from __future__ import annotations
from typing import Any
import numpy as np
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 LCB(AbstractAcquisitionFunction):
r"""Computes the lower confidence bound for a given x over the best so far value as acquisition value.
:math:`LCB(X) = \mu(\mathbf{X}) - \sqrt(\beta_t)\sigma(\mathbf{X})` [SKKS10]_
with
:math:`\beta_t = 2 \log( |D| t^2 / \beta)`
:math:`\text{Input space} D`
:math:`\text{Number of input dimensions} |D|`
:math:`\text{Number of data points} t`
:math:`\text{Exploration/exploitation tradeoff} \beta`
Returns -LCB(X) as the acquisition_function optimizer maximizes the acquisition value.
Parameters
----------
beta : float, defaults to 1.0
Controls the balance between exploration and exploitation of the acquisition function.
Attributes
----------
_beta : float
Exploration-exploitation trade-off parameter.
_num_data : int
Number of data points seen so far.
"""
def __init__(self, beta: float = 1.0) -> None:
super(LCB, self).__init__()
self._beta: float = beta
self._num_data: int | None = None
@property
def name(self) -> str: # noqa: D102
return "Lower Confidence Bound"
@property
def meta(self) -> dict[str, Any]: # noqa: D102
meta = super().meta
meta.update({"beta": self._beta})
return meta
def _update(self, **kwargs: Any) -> None:
"""Update acsquisition function attributes
Parameters
----------
num_data : int
Number of data points
"""
assert "num_data" in kwargs
self._num_data = kwargs["num_data"]
def _compute(self, X: np.ndarray) -> np.ndarray:
"""Compute LCB acquisition value
Parameters
----------
X : np.ndarray [N, D]
The input points where the acquisition function should be evaluated. The dimensionality of X is (N, D),
with N as the number of points to evaluate at and D is the number of dimensions of one X.
Returns
-------
np.ndarray [N,1]
Acquisition function values wrt X.
Raises
------
ValueError
If `update` has not been called before. Number of data points is unspecified in this case.
"""
assert self._model is not None
if self._num_data is None:
raise ValueError(
"No current number of data points specified. Call `update` to inform the acqusition function."
)
if len(X.shape) == 1:
X = X[:, np.newaxis]
m, var_ = self._model.predict_marginalized(X)
std = np.sqrt(var_)
beta_t = 2 * np.log((X.shape[1] * self._num_data**2) / self._beta)
return -(m - np.sqrt(beta_t) * std)