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"""Constraint handling."""
from __future__ import annotations
from typing import TYPE_CHECKING, Any
import numpy as np
from scipy.stats import norm
from sklearn.gaussian_process import GaussianProcessRegressor
from sklearn.gaussian_process.kernels import Matern
if TYPE_CHECKING:
from collections.abc import Callable
from numpy.random import RandomState
from numpy.typing import NDArray
Float = np.floating[Any]
class ConstraintModel:
"""Model constraints using GP regressors.
This class takes the function to optimize as well as the parameters bounds
in order to find which values for the parameters yield the maximum value
using bayesian optimization.
Parameters
----------
fun : None or Callable -> float or np.ndarray
The constraint function. Should be float-valued or array-valued (if
multiple constraints are present). Needs to take the same parameters
as the optimization target with the same argument names.
lb : float or np.ndarray
The lower bound on the constraints. Should have the same
dimensionality as the return value of the constraint function.
ub : float or np.ndarray
The upper bound on the constraints. Should have the same
dimensionality as the return value of the constraint function.
random_state : np.random.RandomState or int or None, default=None
Random state to use.
Note
----
In case of multiple constraints, this model assumes conditional
independence. This means that the overall probability of fulfillment is a
simply the product of the individual probabilities.
"""
def __init__(
self,
fun: Callable[..., float] | Callable[..., NDArray[Float]] | None,
lb: float | NDArray[Float],
ub: float | NDArray[Float],
random_state: int | RandomState | None = None,
) -> None:
self.fun = fun
self._lb = np.atleast_1d(lb)
self._ub = np.atleast_1d(ub)
if np.any(self._lb >= self._ub):
msg = "Lower bounds must be less than upper bounds."
raise ValueError(msg)
self._model = [
GaussianProcessRegressor(
kernel=Matern(nu=2.5),
alpha=1e-6,
normalize_y=True,
n_restarts_optimizer=5,
random_state=random_state,
)
for _ in range(len(self._lb))
]
@property
def lb(self) -> NDArray[Float]:
"""Return lower bounds."""
return self._lb
@property
def ub(self) -> NDArray[Float]:
"""Return upper bounds."""
return self._ub
@property
def model(self) -> list[GaussianProcessRegressor]:
"""Return GP regressors of the constraint function."""
return self._model
def eval(self, **kwargs: Any) -> float | NDArray[Float]: # noqa: D417
r"""Evaluate the constraint function.
Parameters
----------
\*\*kwargs : any
Function arguments to evaluate the constraint function on.
Returns
-------
Value of the constraint function.
Raises
------
TypeError
If the kwargs' keys don't match the function argument names.
"""
if self.fun is None:
error_msg = "No constraint function was provided."
raise ValueError(error_msg)
try:
return self.fun(**kwargs)
except TypeError as e:
msg = (
"Encountered TypeError when evaluating constraint "
"function. This could be because your constraint function "
"doesn't use the same keyword arguments as the target "
f"function. Original error message:\n\n{e}"
)
e.args = (msg,)
raise
def fit(self, X: NDArray[Float], Y: NDArray[Float]) -> None:
"""Fit internal GPRs to the data.
Parameters
----------
X : np.ndarray of shape (n_samples, n_features)
Parameters of the constraint function.
Y : np.ndarray of shape (n_samples, n_constraints)
Values of the constraint function.
Returns
-------
None
"""
if len(self._model) == 1:
self._model[0].fit(X, Y)
else:
for i, gp in enumerate(self._model):
gp.fit(X, Y[:, i])
def predict(self, X: NDArray[Float]) -> NDArray[Float]:
r"""Calculate the probability that the constraint is fulfilled at `X`.
Note that this does not try to approximate the values of the
constraint function (for this, see `ConstraintModel.approx()`.), but
probability that the constraint function is fulfilled. That is, this
function calculates
.. math::
p = \text{Pr}\left\{c^{\text{low}} \leq \tilde{c}(x) \leq
c^{\text{up}} \right\} = \int_{c^{\text{low}}}^{c^{\text{up}}}
\mathcal{N}(c, \mu(x), \sigma^2(x)) \, dc.
with :math:`\mu(x)`, :math:`\sigma^2(x)` the mean and variance at
:math:`x` as given by the GP and :math:`c^{\text{low}}`,
:math:`c^{\text{up}}` the lower and upper bounds of the constraint
respectively.
Note
----
In case of multiple constraints, we assume conditional independence.
This means we calculate the probability of constraint fulfilment
individually, with the joint probability given as their product.
Parameters
----------
X : np.ndarray of shape (n_samples, n_features)
Parameters for which to predict the probability of constraint
fulfilment.
Returns
-------
np.ndarray of shape (n_samples,)
Probability of constraint fulfilment.
"""
X_shape = X.shape
X = X.reshape((-1, self._model[0].n_features_in_))
result: NDArray[Float]
y_mean: NDArray[Float]
y_std: NDArray[Float]
p_lower: NDArray[Float]
p_upper: NDArray[Float]
if len(self._model) == 1:
y_mean, y_std = self._model[0].predict(X, return_std=True)
p_lower = (
norm(loc=y_mean, scale=y_std).cdf(self._lb[0]) if self._lb[0] != -np.inf else np.array([0])
)
p_upper = (
norm(loc=y_mean, scale=y_std).cdf(self._ub[0]) if self._lb[0] != np.inf else np.array([1])
)
result = p_upper - p_lower
return result.reshape(X_shape[:-1])
result = np.ones(X.shape[0])
for j, gp in enumerate(self._model):
y_mean, y_std = gp.predict(X, return_std=True)
p_lower = (
norm(loc=y_mean, scale=y_std).cdf(self._lb[j]) if self._lb[j] != -np.inf else np.array([0])
)
p_upper = (
norm(loc=y_mean, scale=y_std).cdf(self._ub[j]) if self._lb[j] != np.inf else np.array([1])
)
result = result * (p_upper - p_lower)
return result.reshape(X_shape[:-1])
def approx(self, X: NDArray[Float]) -> NDArray[Float]:
"""
Approximate the constraint function using the internal GPR model.
Parameters
----------
X : np.ndarray of shape (n_samples, n_features)
Parameters for which to estimate the constraint function value.
Returns
-------
np.ndarray of shape (n_samples, n_constraints)
Constraint function value estimates.
"""
X_shape = X.shape
X = X.reshape((-1, self._model[0].n_features_in_))
if len(self._model) == 1:
return self._model[0].predict(X).reshape(X_shape[:-1])
result = np.column_stack([gp.predict(X) for gp in self._model])
return result.reshape(X_shape[:-1] + (len(self._lb),))
def allowed(self, constraint_values: NDArray[Float]) -> NDArray[np.bool_]:
"""Check whether `constraint_values` fulfills the specified limits.
Parameters
----------
constraint_values : np.ndarray of shape (n_samples, n_constraints)
The values of the constraint function.
Returns
-------
np.ndarrray of shape (n_samples,)
Specifying wheter the constraints are fulfilled.
"""
if self._lb.size == 1:
return np.less_equal(self._lb, constraint_values) & np.less_equal(constraint_values, self._ub)
return np.all(constraint_values <= self._ub, axis=-1) & np.all(constraint_values >= self._lb, axis=-1)
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