#!/usr/bin/env python3
# Copyright (c) Meta Platforms, Inc. and affiliates.
#
# This source code is licensed under the MIT license found in the
# LICENSE file in the root directory of this source tree.
r"""
Utility functions for constrained optimization.
"""
from __future__ import annotations
from functools import partial
from typing import Callable, Optional, Union
import numpy as np
import torch
from botorch.exceptions.errors import CandidateGenerationError, UnsupportedError
from scipy.optimize import Bounds
from torch import Tensor
ScipyConstraintDict = dict[
str, Union[str, Callable[[np.ndarray], float], Callable[[np.ndarray], np.ndarray]]
]
NLC_TOL = -1e-6
[docs]
def make_scipy_bounds(
X: Tensor,
lower_bounds: Optional[Union[float, Tensor]] = None,
upper_bounds: Optional[Union[float, Tensor]] = None,
) -> Optional[Bounds]:
r"""Creates a scipy Bounds object for optimziation
Args:
X: `... x d` tensor
lower_bounds: Lower bounds on each column (last dimension) of `X`. If
this is a single float, then all columns have the same bound.
upper_bounds: Lower bounds on each column (last dimension) of `X`. If
this is a single float, then all columns have the same bound.
Returns:
A scipy `Bounds` object if either lower_bounds or upper_bounds is not
None, and None otherwise.
Example:
>>> X = torch.rand(5, 2)
>>> scipy_bounds = make_scipy_bounds(X, 0.1, 0.8)
"""
if lower_bounds is None and upper_bounds is None:
return None
def _expand(bounds: Union[float, Tensor], X: Tensor, lower: bool) -> Tensor:
if bounds is None:
ebounds = torch.full_like(X, float("-inf" if lower else "inf"))
else:
if not torch.is_tensor(bounds):
bounds = torch.tensor(bounds)
ebounds = bounds.expand_as(X)
return _arrayify(ebounds).flatten()
lb = _expand(bounds=lower_bounds, X=X, lower=True)
ub = _expand(bounds=upper_bounds, X=X, lower=False)
return Bounds(lb=lb, ub=ub, keep_feasible=True)
[docs]
def make_scipy_linear_constraints(
shapeX: torch.Size,
inequality_constraints: Optional[list[tuple[Tensor, Tensor, float]]] = None,
equality_constraints: Optional[list[tuple[Tensor, Tensor, float]]] = None,
) -> list[ScipyConstraintDict]:
r"""Generate scipy constraints from torch representation.
Args:
shapeX: The shape of the torch.Tensor to optimize over (i.e. `(b) x q x d`)
inequality constraints: A list of tuples (indices, coefficients, rhs),
with each tuple encoding an inequality constraint of the form
`\sum_i (X[indices[i]] * coefficients[i]) >= rhs`, where
`indices` is a single-dimensional index tensor (long dtype) containing
indices into the last dimension of `X`, `coefficients` is a
single-dimensional tensor of coefficients of the same length, and
rhs is a scalar.
equality constraints: A list of tuples (indices, coefficients, rhs),
with each tuple encoding an inequality constraint of the form
`\sum_i (X[indices[i]] * coefficients[i]) == rhs` (with `indices`
and `coefficients` of the same form as in `inequality_constraints`).
Returns:
A list of dictionaries containing callables for constraint function
values and Jacobians and a string indicating the associated constraint
type ("eq", "ineq"), as expected by `scipy.minimize`.
This function assumes that constraints are the same for each input batch,
and broadcasts the constraints accordingly to the input batch shape. This
function does support constraints across elements of a q-batch if the
indices are a 2-d Tensor.
Example:
The following will enforce that `x[1] + 0.5 x[3] >= -0.1` for each `x`
in both elements of the q-batch, and each of the 3 t-batches:
>>> constraints = make_scipy_linear_constraints(
>>> torch.Size([3, 2, 4]),
>>> [(torch.tensor([1, 3]), torch.tensor([1.0, 0.5]), -0.1)],
>>> )
The following will enforce that `x[0, 1] + 0.5 x[1, 3] >= -0.1` where
x[0, :] is the first element of the q-batch and x[1, :] is the second
element of the q-batch, for each of the 3 t-batches:
>>> constraints = make_scipy_linear_constraints(
>>> torch.size([3, 2, 4])
>>> [(torch.tensor([[0, 1], [1, 3]), torch.tensor([1.0, 0.5]), -0.1)],
>>> )
"""
constraints = []
if inequality_constraints is not None:
for indcs, coeffs, rhs in inequality_constraints:
constraints += _make_linear_constraints(
indices=indcs, coefficients=coeffs, rhs=rhs, shapeX=shapeX, eq=False
)
if equality_constraints is not None:
for indcs, coeffs, rhs in equality_constraints:
constraints += _make_linear_constraints(
indices=indcs, coefficients=coeffs, rhs=rhs, shapeX=shapeX, eq=True
)
return constraints
[docs]
def eval_lin_constraint(
x: np.ndarray, flat_idxr: list[int], coeffs: np.ndarray, rhs: float
) -> np.float64:
r"""Evaluate a single linear constraint.
