def test_pi(self):
pi = PI(self.model)
acq = MarginalizationGPMCMC(pi)
X_test = np.random.rand(5, 2)
a = acq.compute(X_test, derivative=False)
assert a.shape[0] == X_test.shape[0]
assert len(a.shape) == 1
def test_pi(self):
pi = PI(self.model)
acq = MarginalizationGPMCMC(pi)
X_test = np.random.rand(5, 2)
a = acq.compute(X_test, derivative=False)
assert a.shape[0] == X_test.shape[0]
assert len(a.shape) == 1
def suggest_configuration(self):
if self.X is None and self.y is None:
new_x = init_random_uniform(self.lower, self.upper,
n_points=1, rng=self.rng)[0, :]
elif self.X.shape[0] == 1:
# We need at least 2 data points to train a GP
new_x = init_random_uniform(self.lower, self.upper,
n_points=1, rng=self.rng)[0, :]
else:
cov_amp = 1
n_dims = self.lower.shape[0]
initial_ls = np.ones([n_dims])
exp_kernel = george.kernels.Matern52Kernel(initial_ls,
ndim=n_dims)
kernel = cov_amp * exp_kernel
prior = DefaultPrior(len(kernel) + 1)
model = GaussianProcessMCMC(kernel, prior=prior,
n_hypers=self.n_hypers,
chain_length=self.chain_length,
burnin_steps=self.burnin,
normalize_input=False,
normalize_output=True,
rng=self.rng,
lower=self.lower,
upper=self.upper)
a = LogEI(model)
acquisition_func = MarginalizationGPMCMC(a)
max_func = Direct(acquisition_func, self.lower, self.upper, verbose=False)
model.train(self.X, self.y)
acquisition_func.update(model)
new_x = max_func.maximize()
next_config = Configuration(self.config_space, vector=new_x)
# Transform to sacred configuration
result = configspace_config_to_sacred(next_config)
return result
def fabolas(objective_function, lower, upper, s_min, s_max,
n_init=40, num_iterations=100, subsets=[256, 128, 64], inc_estimation="mean",
burnin=100, chain_length=100, n_hypers=12, output_path=None, rng=None):
"""
Fast Bayesian Optimization of Machine Learning Hyperparameters
on Large Datasets
Fast Bayesian Optimization of Machine Learning Hyperparameters on Large Datasets
A. Klein and S. Falkner and S. Bartels and P. Hennig and F. Hutter
http://arxiv.org/abs/1605.07079
Parameters
----------
objective_function: function
Objective function that will be optimized
lower: np.array(D,)
Lower bound of the input space
upper: np.array(D,)
Upper bound of the input space
s_min: int
Minimum number of data points for the training data set
s_max: int
Maximum number of data points for the training data set
n_init: int
Number of initial design points
n_hypers: int
Number of hyperparameter samples for the GP
subsets: list
The ratio of the subsets size of the initial design.
For example if subsets=[256, 128, 64] then the each point of the
initial design is evaluated on s_max/256, s_max/128 and s_max/64
num_iterations: int
Number of iterations
chain_length : int
The length of the MCMC chain for each walker.
burnin : int
The number of burnin steps before the actual MCMC sampling starts.
output_path: string
Specifies the path where the intermediate output after each iteration will be saved.
If None no output will be saved to disk.
rng: numpy.random.RandomState
Random number generator
inc_estimation: string
Specifies how the incumbent is estimated:
"last_seen" : determined the incumbent as the configuration that achieved the highest observed value
"mean" : determined the incumbent as the configuration that achieved the highest predicted mean value
Returns
-------
dict
"""
assert n_init <= num_iterations, "Number of initial design point has to be <= than the number of iterations"
assert lower.shape[0] == upper.shape[0], "Dimension miss match between upper and lower bound"
time_start = time.time()
if rng is None:
rng = np.random.RandomState(np.random.randint(0, 10000))
n_dims = lower.shape[0]
# Bookkeeping
time_func_eval = []
time_overhead = []
incumbents = []
runtime = []
X = []
y = []
c = []
# Define model for the objective function
cov_amp = 1 # Covariance amplitude
kernel = cov_amp
# ARD Kernel for the configuration space
for d in range(n_dims):
kernel *= george.kernels.Matern52Kernel(np.ones([1]) * 0.01,
ndim=n_dims+1, dim=d)
# Kernel for the environmental variable
# We use (1-s)**2 as basis function for the Bayesian linear kernel
degree = 1
env_kernel = george.kernels.BayesianLinearRegressionKernel(n_dims+1,
dim=n_dims,
degree=degree)
env_kernel[:] = np.ones([degree + 1]) * 0.1
kernel *= env_kernel
# Take 3 times more samples than we have hyperparameters
if n_hypers < 2*len(kernel):
n_hypers = 3 * len(kernel)
if n_hypers % 2 == 1:
n_hypers += 1
prior = EnvPrior(len(kernel) + 1,
n_ls=n_dims,
n_lr=(degree + 1),
rng=rng)
quadratic_bf = lambda x: (1 - x) ** 2
linear_bf = lambda x: x
model_objective = FabolasGPMCMC(kernel,
prior=prior,
burnin_steps=burnin,
chain_length=chain_length,
n_hypers=n_hypers,
normalize_output=False,
basis_func=quadratic_bf,
lower=lower,
upper=upper,
rng=rng)
# Define model for the cost function
cost_cov_amp = 1
cost_kernel = cost_cov_amp
# ARD Kernel for the configuration space
for d in range(n_dims):
cost_kernel *= george.kernels.Matern52Kernel(np.ones([1]) * 0.01,
ndim=n_dims+1, dim=d)
cost_degree = 1
cost_env_kernel = george.kernels.BayesianLinearRegressionKernel(n_dims+1,
dim=n_dims,
degree=cost_degree)
cost_env_kernel[:] = np.ones([cost_degree + 1]) * 0.1
cost_kernel *= cost_env_kernel
cost_prior = EnvPrior(len(cost_kernel) + 1,
n_ls=n_dims,
n_lr=(cost_degree + 1),
rng=rng)
model_cost = FabolasGPMCMC(cost_kernel,
prior=cost_prior,
burnin_steps=burnin,
chain_length=chain_length,
n_hypers=n_hypers,
basis_func=linear_bf,
