acquisition_functions.hpp File Reference

Bayesian-Optimization acquisition functions over a GP posterior: Expected Improvement, Probability of Improvement, GP-Upper-Confidence-Bound (Snoek, Larochelle, Adams, "Practical Bayesian Optimization of Machine Learning Algorithms," NeurIPS 2012). More...

#include <cmath>
#include <stdexcept>

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Namespaces
namespace	pulsatrix

Functions
double	pulsatrix::StandardNormalPdf (double z)
	Standard normal PDF, phi(z) = (1/sqrt(2*pi)) * exp(-z^2/2).
double	pulsatrix::StandardNormalCdf (double z)
	Standard normal CDF, Phi(z) = 0.5 * (1 + erf(z / sqrt(2))).
double	pulsatrix::ExpectedImprovement (double mean, double variance, double best_value, double xi=0.01)
	Expected Improvement: the expected amount by which a candidate exceeds best_value + xi, under the posterior N(mean, variance).
double	pulsatrix::ProbabilityOfImprovement (double mean, double variance, double best_value, double xi=0.01)
	Probability of Improvement: P(candidate's value > best_value + xi) under the posterior N(mean, variance).
double	pulsatrix::UpperConfidenceBound (double mean, double variance, double kappa=2.0)
	GP-Upper-Confidence-Bound: mean + kappa * sqrt(variance).

Detailed Description

Bayesian-Optimization acquisition functions over a GP posterior: Expected Improvement, Probability of Improvement, GP-Upper-Confidence-Bound (Snoek, Larochelle, Adams, "Practical Bayesian Optimization of Machine Learning Algorithms," NeurIPS 2012).

Note

Maximization convention throughout, matching this campaign's own established convention (Evolutionary DL's selection/crossover operators, this campaign's SearchSpace-driven samplers) – a caller minimizing a loss negates it first.