acquisition_functions.hpp

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#pragma once
 
#include <cmath>
#include <stdexcept>
 
namespace pulsatrix {
 
inline double StandardNormalPdf(double z) {
    constexpr double kInvSqrt2Pi = 0.3989422804014327;  // 1 / sqrt(2*pi)
    return kInvSqrt2Pi * std::exp(-0.5 * z * z);
}
 
inline double StandardNormalCdf(double z) { return 0.5 * (1.0 + std::erf(z / std::sqrt(2.0))); }
 
inline double ExpectedImprovement(double mean, double variance, double best_value, double xi = 0.01) {
    if (variance < 0.0) {
        throw std::invalid_argument("ExpectedImprovement: variance must be non-negative");
    }
    double sigma = std::sqrt(variance);
    if (sigma <= 1e-12) {
        return 0.0;
    }
    double z = (mean - best_value - xi) / sigma;
    return (mean - best_value - xi) * StandardNormalCdf(z) + sigma * StandardNormalPdf(z);
}
 
inline double ProbabilityOfImprovement(double mean, double variance, double best_value, double xi = 0.01) {
    if (variance < 0.0) {
        throw std::invalid_argument("ProbabilityOfImprovement: variance must be non-negative");
    }
    double sigma = std::sqrt(variance);
    if (sigma <= 1e-12) {
        return (mean > best_value + xi) ? 1.0 : 0.0;
    }
    double z = (mean - best_value - xi) / sigma;
    return StandardNormalCdf(z);
}
 
inline double UpperConfidenceBound(double mean, double variance, double kappa = 2.0) {
    if (variance < 0.0) {
        throw std::invalid_argument("UpperConfidenceBound: variance must be non-negative");
    }
    return mean + kappa * std::sqrt(variance);
}
 
}  // namespace pulsatrix