normalize_output=False,
lower=lower,
upper=upper,
rng=rng)
# Extend input space by task variable
extend_lower = np.append(lower, 0)
extend_upper = np.append(upper, 1)
is_env = np.zeros(extend_lower.shape[0])
is_env[-1] = 1
# Define acquisition function and maximizer
ig = InformationGainPerUnitCost(model_objective,
model_cost,
extend_lower,
extend_upper,
sampling_acquisition=EI,
is_env_variable=is_env,
n_representer=50)
acquisition_func = MarginalizationGPMCMC(ig)
# maximizer = Direct(acquisition_func, extend_lower, extend_upper, verbose=True, n_func_evals=200)
# maximizer = DifferentialEvolution(acquisition_func, extend_lower, extend_upper)
maximizer = RandomSampling(acquisition_func, extend_lower, extend_upper)
# Initial Design
logger.info("Initial Design")
x_init = init_latin_hypercube_sampling(lower, upper, n_init, rng)
for it in range(n_init):
for subset in subsets:
start_time_overhead = time.time()
# s = int(s_max / float(subsets[it % len(subsets)]))
s = int(s_max / float(subset))
x = x_init[it]
logger.info("Evaluate %s on subset size %d", str(x), s)
st = time.time()
func_val, cost = objective_function(x, s)
time_func_eval.append(time.time() - st)
logger.info("Configuration achieved a performance of %f with cost %f", func_val, cost)
logger.info("Evaluation of this configuration took %f seconds", time_func_eval[-1])
# Bookkeeping
config = np.append(x, transform(s, s_min, s_max))
X.append(config)
y.append(np.log(func_val)) # Model the target function on a logarithmic scale
c.append(np.log(cost)) # Model the cost on a logarithmic scale
# Estimate incumbent as the best observed value so far
best_idx = np.argmin(y)
#incumbents.append(X[best_idx][:-1]) # Incumbent is always on s=s_max
incumbents.append(X[best_idx])
time_overhead.append(time.time() - start_time_overhead)
runtime.append(time.time() - time_start)
if output_path is not None:
data = dict()
data["optimization_overhead"] = time_overhead[it]
data["runtime"] = runtime[it]
data["incumbent"] = incumbents[it].tolist()
data["time_func_eval"] = time_func_eval[it]
data["iteration"] = it
json.dump(data, open(os.path.join(output_path, "fabolas_iter_%d.json" % it), "w"))
X = np.array(X)
y = np.array(y)
c = np.array(c)
for it in range(n_init, num_iterations):
logger.info("Start iteration %d ... ", it)
start_time = time.time()
# Train models
model_objective.train(X, y, do_optimize=True)
model_cost.train(X, c, do_optimize=True)
if inc_estimation == "last_seen":
# Estimate incumbent as the best observed value so far
best_idx = np.argmin(y)
incumbent = X[best_idx]
#incumbent = X[best_idx][:-1]
#incumbent = np.append(incumbent, 1)
incumbent_value = y[best_idx]
else:
# Estimate incumbent by projecting all observed points to the task of interest and
# pick the point with the lowest mean prediction
incumbent, incumbent_value, idx = projected_incumbent_estimation(model_objective, X[:, :-1],
proj_value=1)
incumbent = np.append(incumbent, X[idx][-1])
#incumbents.append(incumbent[:-1])
logger.info("Current incumbent %s with estimated performance %f",
str(incumbent), np.exp(incumbent_value))
# Maximize acquisition function
acquisition_func.update(model_objective, model_cost)
new_x = maximizer.maximize()
s = retransform(new_x[-1], s_min, s_max) # Map s from log space to original linear space
time_overhead.append(time.time() - start_time)
logger.info("Optimization overhead was %f seconds", time_overhead[-1])
# Evaluate the chosen configuration
logger.info("Evaluate candidate %s on subset size %f", str(new_x[:-1]), s)
start_time = time.time()
new_y, new_c = objective_function(new_x[:-1], s)
time_func_eval.append(time.time() - start_time)
logger.info("Configuration achieved a performance of %f with cost %f", new_y, new_c)
logger.info("Evaluation of this configuration took %f seconds", time_func_eval[-1])
# Add new observation to the data
X = np.concatenate((X, new_x[None, :]), axis=0)
y = np.concatenate((y, np.log(np.array([new_y]))), axis=0) # Model the target function on a logarithmic scale
c = np.concatenate((c, np.log(np.array([new_c]))), axis=0) # Model the cost function on a logarithmic scale
runtime.append(time.time() - time_start)
if output_path is not None:
data = dict()
data["optimization_overhead"] = time_overhead[it]
data["runtime"] = runtime[it]
data["incumbent"] = incumbents[it].tolist()
data["time_func_eval"] = time_func_eval[it]
data["iteration"] = it
json.dump(data, open(os.path.join(output_path, "fabolas_iter_%d.json" % it), "w"))
# Estimate the final incumbent
model_objective.train(X, y, do_optimize=True)
incumbent, incumbent_value, idx = projected_incumbent_estimation(model_objective, X[:, :-1],
proj_value=1)
incumbent = np.append(incumbent, X[idx][-1])
logger.info("Final incumbent %s with estimated performance %f",
str(incumbent), incumbent_value)
results = dict()
results["x_opt"] = incumbent[:-1].tolist()
results["incumbents"] = [inc.tolist() for inc in incumbents]
results["runtime"] = runtime
results["overhead"] = time_overhead
results["time_func_eval"] = time_func_eval
results["X"] = [x.tolist() for x in X]
results["y"] = [yi.tolist() for yi in y]
results["c"] = [ci.tolist() for ci in c]
return results
def bayesian_optimization(objective_function,
lower,
upper,
num_iterations=30,
maximizer="random",
acquisition_func="log_ei",
model_type="gp_mcmc",
n_init=3,
rng=None,
output_path=None):
"""
General interface for Bayesian optimization for global black box
optimization problems.
