"""
---
Copyright (c) 2018 Baskar Ganapathysubramanian, Balaji Sesha Sarath Pokuri
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
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copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
---
"""
## --- 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