botorch.utils¶
botorch.utils.constraints¶
Helpers for handling outcome constraints.

botorch.utils.constraints.
get_outcome_constraint_transforms
(outcome_constraints)[source]¶ Create outcome constraint callables from outcome constraint tensors.
 Parameters
outcome_constraints (
Optional
[Tuple
[Tensor
,Tensor
]]) – A tuple of (A, b). For k outcome constraints and o outputs at f(x)`, A is k x o and b is k x 1 such that A f(x) <= b. Return type
Optional
[List
[Callable
[[Tensor
],Tensor
]]] Returns
A list of callables, each mapping a Tensor of size b x q x o to a tensor of size b x q, where o is the number of outputs of the model. Negative values imply feasibility. The callables support broadcasting (e.g. for calling on a tensor of shape mc_samples x b x q x o).
Example
>>> # constrain `f(x)[0] <= 0` >>> A = torch.tensor([[1., 0.]]) >>> b = torch.tensor([[0.]]) >>> outcome_constraints = get_outcome_constraint_transforms((A, b))
botorch.utils.objective¶
Helpers for handling objectives.

botorch.utils.objective.
apply_constraints
(obj, constraints, samples, infeasible_cost, eta=0.001)[source]¶ Apply constraints using an infeasible_cost M for negative objectives.
This allows feasibilityweighting an objective for the case where the objective can be negative by usingthe following strategy: (1) add M to make obj nonnegative (2) apply constraints using the sigmoid approximation (3) shift by M
 Parameters
obj (
Tensor
) – A n_samples x b x q Tensor of objective values.constraints (
List
[Callable
[[Tensor
],Tensor
]]) – A list of callables, each mapping a Tensor of size b x q x o to a Tensor of size b x q, where negative values imply feasibility. This callable must support broadcasting. Only relevant for multi output models (o > 1).samples (
Tensor
) – A b x q x o Tensor of samples drawn from the posterior.infeasible_cost (
float
) – The infeasible value.eta (
float
) – The temperature parameter of the sigmoid function.
 Return type
Tensor
 Returns
A n_samples x b x qdim tensor of feasibilityweighted objectives.

botorch.utils.objective.
apply_constraints_nonnegative_soft
(obj, constraints, samples, eta)[source]¶ Applies constraints to a nonnegative objective.
This function uses a sigmoid approximation to an indicator function for each constraint.
 Parameters
obj (
Tensor
) – A n_samples x b x q Tensor of objective values.constraints (
List
[Callable
[[Tensor
],Tensor
]]) – A list of callables, each mapping a Tensor of size b x q x o to a Tensor of size b x q, where negative values imply feasibility. This callable must support broadcasting. Only relevant for multi output models (o > 1).samples (
Tensor
) – A b x q x o Tensor of samples drawn from the posterior.eta (
float
) – The temperature parameter for the sigmoid function.
 Return type
Tensor
 Returns
A n_samples x b x qdim tensor of feasibilityweighted objectives.

botorch.utils.objective.
get_objective_weights_transform
(weights)[source]¶ Create a linear objective callable from a set of weights.
Create a callable mapping a Tensor of size b x q x o to a Tensor of size b x q, where o is the number of outputs of the model using scalarization via the objective weights. This callable supports broadcasting (e.g. for calling on a tensor of shape mc_samples x b x q x o). For o = 1, the objective weight is used to determine the optimization direction.
 Parameters
weights (
Optional
[Tensor
]) – a 1dimensional Tensor containing a weight for each task. If not provided, the identity mapping is used. Return type
Callable
[[Tensor
],Tensor
] Returns
Transform function using the objective weights.
Example
>>> weights = torch.tensor([0.75, 0.25]) >>> transform = get_objective_weights_transform(weights)

botorch.utils.objective.
soft_eval_constraint
(lhs, eta=0.001)[source]¶ Elementwise evaluation of a constraint in a ‘soft’ fashion
value(x) = 1 / (1 + exp(x / eta))
 Parameters
lhs (
Tensor
) – The left hand side of the constraint lhs <= 0.eta (
float
) – The temperature parameter of the softmax function. As eta grows larger, this approximates the Heaviside step function.
 Return type
Tensor
 Returns
Elementwise ‘soft’ feasibility indicator of the same shape as lhs. For each element x, value(x) > 0 as x becomes positive, and value(x) > 1 as x becomes negative.
botorch.utils.sampling¶
Utilities for MC and qMC sampling.

