"""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)