Parameters
----------
objective_function: function
The objective function that is minimized. This function gets a numpy
array (D,) as input and returns the function value (scalar)
lower: np.ndarray (D,)
The lower bound of the search space
upper: np.ndarray (D,)
The upper bound of the search space
num_iterations: int
The number of iterations (initial design + BO)
maximizer: {"direct", "cmaes", "random", "scipy"}
The optimizer for the acquisition function. NOTE: "cmaes" only works in D > 1 dimensions
acquisition_func: {"ei", "log_ei", "lcb", "pi"}
The acquisition function
model_type: {"gp", "gp_mcmc", "rf"}
The model for the objective function.
n_init: int
Number of points for the initial design. Make sure that it
is <= num_iterations.
output_path: string
Specifies the path where the intermediate output after each iteration will be saved.
If None no output will be saved to disk.
rng: numpy.random.RandomState
Random number generator
Returns
-------
dict with all results
"""
assert upper.shape[0] == lower.shape[0], "Dimension miss match"
assert np.all(lower < upper), "Lower bound >= upper bound"
assert n_init <= num_iterations, "Number of initial design point has to be <= than the number of iterations"
if rng is None:
rng = np.random.RandomState(np.random.randint(0, 10000))
cov_amp = 2
n_dims = lower.shape[0]
initial_ls = np.ones([n_dims])
exp_kernel = george.kernels.Matern52Kernel(initial_ls, ndim=n_dims)
kernel = cov_amp * exp_kernel
prior = DefaultPrior(len(kernel) + 1)
n_hypers = 3 * len(kernel)
if n_hypers % 2 == 1:
n_hypers += 1
if model_type == "gp":
model = GaussianProcess(kernel,
prior=prior,
rng=rng,
normalize_output=False,
normalize_input=True,
lower=lower,
upper=upper)
elif model_type == "gp_mcmc":
model = GaussianProcessMCMC(kernel,
prior=prior,
n_hypers=n_hypers,
chain_length=200,
burnin_steps=100,
normalize_input=True,
normalize_output=True,
rng=rng,
lower=lower,
upper=upper)
elif model_type == "rf":
model = RandomForest(rng=rng)
else:
raise ValueError("'{}' is not a valid model".format(model_type))
if acquisition_func == "ei":
a = EI(model)
elif acquisition_func == "log_ei":
a = LogEI(model)
elif acquisition_func == "pi":
a = PI(model)
elif acquisition_func == "lcb":
a = LCB(model)
else:
raise ValueError("'{}' is not a valid acquisition function".format(
acquisition_func))
if model_type == "gp_mcmc":
acquisition_func = MarginalizationGPMCMC(a)
else:
acquisition_func = a
if maximizer == "cmaes":
max_func = CMAES(acquisition_func,
lower,
upper,
verbose=False,
rng=rng)
elif maximizer == "direct":
max_func = Direct(acquisition_func, lower, upper, verbose=True)
elif maximizer == "random":
max_func = RandomSampling(acquisition_func, lower, upper, rng=rng)
elif maximizer == "scipy":
max_func = SciPyOptimizer(acquisition_func, lower, upper, rng=rng)
else:
raise ValueError("'{}' is not a valid function to maximize the "
"acquisition function".format(maximizer))
bo = BayesianOptimization(objective_function,
lower,
upper,
acquisition_func,
model,
max_func,
initial_points=n_init,
rng=rng,
output_path=output_path)
x_best, f_min = bo.run(num_iterations)
results = dict()
results["x_opt"] = x_best
results["f_opt"] = f_min
results["incumbents"] = [inc for inc in bo.incumbents]
results["incumbent_values"] = [val for val in bo.incumbents_values]
results["runtime"] = bo.runtime
results["overhead"] = bo.time_overhead
results["X"] = [x.tolist() for x in bo.X]
results["y"] = [y for y in bo.y]
return results
def bayesian_optimization(objective_function,
lower,
upper,
num_iterations=30,
X_init=None,
Y_init=None,
maximizer="random",
acquisition_func="log_ei",
model_type="gp_mcmc",
n_init=3,
rng=None,
output_path=None,
kernel=None,
sampling_method="origin",
distance="cosine",
replacement=True,
pool=None,
best=None):
"""
General interface for Bayesian optimization for global black box
optimization problems.
Parameters
----------
objective_function: function
The objective function that is minimized. This function gets a numpy
array (D,) as input and returns the function value (scalar)
lower: np.ndarray (D,)
The lower bound of the search space
upper: np.ndarray (D,)
The upper bound of the search space
num_iterations: int
The number of iterations (initial design + BO)
X_init: np.ndarray(N,D)
Initial points to warmstart BO
Y_init: np.ndarray(N,1)
Function values of the already initial points
maximizer: {"random", "scipy", "differential_evolution"}
The optimizer for the acquisition function.
acquisition_func: {"ei", "log_ei", "lcb", "pi"}
The acquisition function
model_type: {"gp", "gp_mcmc", "rf", "bohamiann", "dngo"}
The model for the objective function.
n_init: int
Number of points for the initial design. Make sure that it
is <= num_iterations.
output_path: string
Specifies the path where the intermediate output after each iteration will be saved.
If None no output will be saved to disk.
rng: numpy.random.RandomState
Random number generator
kernel: george.kernels.ConstantKernel
{"constant", "polynomial", "linear", "dotproduct",
"exp", "expsquared", "matern32", "matern52", "rationalquadratic",
"cosine", "expsine2", "heuristic"}
Specify the kernel for Gaussian process.
sampling_method: {"origin", "approx", "exact"}
Specify the method to choose next sample to update model.
approx: choose the sample in the candidate pool that is closest (measured by distance
arg) to the one returned from maximizing acquisition function.
exact: evaluate all samples in the candidate pool on acquisition function
and choose the one with maximum output.
distance: {"cosine", "euclidean"}
The distance measurement for approximation sampling.
replacement: boolean
Whether to sample from pool with replacement.
pool: np.ndarray(N,D)
Candidate pool containing possible x
best: float
Stop training when the best point is sampled.