Args:
x: The input array.
flat_idxr: The indices in `x` to consider.
coeffs: The coefficients corresponding to the indices.
rhs: The right-hand-side of the constraint.
Returns:
The evaluted constraint: `\sum_i (coeffs[i] * x[i]) - rhs`
"""
return np.sum(x[flat_idxr] * coeffs, -1) - rhs
[docs]
def lin_constraint_jac(
x: np.ndarray, flat_idxr: list[int], coeffs: np.ndarray, n: int
) -> np.ndarray:
r"""Return the Jacobian associated with a linear constraint.
Args:
x: The input array.
flat_idxr: The indices for the elements of x that appear in the constraint.
coeffs: The coefficients corresponding to the indices.
n: number of elements
Returns:
The Jacobian.
"""
# TODO: Use sparse representation (not sure if scipy optim supports that)
jac = np.zeros(n)
jac[flat_idxr] = coeffs
return jac
def _arrayify(X: Tensor) -> np.ndarray:
r"""Convert a torch.Tensor (any dtype or device) to a numpy (double) array.
Args:
X: The input tensor.
Returns:
A numpy array of double dtype with the same shape and data as `X`.
"""
return X.cpu().detach().contiguous().double().clone().numpy()
def _validate_linear_constraints_shape_input(shapeX: torch.Size) -> torch.Size:
"""
Validate `shapeX` input to `_make_linear_constraints`.
Check that it has either 2 or 3 dimensions, and add a scalar batch
dimension if it is only 2d.
"""
if len(shapeX) not in (2, 3):
raise UnsupportedError(
f"`shapeX` must be `(b) x q x d` (at least two-dimensional). It is "
f"{shapeX}."
)
if len(shapeX) == 2:
shapeX = torch.Size([1, *shapeX])
return shapeX
def _validate_linear_constraints_indices_input(indices: Tensor, q: int, d: int) -> None:
if indices.dim() > 2:
raise UnsupportedError(
"Linear constraints supported only on individual candidates and "
"across q-batches, not across general batch shapes."
)
elif indices.dim() == 2:
if indices[:, 0].max() > q - 1:
raise RuntimeError(f"Index out of bounds for {q}-batch")
if indices[:, 1].max() > d - 1:
raise RuntimeError(f"Index out of bounds for {d}-dim parameter tensor")
elif indices.dim() == 1:
if indices.max() > d - 1:
raise RuntimeError(f"Index out of bounds for {d}-dim parameter tensor")
else:
raise ValueError("`indices` must be at least one-dimensional")
def _make_linear_constraints(
indices: Tensor,
coefficients: Tensor,
rhs: float,
shapeX: torch.Size,
eq: bool = False,
) -> list[ScipyConstraintDict]:
r"""Create linear constraints to be used by `scipy.minimize`.
Encodes constraints of the form
`\sum_i (coefficients[i] * X[..., indices[i]]) ? rhs`
where `?` can be designated either as `>=` by setting `eq=False`, or as
`=` by setting `eq=True`.
If indices is one-dimensional, the constraints are broadcasted across
all elements of the q-batch. If indices is two-dimensional, then
constraints are applied across elements of a q-batch. In either case,
constraints are created for all t-batches.
Args:
indices: A tensor of shape `c` or `c x 2`, where c is the number of terms
in the constraint. If single-dimensional, contains the indices of
the dimensions of the feature space that occur in the linear
constraint. If two-dimensional, contains pairs of indices of the
q-batch (0) and the feature space (1) that occur in the linear
constraint.
coefficients: A single-dimensional tensor of coefficients with the same
number of elements as `indices`.
rhs: The right hand side of the constraint.
shapeX: The shape of the torch tensor to construct the constraints for
(i.e. `(b) x q x d`). Must have two or three dimensions.
eq: If True, return an equality constraint, o/w return an inequality
constraint (indicated by "eq" / "ineq" value of the `type` key).
