def get_gpr_model(X, y, model=None):
"""
Fit a gpr model to the data or update the model to new data
Params ::
X: (sx1) Tensor: Covariates
y: (sx1) Tensor: Observations
model: PyTorch SingleTaskGP model: If model is passed, X and y are used to
update it. If None then model is trained on X and y. Default is None
Return ::
model: PyTorch SingleTaskGP model: Trained or updated model.
Returned in train mode
mll: PyTorch MarginalLogLikelihood object: Returned in train mode
"""
if model is None:
# set up model
model = SingleTaskGP(X, y)
else:
# update model with new observations
model = model.condition_on_observations(X, y)
mll = ExactMarginalLogLikelihood(model.likelihood, model).to(X)
# begin training
model.train()
mll.train()
fit_gpytorch_model(mll)
return model, mll
def get_gpr_model(X, y, model=None):
"""Fit a gpr model to the data or update the model to new data.
Parameters
----------
X: (sx1) Tensor
Covariates
y: (sx1) Tensor
Observations
model: PyTorch SingleTaskGP model
If model is passed, X and y are used to update it.
If None then model is trained on X and y. Default is None.
Returns
-------
model: PyTorch SingleTaskGP model
Trained or updated model. Returned in train mode.
mll: PyTorch MarginalLogLikelihood object
This is the loss used to train hyperparameters. Returned in train mode.
"""
if model is None:
# set up model
print('X', X.shape)
print('y', y.shape)
model = SingleTaskGP(X, y)
else:
# update model with new observations
model = model.condition_on_observations(X, y)
mll = ExactMarginalLogLikelihood(model.likelihood, model).to(X)
# begin training
model.train()
mll.train()
fit_gpytorch_model(mll)
return model, mll
class ParametricArm:
"""
the class of an Arm
"""
def __init__(
self,
function: SyntheticTestFunction,
num_init_samples: int = 10,
retrain_gp: bool = False,
num_restarts: int = 10,
raw_samples: int = 1000,
):
"""
Initialize the Arm
:param function: the function of the arm to sample from
:param num_init_samples: number of samples to initialize with
:param retrain_gp: retrain the model after each sample if True
:param num_restarts: number of random restarts for acquisition function optimization
:param raw_samples: number of raw samples for acquisition function optimization
"""
self.function = function
self.dim = function.dim
self.bounds = Tensor(function._bounds).t()
self.scale = self.bounds[1] - self.bounds[0]
self.l_bounds = self.bounds[0]
self.num_restarts = num_restarts
self.raw_samples = raw_samples
self._initialize_model(num_init_samples)
self._update_current_best()
self._maximize_kg()
self.retrain_gp = retrain_gp
self.num_samples = num_init_samples
def _maximize_kg(self) -> None:
"""
maximizes the KG acquisition function and stores the resulting value and
the candidate
"""
acq_func = qKnowledgeGradient(
model=self.model, current_value=self.current_best_val
)
# acq_func = qExpectedImprovement(model=self.model, best_f=self.current_best_val)
# acq_func = ExpectedImprovement(model=self.model, best_f=self.current_best_val)
self.next_candidate, self.kg_value = optimize_acqf(
acq_func,
Tensor([[0], [1]]).repeat(1, self.dim),
q=1,
num_restarts=self.num_restarts,
raw_samples=self.raw_samples,
)
def _update_current_best(self) -> None:
"""
Updates the current best solution and corresponding value
"""
pm = PosteriorMean(self.model)
self.current_best_sol, self.current_best_val = optimize_acqf(
pm,
Tensor([[0], [1]]).repeat(1, self.dim),
q=1,
num_restarts=self.num_restarts,
raw_samples=self.raw_samples,
)
def _function_call(self, X: Tensor) -> Tensor:
"""
Scales the solutions to the function domain and returns the function value.
:param X: Solutions from the relative scale of [0, 1]
:return: function value
"""
shape = list(X.size())
shape[-1] = 1
X = X * self.scale.repeat(shape) + self.l_bounds.repeat(shape)
# TODO: adjust for minimization
return -self.function(X).unsqueeze(1)
def _initialize_model(self, num_init_samples: int) -> None:
"""
initialize the GP model with num_init_samples of initial samples
"""
self.train_X = torch.rand((num_init_samples, self.dim))
self.train_Y = self._function_call(self.train_X)
self.model = SingleTaskGP(
self.train_X, self.train_Y, outcome_transform=Standardize(m=1)
)
mll = ExactMarginalLogLikelihood(self.model.likelihood, self.model)
fit_gpytorch_model(mll)
def _update_model(self, new_sample: Tensor, new_observation: Tensor) -> None:
"""
Update the GP model with the new observation(s)
:param new_sample: sampled point
:param new_observation: observed function value
"""
self.train_X = torch.cat((self.train_X, new_sample), 0)
self.train_Y = torch.cat((self.train_Y, new_observation), 0)
self.model = self.model.condition_on_observations(new_sample, new_observation)
if self.retrain_gp:
mll = ExactMarginalLogLikelihood(self.model.likelihood, self.model)
fit_gpytorch_model(mll)
def sample_next(self):
"""
sample the next point, i.e. the point that maximizes KG
update the model and retrain if needed
update the relevant values
"""
Y = self._function_call(self.next_candidate)
self._update_model(self.next_candidate, Y)
self._update_current_best()
self._maximize_kg()
# model.likelihood.noise_covar.register_constraint("raw_noise", GreaterThan(1e1))
for it in range(25):
# Acquisition function...
candidate_x, acq_value = optimize_acqf(
UpperConfidenceBound(model, beta=0.1),
# ExpectedImprovement(model, best_f=torch.max(train_y))
bounds=torch.Tensor([[-1], [1]]),
q=1,
num_restarts=5,
raw_samples=20,
)
candidate_y = obj_noisy(candidate_x)
train_x = torch.cat([train_x, candidate_x])
train_y = torch.cat([train_y, candidate_y])
model = model.condition_on_observations(X=candidate_x, Y=candidate_y)
# Train GP...
mll = ExactMarginalLogLikelihood(model.likelihood, model)
fit_gpytorch_model(mll)
# Plotting...
model.eval()
fig, ax = plt.subplots(1, 1, figsize=(6, 4))
plt.title(f"Bayesian Opt. without derivatives, Iteration {it}")
test_x = torch.linspace(-1, 1, steps=100)
with torch.no_grad():
posterior = model.posterior(test_x)
# these are 2 std devs from mean