Returns
-------
dict with all results
"""
assert upper.shape[0] == lower.shape[0], "Dimension miss match"
assert np.all(lower < upper), "Lower bound >= upper bound"
assert n_init <= num_iterations, "Number of initial design point has to be <= than the number of iterations"
if rng is None:
rng = np.random.RandomState(np.random.randint(0, 10000))
cov_amp = 2
#n_dims = lower.shape[0]
#initial_ls = np.ones([n_dims])
# if kernel == "constant":
# exp_kernel = george.kernels.ConstantKernel(1, ndim=n_dims)
# elif kernel == "polynomial":
# exp_kernel = george.kernels.PolynomialKernel(log_sigma2=1, order=3, ndim=n_dims)
# elif kernel == "linear":
# exp_kernel = george.kernels.LinearKernel(log_gamma2=1, order=3, ndim=n_dims)
# elif kernel == "dotproduct":
# exp_kernel = george.kernels.DotProductKernel(ndim=n_dims)
# elif kernel == "exp":
# exp_kernel = george.kernels.ExpKernel(initial_ls, ndim=n_dims)
# elif kernel == "expsquared":
# exp_kernel = george.kernels.ExpSquaredKernel(initial_ls, ndim=n_dims)
# elif kernel == "matern32":
# exp_kernel = george.kernels.Matern32Kernel(initial_ls, ndim=n_dims)
# elif kernel == "matern52":
# exp_kernel = george.kernels.Matern52Kernel(initial_ls, ndim=n_dims)
# elif kernel == "rationalquadratic":
# exp_kernel = george.kernels.RationalQuadraticKernel(log_alpha=1, metric=initial_ls, ndim=n_dims)
# elif kernel == "cosine":
# exp_kernel = george.kernels.CosineKernel(4, ndim=n_dims)
# elif kernel == "expsine2":
# exp_kernel = george.kerngels.ExpSine2Kernel(1, 2, ndim=n_dims)
# elif kernel == "heuristic":
# exp_kernel = george.kernels.PythonKernel(heuristic_kernel_function, ndim=n_dims)
# else:
# raise ValueError("'{}' is not a valid kernel".format(kernel))
kernel = cov_amp * kernel
prior = DefaultPrior(len(kernel) + 1)
n_hypers = 3 * len(kernel)
if n_hypers % 2 == 1:
n_hypers += 1
if model_type == "gp":
model = GaussianProcess(kernel,
prior=prior,
rng=rng,
normalize_output=False,
normalize_input=True,
lower=lower,
upper=upper)
elif model_type == "gp_mcmc":
model = GaussianProcessMCMC(kernel,
prior=prior,
n_hypers=n_hypers,
chain_length=200,
burnin_steps=100,
normalize_input=True,
normalize_output=False,
rng=rng,
lower=lower,
upper=upper)
elif model_type == "rf":
model = RandomForest(rng=rng)
elif model_type == "bohamiann":
model = WrapperBohamiann()
elif model_type == "dngo":
model = DNGO()
else:
raise ValueError("'{}' is not a valid model".format(model_type))
if acquisition_func == "ei":
a = EI(model)
elif acquisition_func == "log_ei":
a = LogEI(model)
elif acquisition_func == "pi":
a = PI(model)
elif acquisition_func == "lcb":
a = LCB(model)
else:
raise ValueError("'{}' is not a valid acquisition function".format(
acquisition_func))
if model_type == "gp_mcmc":
acquisition_func = MarginalizationGPMCMC(a)
else:
acquisition_func = a
if maximizer == "random":
max_func = RandomSampling(acquisition_func, lower, upper, rng=rng)
elif maximizer == "scipy":
max_func = SciPyOptimizer(acquisition_func, lower, upper, rng=rng)
elif maximizer == "differential_evolution":
max_func = DifferentialEvolution(acquisition_func,
lower,
upper,
rng=rng)
else:
raise ValueError("'{}' is not a valid function to maximize the "
"acquisition function".format(maximizer))
if sampling_method == "exact":
max_func = ExactSampling(acquisition_func,
lower,
upper,
pool,
replacement,
rng=rng)
init_design = init_exact_random
elif sampling_method == "approx":
max_func = ApproxSampling(acquisition_func,
lower,
upper,
pool,
replacement,
distance,
rng=rng)
init_design = init_exact_random
else:
init_design = init_latin_hypercube_sampling
bo = BayesianOptimization(objective_function,
lower,
upper,
acquisition_func,
model,
max_func,
pool,
best,
sampling_method,
distance,
replacement,
initial_points=n_init,
rng=rng,
initial_design=init_design,
output_path=output_path)
x_best, f_min = bo.run(num_iterations, X=X_init, y=Y_init)
results = dict()
results["x_opt"] = x_best
results["f_opt"] = f_min
results["incumbents"] = [inc for inc in bo.incumbents]
results["incumbent_values"] = [val for val in bo.incumbents_values]
results["runtime"] = bo.runtime
results["overhead"] = bo.time_overhead
results["X"] = [x.tolist() for x in bo.X]
results["y"] = [y for y in bo.y]
return results
def build_acquisition_func(self):
"""Build a marginalized acquisition function with MCMC."""
return MarginalizationGPMCMC(super(RoBO_GP_MCMC, self).build_acquisition_func())
def entropy_search(objective_function,
lower,
upper,
num_iterations=30,
maximizer="random",
model="gp_mcmc",
n_init=3,
output_path=None,
rng=None):
"""
Entropy search for global black box optimization problems. This is a reimplemenation of the entropy search
algorithm by Henning and Schuler[1].
[1] Entropy search for information-efficient global optimization.
P. Hennig and C. Schuler.
JMLR, (1), 2012.
Parameters
----------
objective_function: function
The objective function that is minimized. This function gets a numpy array (D,) as input and returns
the function value (scalar)
lower: np.ndarray (D,)
The lower bound of the search space
upper: np.ndarray (D,)
The upper bound of the search space
num_iterations: int
The number of iterations (initial design + BO)
maximizer: {"random", "scipy", "differential_evolution"}
Defines how the acquisition function is maximized.
model: {"gp", "gp_mcmc"}
The model for the objective function.
n_init: int
Number of points for the initial design. Make sure that it is <= num_iterations.
output_path: string
Specifies the path where the intermediate output after each iteration will be saved.