botorch.utils.sampling.
construct_base_samples
(batch_shape, output_shape, sample_shape, qmc=True, seed=None, device=None, dtype=None)[source]¶ Construct base samples from a multivariate standard normal N(0, I_qo).
 Parameters
batch_shape (
Size
) – The batch shape of the base samples to generate. Typically, this is used with each dimension of size 1, so as to eliminate sampling variance across batches.output_shape (
Size
) – The output shape (q x o) of the base samples to generate.sample_shape (
Size
) – The sample shape of the samples to draw.qmc (
bool
) – If True, use quasiMC sampling (instead of iid draws).seed (
Optional
[int
]) – If provided, use as a seed for the RNG.
 Return type
Tensor
 Returns
A sample_shape x batch_shape x output_shape dimensional tensor of base samples, drawn from a N(0, I_qo) distribution (using QMC if qmc=True). Here output_shape = q x o.
Example
>>> batch_shape = torch.Size([2]) >>> output_shape = torch.Size([3]) >>> sample_shape = torch.Size([10]) >>> samples = construct_base_samples(batch_shape, output_shape, sample_shape)

botorch.utils.sampling.
construct_base_samples_from_posterior
(posterior, sample_shape, qmc=True, collapse_batch_dims=True, seed=None)[source]¶ Construct a tensor of normally distributed base samples.
 Parameters
posterior (
Posterior
) – A Posterior object.sample_shape (
Size
) – The sample shape of the samples to draw.qmc (
bool
) – If True, use quasiMC sampling (instead of iid draws).seed (
Optional
[int
]) – If provided, use as a seed for the RNG.
 Return type
Tensor
 Returns
A num_samples x 1 x q x o dimensional Tensor of base samples, drawn from a N(0, I_qo) distribution (using QMC if qmc=True). Here q and o are the same as in the posterior’s event_shape b x q x o. Importantly, this only obtain a single tbatch of samples, so as to not introduce any sampling variance across tbatches.
Example
>>> sample_shape = torch.Size([10]) >>> samples = construct_base_samples_from_posterior(posterior, sample_shape)

botorch.utils.sampling.
draw_sobol_normal_samples
(d, n, device=None, dtype=None, seed=None)[source]¶ Draw qMC samples from a multivariate standard normal N(0, I_d)
A primary usecase for this functionality is to compute an QMC average of f(X) over X where each element of X is drawn N(0, 1).
 Parameters
d (
int
) – The dimension of the normal distributionn (
int
) – The number of samples to returndevice (
Optional
[device
]) – The torch devicedtype (
Optional
[dtype
]) – The torch dtypeseed (
Optional
[int
]) – The seed used for initializing Owen scrambling. If None (default), use a random seed.
 Return type
Tensor
 Returns
A tensor of qMC standard normal samples with dimension n x d with device and dtype specified by the input.
Example
>>> samples = draw_sobol_normal_samples(2, 10)

botorch.utils.sampling.
draw_sobol_samples
(bounds, n, q, seed=None)[source]¶ Draw qMC samples from the box defined by bounds.
 Parameters
bounds (
Tensor
) – A 2 x d dimensional tensor specifying box constraints on a ddimensional space, where bounds[0, :] and bounds[1, :] correspond to lower and upper bounds, respectively.n (
int
) – The number of (qbatch) samples.q (
int
) – The size of each qbatch.seed (
Optional
[int
]) – The seed used for initializing Owen scrambling. If None (default), use a random seed.
 Return type
Tensor
 Returns
A n x q x ddim tensor of qMC samples from the box defined by bounds.
Example
>>> bounds = torch.stack([torch.zeros(3), torch.ones(3)]) >>> samples = draw_sobol_samples(bounds, 10, 2)a

botorch.utils.sampling.
manual_seed
(seed=None)[source]¶ Contextmanager for manual setting the torch.random seed.
 Parameters
seed (
Optional
[int
]) – The seed to set the random number generator to. Return type
Generator
[None
,None
,None
] Returns
Generator
Example
>>> with manual_seed(1234): >>> X = torch.rand(3)
botorch.utils.transforms¶
Some basic data transformation helpers.

