class_docstr: 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.
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code: def name(self) -> str:  # noqa: D102
      return "Lower Confidence Bound"
  
file_path: SMAC3/smac/acquisition/function/confidence_bound.py
imports: from __future__ import annotations
  from typing import Any
  import numpy
  from smac.acquisition.function.abstract_acquisition_function import AbstractAcquisitionFunction
  from smac.utils.logging import get_logger
label_desc: Use image node_id 2 for calling the LCB obj's underlying member method code with example usage: obj.name() and returns: str