x_test2.shape[0]
assert var.shape[1] == 1
# Check compatibility with all acquisition functions
acq_func = EI(model,
X_upper=X_upper,
X_lower=X_lower)
acq_func.update(model)
acq_func(x_test)
acq_func = PI(model,
X_upper=X_upper,
X_lower=X_lower)
acq_func.update(model)
acq_func(x_test)
acq_func = LCB(model,
X_upper=X_upper,
X_lower=X_lower)
acq_func.update(model)
acq_func(x_test)
acq_func = InformationGain(model,
X_upper=X_upper,
X_lower=X_lower)
acq_func.update(model)
acq_func(x_test)
# Check compatibility with all incumbent estimation methods
rec = BestObservation(model, X_lower, X_upper)
inc, inc_val = rec.estimate_incumbent(None)
assert len(inc.shape) == 2
assert inc.shape[0] == 1
assert inc.shape[1] == X_upper.shape[0]
assert len(inc_val.shape) == 2
assert inc_val.shape[0] == 1
assert inc_val.shape[1] == 1
rec = PosteriorMeanOptimization(model, X_lower, X_upper)
startpoints = init_random_uniform(X_lower, X_upper, 4)
inc, inc_val = rec.estimate_incumbent(startpoints)
assert len(inc.shape) == 2
assert inc.shape[0] == 1
assert inc.shape[1] == X_upper.shape[0]
assert len(inc_val.shape) == 2
assert inc_val.shape[0] == 1
assert inc_val.shape[1] == 1
rec = PosteriorMeanAndStdOptimization(model, X_lower, X_upper)
startpoints = init_random_uniform(X_lower, X_upper, 4)
inc, inc_val = rec.estimate_incumbent(startpoints)
assert len(inc.shape) == 2
assert inc.shape[0] == 1
assert inc.shape[1] == X_upper.shape[0]
assert len(inc_val.shape) == 2
assert inc_val.shape[0] == 1
assert inc_val.shape[1] == 1
class EI(BaseAcquisitionFunction):
def __init__(self, model, X_lower, X_upper, par=0.0, **kwargs):
r"""
Computes for a given x the expected improvement as
acquisition value.
:math:`EI(X) :=
\mathbb{E}\left[ \max\{0, f(\mathbf{X^+}) -
f_{t+1}(\mathbf{X}) - \xi\right] \} ]`, with
:math:`f(X^+)` as the incumbent.
Parameters
----------
model: Model object
A model that implements at least
- predict(X)
- getCurrentBestX().
If you want to calculate derivatives than it should also support
- predictive_gradients(X)
X_lower: np.ndarray (D)
Lower bounds of the input space
X_upper: np.ndarray (D)
Upper bounds of the input space
compute_incumbent: func
A python function that takes as input a model and returns
a np.array as incumbent
par: float
Controls the balance between exploration
and exploitation of the acquisition function. Default is 0.01
"""
super(EI, self).__init__(model, X_lower, X_upper)
self.par = par
self.rec = BestObservation(self.model, self.X_lower, self.X_upper)
def update(self, model):
"""
This method will be called if the model is updated.
Parameters
----------
model : Model object
Models the objective function.
"""
super(EI, self).update(model)
self.rec = BestObservation(self.model, self.X_lower, self.X_upper)
def compute(self, X, derivative=False, **kwargs):
"""
Computes the EI value and its derivatives.
Parameters
----------
X: np.ndarray(1, D), The input point where the acquisition function
should be evaluate. The dimensionality of X is (N, D), with N as
the number of points to evaluate at and D is the number of
dimensions of one X.
derivative: Boolean
If is set to true also the derivative of the acquisition
function at X is returned
Returns
-------
np.ndarray(1,1)
Expected Improvement of X
np.ndarray(1,D)
Derivative of Expected Improvement at X (only if derivative=True)
"""
if X.shape[0] > 1:
raise ValueError("EI is only for single test points")
if len(X.shape) == 1:
X = X[:, np.newaxis]
if np.any(X < self.X_lower) or np.any(X > self.X_upper):
if derivative:
f = 0
df = np.zeros((1, X.shape[1]))
return np.array([[f]]), np.array([df])
else:
return np.array([[0]])
m, v = self.model.predict(X)
# Use the best seen observation as incumbent
_, eta = self.rec.estimate_incumbent(None)
s = np.sqrt(v)
if (s == 0).any():
f = np.array([[0]])
df = np.zeros((1, X.shape[1]))
else:
z = (eta - m - self.par) / s
# f = (eta - m - self.par) * norm.cdf(z) + s * norm.pdf(z)
f = s * (z * norm.cdf(z) + norm.pdf(z))
if derivative:
dmdx, ds2dx = self.model.predictive_gradients(X)
dmdx = dmdx[0]
ds2dx = ds2dx[0][:, None]
dsdx = ds2dx / (2 * s)
df = (-dmdx * norm.cdf(z) + (dsdx * norm.pdf(z))).T
if (f < 0).any():
logger.error("Expected Improvement is smaller than 0!")
raise ValueError
if derivative:
return f, df
else:
return f