If None no output will be saved to disk.
rng: numpy.random.RandomState
Random number generator
Returns
-------
dict with all results
"""
assert upper.shape[0] == lower.shape[0], "Dimension miss match"
assert np.all(lower < upper), "Lower bound >= upper bound"
assert n_init <= num_iterations, "Number of initial design point has to be <= than the number of iterations"
if rng is None:
rng = np.random.RandomState(np.random.randint(0, 10000))
cov_amp = 2
n_dims = lower.shape[0]
initial_ls = np.ones([n_dims])
exp_kernel = george.kernels.Matern52Kernel(initial_ls, ndim=n_dims)
kernel = cov_amp * exp_kernel
prior = DefaultPrior(len(kernel) + 1)
n_hypers = 3 * len(kernel)
if n_hypers % 2 == 1:
n_hypers += 1
if model == "gp":
gp = GaussianProcess(kernel,
prior=prior,
rng=rng,
normalize_output=False,
normalize_input=True,
lower=lower,
upper=upper)
elif model == "gp_mcmc":
gp = GaussianProcessMCMC(kernel,
prior=prior,
n_hypers=n_hypers,
chain_length=200,
burnin_steps=100,
normalize_input=True,
normalize_output=False,
rng=rng,
lower=lower,
upper=upper)
else:
print("ERROR: %s is not a valid model!" % model)
return
a = InformationGain(gp, lower=lower, upper=upper, sampling_acquisition=EI)
if model == "gp":
acquisition_func = a
elif model == "gp_mcmc":
acquisition_func = MarginalizationGPMCMC(a)
if maximizer == "random":
max_func = RandomSampling(acquisition_func, lower, upper, rng=rng)
elif maximizer == "scipy":
max_func = SciPyOptimizer(acquisition_func, lower, upper, rng=rng)
elif maximizer == "differential_evolution":
max_func = DifferentialEvolution(acquisition_func,
lower,
upper,
rng=rng)
else:
print(
"ERROR: %s is not a valid function to maximize the acquisition function!"
% maximizer)
return
bo = BayesianOptimization(objective_function,
lower,
upper,
acquisition_func,
gp,
max_func,
initial_design=init_latin_hypercube_sampling,
initial_points=n_init,
rng=rng,
output_path=output_path)
x_best, f_min = bo.run(num_iterations)
results = dict()
results["x_opt"] = x_best
results["f_opt"] = f_min
results["incumbents"] = [inc for inc in bo.incumbents]
results["incumbent_values"] = [val for val in bo.incumbents_values]
results["runtime"] = bo.runtime
results["overhead"] = bo.time_overhead
results["X"] = [x.tolist() for x in bo.X]
results["y"] = [y for y in bo.y]
return results
def mtbo(objective_function,
lower,
upper,
n_tasks=2,
n_init=2,
num_iterations=30,
burnin=100,
chain_length=200,
n_hypers=20,
output_path=None,
rng=None):
"""
Interface to MTBO[1] which uses an auxiliary cheaper task to speed up the optimization
of a more expensive but similar task.
[1] Multi-Task Bayesian Optimization
K. Swersky and J. Snoek and R. Adams
Proceedings of the 27th International Conference on Advances in Neural Information Processing Systems (NIPS'13)
Parameters
----------
objective_function: function
Objective function that will be optimized
lower: np.array(D,)
Lower bound of the input space
upper: np.array(D,)
Upper bound of the input space
n_tasks: int
Number of task
n_init: int
Number of initial design points
num_iterations: int
Number of iterations
chain_length : int
The length of the MCMC chain for each walker.
burnin : int
The number of burnin steps before the actual MCMC sampling starts.
output_path: string
Specifies the path where the intermediate output after each iteration will be saved.
If None no output will be saved to disk.
rng: numpy.random.RandomState
Random number generator
Returns
-------
dict with all results
"""
assert n_init <= num_iterations, "Number of initial design point has to be <= than the number of iterations"
assert lower.shape[0] == upper.shape[
0], "Dimension miss match between upper and lower bound"
time_start = time.time()
if rng is None:
rng = np.random.RandomState(np.random.randint(0, 10000))
n_dims = lower.shape[0]
# Bookkeeping
time_func_eval = []
time_overhead = []
incumbents = []
runtime = []
X = []
y = []
c = []
# Define model for the objective function
cov_amp = 1 # Covariance amplitude
kernel = cov_amp
# ARD Kernel for the configuration space
for d in range(n_dims):
kernel *= george.kernels.Matern52Kernel(np.ones([1]) * 0.01,
ndim=n_dims + 1,
dim=d)
task_kernel = george.kernels.TaskKernel(n_dims + 1, n_dims, n_tasks)
kernel *= task_kernel
# Take 3 times more samples than we have hyperparameters
if n_hypers < 2 * len(kernel):
n_hypers = 3 * len(kernel)
if n_hypers % 2 == 1:
n_hypers += 1
prior = MTBOPrior(len(kernel) + 1,
n_ls=n_dims,
n_kt=len(task_kernel),
rng=rng)
model_objective = MTBOGPMCMC(kernel,
prior=prior,
burnin_steps=burnin,
chain_length=chain_length,
n_hypers=n_hypers,
lower=lower,
upper=upper,
rng=rng)
# Define model for the cost function
cost_cov_amp = 1
cost_kernel = cost_cov_amp
# ARD Kernel for the configuration space
for d in range(n_dims):
cost_kernel *= george.kernels.Matern52Kernel(np.ones([1]) * 0.01,
ndim=n_dims + 1,
dim=d)
cost_task_kernel = george.kernels.TaskKernel(n_dims + 1, n_dims, n_tasks)
cost_kernel *= cost_task_kernel
cost_prior = MTBOPrior(len(cost_kernel) + 1,
n_ls=n_dims,
n_kt=len(task_kernel),
rng=rng)
model_cost = MTBOGPMCMC(cost_kernel,
prior=cost_prior,
burnin_steps=burnin,
chain_length=chain_length,
n_hypers=n_hypers,
lower=lower,
upper=upper,
rng=rng)
# Extend input space by task variable
extend_lower = np.append(lower, 0)
extend_upper = np.append(upper, n_tasks - 1)
is_env = np.zeros(extend_lower.shape[0])
is_env[-1] = 1
# Define acquisition function and maximizer
ig = InformationGainPerUnitCost(model_objective,
model_cost,
extend_lower,
extend_upper,
sampling_acquisition=EI,
is_env_variable=is_env,
n_representer=50)
acquisition_func = MarginalizationGPMCMC(ig)
maximizer = Direct(acquisition_func,
extend_lower,
extend_upper,
n_func_evals=200)
# Initial Design
logger.info("Initial Design")
for it in range(n_init):
start_time_overhead = time.time()
# Draw random configuration and evaluate it just on the auxiliary task
task = 0
x = init_random_uniform(lower, upper, 1, rng)[0]
logger.info("Evaluate candidate %s", str(x))
st = time.time()
func_val, cost = objective_function(x, task)