botorch.utils.transforms.
convert_to_target_pre_hook
(module, *args)[source]¶ Prehook for automatically calling .to(X) on module prior to forward

botorch.utils.transforms.
match_batch_shape
(X, Y)[source]¶ Matches the batch dimension of a tensor to that of another tensor.
 Parameters
X (
Tensor
) – A batch_shape_X x q x d tensor, whose batch dimensions that correspond to batch dimensions of Y are to be matched to those (if compatible).Y (
Tensor
) – A batch_shape_Y x q’ x d tensor.
 Return type
Tensor
 Returns
A batch_shape_Y x q x d tensor containing the data of X expanded to the batch dimensions of Y (if compatible). For instance, if X is b’’ x b’ x q x d and Y is b x q x d, then the returned tensor is b’’ x b x q x d.
Example
>>> X = torch.rand(2, 1, 5, 3) >>> Y = torch.rand(2, 6, 4, 3) >>> X_matched = match_batch_shape(X, Y) >>> X_matched.shape torch.Size([2, 6, 5, 3])

botorch.utils.transforms.
normalize
(X, bounds)[source]¶ Minmax normalize X w.r.t. the provided bounds.
 Parameters
X (
Tensor
) – … x d tensor of databounds (
Tensor
) – 2 x d tensor of lower and upper bounds for each of the X’s d columns.
 Return type
Tensor
 Returns
 A … x ddim tensor of normalized data, given by
(X  bounds[0]) / (bounds[1]  bounds[0]). If all elements of X are contained within bounds, the normalized values will be contained within [0, 1]^d.
Example
>>> X = torch.rand(4, 3) >>> bounds = torch.stack([torch.zeros(3), 0.5 * torch.ones(3)]) >>> X_normalized = normalize(X, bounds)

botorch.utils.transforms.
squeeze_last_dim
(Y)[source]¶ Squeeze the last dimension of a Tensor.
 Parameters
Y (
Tensor
) – A … x ddim Tensor. Return type
Tensor
 Returns
The input tensor with last dimension squeezed.
Example
>>> Y = torch.rand(4, 3) >>> Y_squeezed = squeeze_last_dim(Y)

botorch.utils.transforms.
standardize
(X)[source]¶ Standardize a tensor by dim=0.
 Parameters
X (
Tensor
) – A n or n x ddim tensor Return type
Tensor
 Returns
The standardized X.
Example
>>> X = torch.rand(4, 3) >>> X_standardized = standardize(X)

botorch.utils.transforms.
t_batch_mode_transform
(expected_q=None)[source]¶ Factory for decorators taking a tbatched X tensor.
This method creates decorators for instance methods to transform an input tensor X to tbatch mode (i.e. with at least 3 dimensions). This assumes the tensor has a qbatch dimension. The decorator also checks the qbatch size if expected_q is provided.
 Parameters
expected_q (
Optional
[int
]) – The expected qbatch size of X. If specified, this will raise an AssertitionError if X’s qbatch size does not equal expected_q. Return type
Callable
[[Callable
[[Any
,Tensor
],Any
]],Callable
[[Any
,Tensor
],Any
]] Returns
The decorated instance method.
Example
>>> class ExampleClass: >>> @t_batch_mode_transform(expected_q=1) >>> def single_q_method(self, X): >>> ... >>> >>> @t_batch_mode_transform() >>> def arbitrary_q_method(self, X): >>> ...

botorch.utils.transforms.
unnormalize
(X, bounds)[source]¶ Unnormalizes X w.r.t. the provided bounds.
 Parameters
X (
Tensor
) – … x d tensor of databounds (
Tensor
) – 2 x d tensor of lower and upper bounds for each of the X’s d columns.
 Return type
Tensor
 Returns
 A … x ddim tensor of unnormalized data, given by
X * (bounds[1]  bounds[0]) + bounds[0]. If all elements of X are contained in [0, 1]^d, the unnormalized values will be contained within bounds.
Example
>>> X_normalized = torch.rand(4, 3) >>> bounds = torch.stack([torch.zeros(3), 0.5 * torch.ones(3)]) >>> X = unnormalize(X_normalized, bounds)