Returns:
A list of constraint dictionaries with the following keys
- "type": Indicates the type of the constraint ("eq" if `eq=True`, "ineq" o/w)
- "fun": A callable evaluating the constraint value on `x`, a flattened
version of the input tensor `X`, returning a scalar.
- "jac": A callable evaluating the constraint's Jacobian on `x`, a flattened
version of the input tensor `X`, returning a numpy array.
>>> shapeX = torch.Size([3, 5, 4])
>>> constraints = _make_linear_constraints(
... indices=torch.tensor([1., 2.]),
... coefficients=torch.tensor([-0.5, 1.3]),
... rhs=0.49,
... shapeX=shapeX,
... eq=True
... )
>>> len(constraints)
15
>>> constraints[0].keys()
dict_keys(['type', 'fun', 'jac'])
>>> x = np.arange(60).reshape(shapeX)
>>> constraints[0]["fun"](x)
1.61 # 1 * -0.5 + 2 * 1.3 - 0.49
>>> constraints[0]["jac"](x)
[0., -0.5, 1.3, 0., 0., ...]
>>> constraints[1]["fun"](x) #
4.81
"""
shapeX = _validate_linear_constraints_shape_input(shapeX)
b, q, d = shapeX
_validate_linear_constraints_indices_input(indices, q, d)
n = shapeX.numel()
constraints: list[ScipyConstraintDict] = []
coeffs = _arrayify(coefficients)
ctype = "eq" if eq else "ineq"
offsets = [q * d, d]
if indices.dim() == 2:
# indices has two dimensions (potential constraints across q-batch elements)
# rule is [i, j, k] is at
# i * offsets[0] + j * offsets[1] + k
for i in range(b):
list_ind = (idx.tolist() for idx in indices)
idxr = [i * offsets[0] + idx[0] * offsets[1] + idx[1] for idx in list_ind]
fun = partial(
eval_lin_constraint, flat_idxr=idxr, coeffs=coeffs, rhs=float(rhs)
)
jac = partial(lin_constraint_jac, flat_idxr=idxr, coeffs=coeffs, n=n)
constraints.append({"type": ctype, "fun": fun, "jac": jac})
elif indices.dim() == 1:
# indices is one-dim - broadcast constraints across q-batches and t-batches
for i in range(b):
for j in range(q):
idxr = (i * offsets[0] + j * offsets[1] + indices).tolist()
fun = partial(
eval_lin_constraint, flat_idxr=idxr, coeffs=coeffs, rhs=float(rhs)
)
jac = partial(lin_constraint_jac, flat_idxr=idxr, coeffs=coeffs, n=n)
constraints.append({"type": ctype, "fun": fun, "jac": jac})
return constraints
def _make_nonlinear_constraints(
f_np_wrapper: Callable, nlc: Callable, is_intrapoint: bool, shapeX: torch.Size
) -> list[ScipyConstraintDict]:
"""Create nonlinear constraints to be used by `scipy.minimize`.
Args:
f_np_wrapper: A wrapper function that given a constraint evaluates
the value and gradient (using autograd) of a numpy input and returns both
the objective and the gradient.
nlc: Callable representing a constraint of the form `callable(x) >= 0`. In case
of an intra-point constraint, `callable()`takes in an one-dimensional tensor
of shape `d` and returns a scalar. In case of an inter-point constraint,
`callable()` takes a two dimensional tensor of shape `q x d` and again
returns a scalar.
is_intrapoint: A Boolean indicating if a constraint is an intra-point or
inter-point constraint (see the docstring of the `inequality_constraints`
argument to `optimize_acqf()`).
shapeX: Shape of the three-dimensional batch X, that should be optimized.
Returns:
A list of constraint dictionaries with the following keys
- "type": Indicates the type of the constraint, here always "ineq".
- "fun": A callable evaluating the constraint value on `x`, a flattened
version of the input tensor `X`, returning a scalar.
- "jac": A callable evaluating the constraint's Jacobian on `x`, a flattened
version of the input tensor `X`, returning a numpy array.
