from __future__ import annotations
from typing import Any
import numpy as np
from scipy.stats import norm
from smac.acquisition.function.abstract_acquisition_function import (
AbstractAcquisitionFunction,
)
from smac.utils.logging import get_logger
__copyright__ = "Copyright 2022, automl.org"
__license__ = "3-clause BSD"
logger = get_logger(__name__)
[docs]
class PI(AbstractAcquisitionFunction):
r"""Probability of Improvement
:math:`P(f_{t+1}(\mathbf{X})\geq f(\mathbf{X^+}))` :math:`:= \Phi(\\frac{ \mu(\mathbf{X})-f(\mathbf{X^+}) }
{ \sigma(\mathbf{X}) })` with :math:`f(X^+)` as the incumbent and :math:`\Phi` the cdf of the standard normal.
Parameters
----------
xi : float, defaults to 0.0
Controls the balance between exploration and exploitation of the acquisition function.
"""
def __init__(self, xi: float = 0.0):
super(PI, self).__init__()
self._xi: float = xi
self._eta: float | None = None
@property
def name(self) -> str: # noqa: D102
return "Probability of Improvement"
@property
def meta(self) -> dict[str, Any]: # noqa: D102
meta = super().meta
meta.update({"xi": self._xi})
return meta
def _update(self, **kwargs: Any) -> None:
"""Update acsquisition function attributes
Parameters
----------
eta : float
Function value of current incumbent.
xi : float, optional
Exploration-exploitation trade-off parameter
"""
assert "eta" in kwargs
self._eta = kwargs["eta"]
if "xi" in kwargs and kwargs["xi"] is not None:
self._xi = kwargs["xi"]
def _compute(self, X: np.ndarray) -> np.ndarray:
"""Compute the PI value.
Parameters
----------
X: np.ndarray [N, D]
Points to evaluate PI. N is the number of points and D the dimension for the points.
Returns
-------
np.ndarray [N, 1]
Expected Improvement of X.
Raises
------
ValueError
If `update` has not been called before (current incumbent value `eta` unspecified).
"""
assert self._model is not None
if self._eta is None:
raise ValueError(
"No current best specified. Call update("
"eta=<float>) to inform the acquisition function "
"about the current best value."
)
if len(X.shape) == 1:
X = X[:, np.newaxis]
m, var_ = self._model.predict_marginalized(X)
std = np.sqrt(var_)
return norm.cdf((self._eta - m - self._xi) / std)