bayes_opt.util.UtilityFunction¶
-
class bayes_opt.util.UtilityFunction(kind=
'ucb', kappa=2.576, xi=0, kappa_decay=1, kappa_decay_delay=0)¶ An object to compute the acquisition functions.
- Parameters:¶
- kind : {'ucb', 'ei', 'poi'}¶
‘ucb’ stands for the Upper Confidence Bounds method
’ei’ is the Expected Improvement method
’poi’ is the Probability Of Improvement criterion.
- kappa : float, optional(default=2.576)¶
Parameter to indicate how closed are the next parameters sampled. Higher value = favors spaces that are least explored. Lower value = favors spaces where the regression function is the highest.
- kappa_decay : float, optional(default=1)¶
kappa is multiplied by this factor every iteration.
- kappa_decay_delay : int, optional(default=0)¶
Number of iterations that must have passed before applying the decay to kappa.
- xi : float, optional(default=0.0)¶
- static ei(x, gp, y_max, xi)¶
Calculate Expected Improvement acqusition function.
Similar to Probability of Improvement (UtilityFunction.poi), but also considers the magnitude of improvement. Calculated as
\[\text{EI}(x) = (\mu(x)-y_{\text{max}} - \xi) \Phi\left( \frac{\mu(x)-y_{\text{max}} - \xi }{\sigma(x)} \right) + \sigma(x) \phi\left( \frac{\mu(x)-y_{\text{max}} - \xi }{\sigma(x)} \right)\]where \(\Phi\) is the CDF and \(\phi\) the PDF of the normal distribution.
- Parameters:¶
- x : np.ndarray¶
Parameters to evaluate the function at.
- gp : sklearn.gaussian_process.GaussianProcessRegressor¶
A gaussian process regressor modelling the target function based on previous observations.
- y_max : number¶
Highest found value of the target function.
- xi : float, positive¶
Governs the exploration/exploitation tradeoff. Lower prefers exploitation, higher prefers exploration.
- Returns:¶
Values of the acquisition function
- static poi(x, gp, y_max, xi)¶
Calculate Probability of Improvement acqusition function.
Calculated as
\[\text{POI}(x) = \Phi\left( \frac{\mu(x)-y_{\text{max}} - \xi }{\sigma(x)} \right)\]where \(\Phi\) is the CDF of the normal distribution.
- Parameters:¶
- x : np.ndarray¶
Parameters to evaluate the function at.
- gp : sklearn.gaussian_process.GaussianProcessRegressor¶
A gaussian process regressor modelling the target function based on previous observations.
- y_max : number¶
Highest found value of the target function.
- xi : float, positive¶
Governs the exploration/exploitation tradeoff. Lower prefers exploitation, higher prefers exploration.
- Returns:¶
Values of the acquisition function
- static ucb(x, gp, kappa)¶
Calculate Upper Confidence Bound acquisition function.
Similar to Probability of Improvement (UtilityFunction.poi), but also considers the magnitude of improvement. Calculated as
\[\text{UCB}(x) = \mu(x) + \kappa \sigma(x)\]where \(\Phi\) is the CDF and \(\phi\) the PDF of the normal distribution.
- Parameters:¶
- x : np.ndarray¶
Parameters to evaluate the function at.
- gp : sklearn.gaussian_process.GaussianProcessRegressor¶
A gaussian process regressor modelling the target function based on previous observations.
- y_max : number
Highest found value of the target function.
- kappa : float, positive¶
Governs the exploration/exploitation tradeoff. Lower prefers exploitation, higher prefers exploration.
- Returns:¶
Values of the acquisition function
- update_params()¶
Update internal parameters.
- utility(x, gp, y_max)¶
Calculate acquisition function.
- Parameters:¶
- x : np.ndarray¶
Parameters to evaluate the function at.
- gp : sklearn.gaussian_process.GaussianProcessRegressor¶
A gaussian process regressor modelling the target function based on previous observations.
- y_max : number¶
Highest found value of the target function.
- Returns:¶
Values of the acquisition function