"""
shapeX = _validate_linear_constraints_shape_input(shapeX)
b, q, _ = shapeX
constraints = []
def get_intrapoint_constraint(b: int, q: int, nlc: Callable) -> Callable:
return lambda x: nlc(x[b, q])
def get_interpoint_constraint(b: int, nlc: Callable) -> Callable:
return lambda x: nlc(x[b])
if is_intrapoint:
for i in range(b):
for j in range(q):
f_obj, f_grad = _make_f_and_grad_nonlinear_inequality_constraints(
f_np_wrapper=f_np_wrapper,
nlc=get_intrapoint_constraint(b=i, q=j, nlc=nlc),
)
constraints.append({"type": "ineq", "fun": f_obj, "jac": f_grad})
else:
for i in range(b):
f_obj, f_grad = _make_f_and_grad_nonlinear_inequality_constraints(
f_np_wrapper=f_np_wrapper,
nlc=get_interpoint_constraint(b=i, nlc=nlc),
)
constraints.append({"type": "ineq", "fun": f_obj, "jac": f_grad})
return constraints
def _generate_unfixed_nonlin_constraints(
constraints: Optional[list[tuple[Callable[[Tensor], Tensor], bool]]],
fixed_features: dict[int, float],
dimension: int,
) -> Optional[list[Callable[[Tensor], Tensor]]]:
"""Given a dictionary of fixed features, returns a list of callables for
nonlinear inequality constraints expecting only a tensor with the non-fixed
features as input.
"""
if not constraints:
return constraints
selector = []
idx_X, idx_f = 0, dimension - len(fixed_features)
for i in range(dimension):
if i in fixed_features.keys():
selector.append(idx_f)
idx_f += 1
else:
selector.append(idx_X)
idx_X += 1
values = torch.tensor(list(fixed_features.values()), dtype=torch.double)
def _wrap_nonlin_constraint(
constraint: Callable[[Tensor], Tensor]
) -> Callable[[Tensor], Tensor]:
def new_nonlin_constraint(X: Tensor) -> Tensor:
ivalues = values.to(X).expand(*X.shape[:-1], len(fixed_features))
X_perm = torch.cat([X, ivalues], dim=-1)
return constraint(X_perm[..., selector])
return new_nonlin_constraint
return [
(_wrap_nonlin_constraint(constraint=nlc), is_intrapoint)
for nlc, is_intrapoint in constraints
]
def _generate_unfixed_lin_constraints(
constraints: Optional[list[tuple[Tensor, Tensor, float]]],
fixed_features: dict[int, float],
dimension: int,
eq: bool,
) -> Optional[list[tuple[Tensor, Tensor, float]]]:
# If constraints is None or an empty list, then return itself
if not constraints:
return constraints
# replace_index generates the new indices for the unfixed dimensions
# after eliminating the fixed dimensions.
# Example: dimension = 5, ff.keys() = [1, 3], replace_index = {0: 0, 2: 1, 4: 2}
unfixed_keys = sorted(set(range(dimension)) - set(fixed_features))
unfixed_keys = torch.tensor(unfixed_keys).to(constraints[0][0])
replace_index = torch.arange(dimension - len(fixed_features)).to(constraints[0][0])
new_constraints = []
# parse constraints one-by-one
for constraint_id, (indices, coefficients, rhs) in enumerate(constraints):
new_rhs = rhs
new_indices = []
new_coefficients = []
# the following unsqueeze is done to facilitate a simpler for-loop.
indices_2dim = indices if indices.ndim == 2 else indices.unsqueeze(-1)
for coefficient, index in zip(coefficients, indices_2dim):
ffval_or_None = fixed_features.get(index[-1].item())
# if ffval_or_None is None, then the index is not fixed
if ffval_or_None is None:
new_indices.append(index)
new_coefficients.append(coefficient)
# otherwise, we "remove" the constraints corresponding to that index
else:
new_rhs = new_rhs - coefficient.item() * ffval_or_None
# all indices were fixed, so the constraint is gone.
if len(new_indices) == 0:
if (eq and new_rhs != 0) or (not eq and new_rhs > 0):
prefix = "Eq" if eq else "Ineq"
raise CandidateGenerationError(
f"{prefix}uality constraint {constraint_id} not met "
"with fixed_features."
)
else:
# However, one key transformation has to be noted.
# new_indices is with respect to the older (fuller) domain, and so it will
# have to be converted using replace_index.
new_indices = torch.stack(new_indices, dim=0)
# generate new index location after the removal of fixed_features indices
new_indices_dim_d = new_indices[:, -1].unsqueeze(-1)
new_indices_dim_d = replace_index[
torch.nonzero(new_indices_dim_d == unfixed_keys, as_tuple=True)[1]
]
new_indices[:, -1] = new_indices_dim_d
# squeeze(-1) is a no-op if dim -1 is not singleton
new_indices.squeeze_(-1)
# convert new_coefficients to Tensor
new_coefficients = torch.stack(new_coefficients)
new_constraints.append((new_indices, new_coefficients, new_rhs))
return new_constraints
def _make_f_and_grad_nonlinear_inequality_constraints(
f_np_wrapper: Callable, nlc: Callable
) -> tuple[Callable[[Tensor], Tensor], Callable[[Tensor], Tensor]]:
"""
Create callables for objective + grad for the nonlinear inequality constraints.
