Source code for PARyOpt.acquisition_functions

"""
---
    Copyright (c) 2018 Baskar Ganapathysubramanian, Balaji Sesha Sarath Pokuri
    
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---
"""

## --- end license text --- ##
"""
Contains a library of acquisition functions that can be used in bayesian optimization
"""
import numpy as np

import PARyOpt.utils as utils


[docs]def lower_confidence_bound(mean: float, variance: float, curr_best: float = 0., kappa: float = 1.) -> float: """ lower confidence bound of improvement : used for minimization problems :param mean: mean of surrogate :param variance: variance of surrogate :param curr_best: current best evaluated point :param kappa: exploration - exploitation tradeoff parameter :return: lower confidence bound """
return mean - kappa * variance - curr_best
[docs]def upper_confidence_bound(mean: float, variance: float, curr_best: float=0., kappa: float = 1.) -> float: """ upper confidence bound of improvement: used in the case of maximization problems :param mean: mean of surrogate :param variance: variance of surrogate :param curr_best: current best evaluated point :param kappa: exploration - exploitation tradeoff parameter :return: upper confidence bound """
return mean + kappa * variance - curr_best
[docs]def expected_improvement(mean: float, variance: float, curr_best: float=0., _: float = 1.) -> float: """ Expected improvement of objective function \ 'A Tutorial on Bayesian Optimization of Expensive Cost Functions, \ with Application to Active User Modeling and Hierarchical Reinforcement Learning' :param mean: mean of surrogate :param variance: variance of surrogate :param curr_best: current best evaluated point :param kappa: exploration - exploitation tradeoff parameter :return: expectation of improvement """ if variance > 1e-30: gamma = -1.0 * (curr_best - mean) / np.sqrt(variance) return np.sqrt(variance) * (gamma * utils.cdf_normal(gamma) + utils.pdf_normal(gamma)) else:
return 0.0
[docs]def probability_improvement(mean: float, variance: float, curr_best: float=0., _: float = 1.) -> float: """ Probability of improvement of objective function \ 'A Tutorial on Bayesian Optimization of Expensive Cost Functions, \ with Application to Active User Modeling and Hierarchical Reinforcement Learning' :param mean: mean of surrogate :param variance: variance of surrogate :param curr_best: current best evaluated point :param kappa: exploration - exploitation tradeoff parameter :return: probability of improvement """ if variance > 1e-16: gamma = -(curr_best - mean) / np.sqrt(variance) return utils.cdf_normal(gamma) else:
return 0.0