# Source code for PARyOpt.acquisition_functions

```
"""
---
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
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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
copies or substantial portions of the Software.
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
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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
```