The Scipy interface requires specifying separate callables and we use caching to
avoid evaluating the same input twice. This caching only works if
the returned functions are evaluated on the same input in immediate
sequence (i.e., calling `f_obj(X_1)`, `f_grad(X_1)` will result in a
single forward pass, while `f_obj(X_1)`, `f_grad(X_2)`, `f_obj(X_1)`
will result in three forward passes).
"""
def f_obj_and_grad(x):
obj, grad = f_np_wrapper(x, f=nlc)
return obj, grad
cache = {"X": None, "obj": None, "grad": None}
def f_obj(X):
X_c = cache["X"]
if X_c is None or not np.array_equal(X_c, X):
cache["X"] = X.copy()
cache["obj"], cache["grad"] = f_obj_and_grad(X)
return cache["obj"]
def f_grad(X):
X_c = cache["X"]
if X_c is None or not np.array_equal(X_c, X):
cache["X"] = X.copy()
cache["obj"], cache["grad"] = f_obj_and_grad(X)
return cache["grad"]
return f_obj, f_grad
[docs]
def nonlinear_constraint_is_feasible(
nonlinear_inequality_constraint: Callable, is_intrapoint: bool, x: Tensor
) -> bool:
"""Checks if a nonlinear inequality constraint is fulfilled.
Args:
nonlinear_inequality_constraint: Callable to evaluate the
constraint.
intra: If True, the constraint is an intra-point constraint that
is applied pointwise and is broadcasted over the q-batch. Else, the
constraint has to evaluated over the whole q-batch and is a an
inter-point constraint.
x: Tensor of shape (b x q x d).
Returns:
bool: True if the constraint is fulfilled, else False.
"""
def check_x(x: Tensor) -> bool:
return _arrayify(nonlinear_inequality_constraint(x)).item() >= NLC_TOL
for x_ in x:
if is_intrapoint:
if not all(check_x(x__) for x__ in x_):
return False
else:
if not check_x(x_):
return False
return True
[docs]
def make_scipy_nonlinear_inequality_constraints(
nonlinear_inequality_constraints: list[tuple[Callable, bool]],
f_np_wrapper: Callable,
x0: Tensor,
shapeX: torch.Size,
) -> list[dict]:
r"""Generate Scipy nonlinear inequality constraints from callables.
Args:
nonlinear_inequality_constraints: A list of tuples representing the nonlinear
inequality constraints. The first element in the tuple is a callable
representing a constraint of the form `callable(x) >= 0`. In case of an
intra-point constraint, `callable()`takes in an one-dimensional tensor of
shape `d` and returns a scalar. In case of an inter-point constraint,
`callable()` takes a two dimensional tensor of shape `q x d` and again
returns a scalar. The second element is a boolean, indicating if it is an
intra-point or inter-point constraint (`True` for intra-point. `False` for
inter-point). For more information on intra-point vs inter-point
constraints, see the docstring of the `inequality_constraints` argument to
`optimize_acqf()`. The constraints will later be passed to the scipy
solver.
f_np_wrapper: A wrapper function that given a constraint evaluates the value
and gradient (using autograd) of a numpy input and returns both the
objective and the gradient.
x0: The starting point for SLSQP. We return this starting point in (rare)
cases where SLSQP fails and thus require it to be feasible.
shapeX: Shape of the three-dimensional batch X, that should be optimized.
Returns:
A list of dictionaries containing callables for constraint function
values and Jacobians and a string indicating the associated constraint
type ("eq", "ineq"), as expected by `scipy.minimize`.
"""
scipy_nonlinear_inequality_constraints = []
for constraint in nonlinear_inequality_constraints:
if not isinstance(constraint, tuple):
raise ValueError(
f"A nonlinear constraint has to be a tuple, got {type(constraint)}."
)
if len(constraint) != 2:
raise ValueError(
"A nonlinear constraint has to be a tuple of length 2, "
f"got length {len(constraint)}."
)
nlc, is_intrapoint = constraint
if not nonlinear_constraint_is_feasible(
nlc, is_intrapoint=is_intrapoint, x=x0.reshape(shapeX)
):
raise ValueError(
"`batch_initial_conditions` must satisfy the non-linear inequality "
"constraints."
)
scipy_nonlinear_inequality_constraints += _make_nonlinear_constraints(
f_np_wrapper=f_np_wrapper,
nlc=nlc,
is_intrapoint=is_intrapoint,
shapeX=shapeX,
)
return scipy_nonlinear_inequality_constraints