time_func_eval.append(time.time() - st)
logger.info("Configuration achieved a performance of %f with cost %f",
func_val, cost)
logger.info("Evaluation of this configuration took %f seconds",
time_func_eval[-1])
# Bookkeeping
config = np.append(x, task)
X.append(config)
y.append(np.log(
func_val)) # Model the target function on a logarithmic scale
c.append(np.log(cost)) # Model the cost on a logarithmic scale
# Estimate incumbent as the best observed value so far
best_idx = np.argmin(y)
incumbents.append(X[best_idx][:-1])
time_overhead.append(time.time() - start_time_overhead)
runtime.append(time.time() - time_start)
if output_path is not None:
data = dict()
data["optimization_overhead"] = time_overhead[it]
data["runtime"] = runtime[it]
data["incumbent"] = incumbents[it].tolist()
data["time_func_eval"] = time_func_eval[it]
data["iteration"] = it
json.dump(
data,
open(os.path.join(output_path, "mtbo_iter_%d.json" % it), "w"))
X = np.array(X)
y = np.array(y)
c = np.array(c)
for it in range(n_init, num_iterations):
logger.info("Start iteration %d ... ", it)
start_time = time.time()
# Train models
model_objective.train(X, y, do_optimize=True)
model_cost.train(X, c, do_optimize=True)
# Estimate incumbent as the best observed value so far
best_idx = np.argmin(y)
incumbent = X[best_idx][:-1]
incumbent = np.append(incumbent, 1)
incumbent_value = y[best_idx]
incumbents.append(incumbent[:-1])
logger.info("Current incumbent %s with estimated performance %f",
str(incumbent), incumbent_value)
# Maximize acquisition function
acquisition_func.update(model_objective, model_cost)
new_x = maximizer.maximize()
new_x[-1] = np.rint(
new_x[-1]) # Map float value to discrete task variable
time_overhead.append(time.time() - start_time)
logger.info("Optimization overhead was %f seconds", time_overhead[-1])
# Evaluate the chosen configuration
logger.info("Evaluate candidate %s", str(new_x))
start_time = time.time()
new_y, new_c = objective_function(new_x[:-1], new_x[-1])
time_func_eval.append(time.time() - start_time)
logger.info("Configuration achieved a performance of %f with cost %f",
new_y, new_c)
logger.info("Evaluation of this configuration took %f seconds",
time_func_eval[-1])
# Add new observation to the data
X = np.concatenate((X, new_x[None, :]), axis=0)
y = np.concatenate(
(y, np.log(np.array([new_y]))),
axis=0) # Model the target function on a logarithmic scale
c = np.concatenate(
(c, np.log(np.array([new_c]))),
axis=0) # Model the cost function on a logarithmic scale
runtime.append(time.time() - time_start)
if output_path is not None:
data = dict()
data["optimization_overhead"] = time_overhead[it]
data["runtime"] = runtime[it]
data["incumbent"] = incumbents[it].tolist()
data["time_func_eval"] = time_func_eval[it]
data["iteration"] = it
json.dump(
data,
open(os.path.join(output_path, "mtbo_iter_%d.json" % it), "w"))
# Estimate the final incumbent
model_objective.train(X, y)
incumbent, incumbent_value = projected_incumbent_estimation(
model_objective, X[:, :-1], proj_value=n_tasks - 1)
logger.info("Final incumbent %s with estimated performance %f",
str(incumbent), incumbent_value)
results = dict()
results["x_opt"] = incumbent[:-1].tolist()
results["incumbents"] = [inc.tolist() for inc in incumbents]
results["runtime"] = runtime
results["overhead"] = time_overhead
results["time_func_eval"] = time_func_eval
results["X"] = X
results["y"] = y
results["c"] = c
return results
def bayesian_optimization(objective_function,
lower,
upper,
num_iterations=30,
maximizer="direct",
acquisition_func="log_ei",
model="gp_mcmc",
n_init=3,
rng=None):
"""
General interface for Bayesian optimization for global black box optimization problems.
Parameters
----------
objective_function: function
The objective function that is minimized. This function gets a numpy array (D,) as input and returns
the function value (scalar)
lower: np.ndarray (D,)
The lower bound of the search space
upper: np.ndarray (D,)
The upper bound of the search space
num_iterations: int
The number of iterations (initial design + BO)
maximizer: {"direct", "cmaes"}
Defines how the acquisition function is maximized. NOTE: "cmaes" only works in D > 1 dimensions
acquisition_func: {"ei", "log_ei", "lcb", "pi"}
The acquisition function
model: {"gp", "gp_mcmc"}
The model for the objective function.
n_init: int
Number of points for the initial design. Make sure that it is <= num_iterations.
rng: numpy.random.RandomState
Random number generator
Returns
-------
dict with all results
"""
assert upper.shape[0] == lower.shape[0]
assert n_init <= num_iterations, "Number of initial design point has to be <= than the number of iterations"
if rng is None:
rng = np.random.RandomState(np.random.randint(0, 10000))
cov_amp = 2
n_dims = lower.shape[0]
initial_ls = np.ones([n_dims])
exp_kernel = george.kernels.Matern52Kernel(initial_ls, ndim=n_dims)
kernel = cov_amp * exp_kernel
prior = DefaultPrior(len(kernel) + 1)
n_hypers = 3 * len(kernel)
if n_hypers % 2 == 1:
n_hypers += 1
if model == "gp":
gp = GaussianProcess(kernel,
prior=prior,
rng=rng,
normalize_output=True,
normalize_input=True,
lower=lower,
upper=upper)
elif model == "gp_mcmc":
gp = GaussianProcessMCMC(kernel,
prior=prior,
n_hypers=n_hypers,
chain_length=200,
burnin_steps=100,
normalize_input=True,
normalize_output=True,
rng=rng,
lower=lower,
upper=upper)
else:
print("ERROR: %s is not a valid model!" % model)
return
if acquisition_func == "ei":
a = EI(gp)
elif acquisition_func == "log_ei":
a = LogEI(gp)
elif acquisition_func == "pi":
a = PI(gp)
elif acquisition_func == "lcb":
a = LCB(gp)
else:
print("ERROR: %s is not a valid acquisition function!" %
acquisition_func)
return
if model == "gp":
acquisition_func = a
elif model == "gp_mcmc":
acquisition_func = MarginalizationGPMCMC(a)
if maximizer == "cmaes":
max_func = CMAES(acquisition_func,
lower,
upper,
verbose=False,
rng=rng)
elif maximizer == "direct":
max_func = Direct(acquisition_func, lower, upper, verbose=False)
else:
print(
"ERROR: %s is not a valid function to maximize the acquisition function!"
% maximizer)
return
bo = BayesianOptimization(objective_function,
lower,
upper,
acquisition_func,
gp,
max_func,
initial_points=n_init,
rng=rng)
x_best, f_min = bo.run(num_iterations)
results = dict()
results["x_opt"] = x_best
results["f_opt"] = f_min
results["incumbents"] = [inc for inc in bo.incumbents]
results["incumbent_values"] = [val for val in bo.incumbents_values]
results["runtime"] = bo.runtime
results["overhead"] = bo.time_overhead
return results
def build_optimizer(model,
maximizer="random",
acquisition_func="log_ei",
maximizer_seed=1):
"""
General interface for Bayesian optimization for global black box
optimization problems.
Parameters
----------
maximizer: {"random", "scipy", "differential_evolution"}
The optimizer for the acquisition function.
acquisition_func: {"ei", "log_ei", "lcb", "pi"}
The acquisition function
maximizer_seed: int
Seed for random number generator of the acquisition function maximizer
Returns
-------
Optimizer
"""
if acquisition_func == "ei":
a = EI(model)
elif acquisition_func == "log_ei":
a = LogEI(model)
elif acquisition_func == "pi":
a = PI(model)
elif acquisition_func == "lcb":
a = LCB(model)
else:
raise ValueError("'{}' is not a valid acquisition function".format(
acquisition_func))
if isinstance(model, GaussianProcessMCMC):
acquisition_func = MarginalizationGPMCMC(a)
else:
acquisition_func = a
maximizer_rng = numpy.random.RandomState(maximizer_seed)
if maximizer == "random":
max_func = RandomSampling(acquisition_func,
model.lower,
model.upper,
rng=maximizer_rng)
elif maximizer == "scipy":
max_func = SciPyOptimizer(acquisition_func,
model.lower,
model.upper,
rng=maximizer_rng)
elif maximizer == "differential_evolution":
max_func = DifferentialEvolution(acquisition_func,
model.lower,
model.upper,
rng=maximizer_rng)
else:
raise ValueError("'{}' is not a valid function to maximize the "
"acquisition function".format(maximizer))
# NOTE: Internal RNG of BO won't be used.
# NOTE: Nb of initial points won't be used within BO, but rather outside
bo = BayesianOptimization(lambda: None,
model.lower,
model.upper,
acquisition_func,
model,
max_func,
initial_points=None,
rng=None,
initial_design=init_latin_hypercube_sampling,
output_path=None)
return bo
def fabolas(objective_function, lower, upper, s_min, s_max,
n_init=40, num_iterations=100, subsets=[256, 128, 64], inc_estimation="mean",
burnin=100, chain_length=100, n_hypers=12, output_path=None, rng=None):
"""
Fast Bayesian Optimization of Machine Learning Hyperparameters
on Large Datasets
Fast Bayesian Optimization of Machine Learning Hyperparameters on Large Datasets
A. Klein and S. Falkner and S. Bartels and P. Hennig and F. Hutter
http://arxiv.org/abs/1605.07079
Parameters
----------
objective_function: function
Objective function that will be optimized
lower: np.array(D,)
Lower bound of the input space
upper: np.array(D,)
Upper bound of the input space
s_min: int
Minimum number of data points for the training data set
s_max: int
Maximum number of data points for the training data set
n_init: int
Number of initial design points
n_hypers: int
Number of hyperparameter samples for the GP
subsets: list
The ratio of the subsets size of the initial design.
For example if subsets=[256, 128, 64] then the first random point from the
initial design is evaluated on s_max/256 of the data, the second point on
s_max/256 of the data and so on.
num_iterations: int
Number of iterations
chain_length : int
The length of the MCMC chain for each walker.
burnin : int
The number of burnin steps before the actual MCMC sampling starts.
output_path: string
Specifies the path where the intermediate output after each iteration will be saved.
If None no output will be saved to disk.
rng: numpy.random.RandomState
Random number generator
Returns
-------
dict
"""
assert n_init <= num_iterations, "Number of initial design point has to be <= than the number of iterations"
assert lower.shape[0] == upper.shape[0], "Dimension miss match between upper and lower bound"
time_start = time.time()
if rng is None:
rng = np.random.RandomState(np.random.randint(0, 10000))
n_dims = lower.shape[0]
# Bookkeeping
time_func_eval = []
time_overhead = []
incumbents = []
runtime = []
X = []
y = []
c = []
# Define model for the objective function
cov_amp = 1 # Covariance amplitude
kernel = cov_amp
# ARD Kernel for the configuration space
for d in range(n_dims):
kernel *= george.kernels.Matern52Kernel(np.ones([1]) * 0.01,
ndim=n_dims+1, dim=d)
# Kernel for the environmental variable
# We use (1-s)**2 as basis function for the Bayesian linear kernel
degree = 1
env_kernel = george.kernels.BayesianLinearRegressionKernel(n_dims+1,
dim=n_dims,
degree=degree)
env_kernel[:] = np.ones([degree + 1]) * 0.1
kernel *= env_kernel
# Take 3 times more samples than we have hyperparameters
if n_hypers < 2*len(kernel):
n_hypers = 3 * len(kernel)
if n_hypers % 2 == 1:
n_hypers += 1
prior = EnvPrior(len(kernel) + 1,
n_ls=n_dims,
n_lr=(degree + 1),
rng=rng)
quadratic_bf = lambda x: (1 - x) ** 2
linear_bf = lambda x: x
model_objective = FabolasGPMCMC(kernel,
prior=prior,
burnin_steps=burnin,
chain_length=chain_length,
n_hypers=n_hypers,
normalize_output=False,
basis_func=quadratic_bf,
lower=lower,
upper=upper,
rng=rng)
# Define model for the cost function
cost_cov_amp = 1
cost_kernel = cost_cov_amp
# ARD Kernel for the configuration space
for d in range(n_dims):
cost_kernel *= george.kernels.Matern52Kernel(np.ones([1]) * 0.01,
ndim=n_dims+1, dim=d)
cost_degree = 1
cost_env_kernel = george.kernels.BayesianLinearRegressionKernel(n_dims+1,
dim=n_dims,
degree=cost_degree)
cost_env_kernel[:] = np.ones([cost_degree + 1]) * 0.1
cost_kernel *= cost_env_kernel
cost_prior = EnvPrior(len(cost_kernel) + 1,
n_ls=n_dims,
n_lr=(cost_degree + 1),
rng=rng)
model_cost = FabolasGPMCMC(cost_kernel,
prior=cost_prior,
burnin_steps=burnin,
chain_length=chain_length,
n_hypers=n_hypers,
basis_func=linear_bf,
normalize_output=False,
lower=lower,
upper=upper,
rng=rng)
# Extend input space by task variable
extend_lower = np.append(lower, 0)
extend_upper = np.append(upper, 1)
is_env = np.zeros(extend_lower.shape[0])
is_env[-1] = 1
# Define acquisition function and maximizer
ig = InformationGainPerUnitCost(model_objective,
model_cost,
extend_lower,
extend_upper,
sampling_acquisition=EI,
is_env_variable=is_env,
n_representer=50)
acquisition_func = MarginalizationGPMCMC(ig)
maximizer = Direct(acquisition_func, extend_lower, extend_upper, verbose=True, n_func_evals=200)
# Initial Design
logger.info("Initial Design")
for it in range(n_init):
start_time_overhead = time.time()
# Draw random configuration
s = int(s_max / float(subsets[it]))
x = init_random_uniform(lower, upper, 1, rng)[0]
logger.info("Evaluate %s on subset size %d", str(x), s)
st = time.time()
func_val, cost = objective_function(x, s)
time_func_eval.append(time.time() - st)
logger.info("Configuration achieved a performance of %f with cost %f", func_val, cost)
logger.info("Evaluation of this configuration took %f seconds", time_func_eval[-1])
# Bookkeeping
config = np.append(x, transform(s, s_min, s_max))
X.append(config)
y.append(np.log(func_val)) # Model the target function on a logarithmic scale
c.append(np.log(cost)) # Model the cost on a logarithmic scale
# Estimate incumbent as the best observed value so far
best_idx = np.argmin(y)
incumbents.append(X[best_idx][:-1]) # Incumbent is always on s=s_max
time_overhead.append(time.time() - start_time_overhead)
runtime.append(time.time() - time_start)
if output_path is not None:
data = dict()
data["optimization_overhead"] = time_overhead[it]
data["runtime"] = runtime[it]
data["incumbent"] = incumbents[it].tolist()
data["time_func_eval"] = time_func_eval[it]
data["iteration"] = it
json.dump(data, open(os.path.join(output_path, "fabolas_iter_%d.json" % it), "w"))
X = np.array(X)
y = np.array(y)
c = np.array(c)
for it in range(n_init, num_iterations):
logger.info("Start iteration %d ... ", it)
start_time = time.time()
# Train models
model_objective.train(X, y, do_optimize=True)
model_cost.train(X, c, do_optimize=True)
if inc_estimation == "last_seen":
# Estimate incumbent as the best observed value so far
best_idx = np.argmin(y)
incumbent = X[best_idx][:-1]
incumbent = np.append(incumbent, 1)
incumbent_value = y[best_idx]
else:
# Estimate incumbent by projecting all observed points to the task of interest and
# pick the point with the lowest mean prediction
incumbent, incumbent_value = projected_incumbent_estimation(model_objective, X[:, :-1],
proj_value=1)
incumbents.append(incumbent[:-1])
logger.info("Current incumbent %s with estimated performance %f",
str(incumbent), np.exp(incumbent_value))
# Maximize acquisition function
acquisition_func.update(model_objective, model_cost)
new_x = maximizer.maximize()
s = retransform(new_x[-1], s_min, s_max) # Map s from log space to original linear space
time_overhead.append(time.time() - start_time)
logger.info("Optimization overhead was %f seconds", time_overhead[-1])
# Evaluate the chosen configuration
logger.info("Evaluate candidate %s on subset size %f", str(new_x[:-1]), s)
start_time = time.time()
new_y, new_c = objective_function(new_x[:-1], s)
time_func_eval.append(time.time() - start_time)
logger.info("Configuration achieved a performance of %f with cost %f", new_y, new_c)
logger.info("Evaluation of this configuration took %f seconds", time_func_eval[-1])
# Add new observation to the data
X = np.concatenate((X, new_x[None, :]), axis=0)
y = np.concatenate((y, np.log(np.array([new_y]))), axis=0) # Model the target function on a logarithmic scale
c = np.concatenate((c, np.log(np.array([new_c]))), axis=0) # Model the cost function on a logarithmic scale
runtime.append(time.time() - time_start)
if output_path is not None:
data = dict()
data["optimization_overhead"] = time_overhead[it]
data["runtime"] = runtime[it]
data["incumbent"] = incumbents[it].tolist()
data["time_func_eval"] = time_func_eval[it]
data["iteration"] = it
json.dump(data, open(os.path.join(output_path, "fabolas_iter_%d.json" % it), "w"))
# Estimate the final incumbent
model_objective.train(X, y, do_optimize=True)
incumbent, incumbent_value = projected_incumbent_estimation(model_objective, X[:, :-1],
proj_value=1)
logger.info("Final incumbent %s with estimated performance %f",
str(incumbent), incumbent_value)
results = dict()
results["x_opt"] = incumbent[:-1].tolist()
results["incumbents"] = [inc.tolist() for inc in incumbents]
results["runtime"] = runtime
results["overhead"] = time_overhead
results["time_func_eval"] = time_func_eval
results["X"] = X
results["y"] = y
results["c"] = c
return results
