ROL
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ROL::MixedCVaR< Real > Class Template Reference
Algorithmic Extensions » Stochastic Optimization » Risk Measures

Provides an interface for a convex combination of conditional value-at-risks. More...

#include <ROL_MixedCVaR.hpp>

Inheritance diagram for ROL::MixedCVaR< Real >:

Public Member Functions

 MixedCVaR (ROL::ParameterList &parlist)
 MixedCVaR (const std::vector< Real > &prob, const std::vector< Real > &coeff, const ROL::Ptr< PlusFunction< Real > > &pf)
void initialize (const Vector< Real > &x) override
Real computeStatistic (const Ptr< const std::vector< Real > > &xstat) const override
void updateValue (Objective< Real > &obj, const Vector< Real > &x, const std::vector< Real > &xstat, Real &tol) override
Real getValue (const Vector< Real > &x, const std::vector< Real > &xstat, SampleGenerator< Real > &sampler) override
void updateGradient (Objective< Real > &obj, const Vector< Real > &x, const std::vector< Real > &xstat, Real &tol) override
void getGradient (Vector< Real > &g, std::vector< Real > &gstat, const Vector< Real > &x, const std::vector< Real > &xstat, SampleGenerator< Real > &sampler) override
void updateHessVec (Objective< Real > &obj, const Vector< Real > &v, const std::vector< Real > &vstat, const Vector< Real > &x, const std::vector< Real > &xstat, Real &tol) override
void getHessVec (Vector< Real > &hv, std::vector< Real > &hvstat, const Vector< Real > &v, const std::vector< Real > &vstat, const Vector< Real > &x, const std::vector< Real > &xstat, SampleGenerator< Real > &sampler) override

Private Member Functions

void initializeMCVAR (void)
void checkInputs (void)

Private Attributes

ROL::Ptr< PlusFunction< Real > > plusFunction_
std::vector< Real > prob_
std::vector< Real > coeff_
std::vector< Real > vec_
int size_

Detailed Description

template<class Real>
class ROL::MixedCVaR< Real >

Provides an interface for a convex combination of conditional value-at-risks.

The risk measure associated with the mixed-quantile quadrangle is defined as

\[ \mathcal{R}(X) = \lambda_1 \mathrm{CVaR}_{\beta_1}(X) + \ldots + \lambda_n \mathrm{CVaR}_{\beta_n}(X) \]

where \(0 \le \beta_1 \le \cdots \le \beta_n < 1\) and \(0 \le \lambda_i\), \(i=1,\ldots,n\), satisfies

\[ \lambda_1 + \ldots + \lambda_n = 1. \]

Here, the conditional value-at-risk (CVaR) with confidence level \(0\le \beta < 1\) is

\[ \mathrm{CVaR}_\beta(X) = \inf_{t\in\mathbb{R}} \left\{ t + \frac{1}{1-\beta} \mathbb{E}\left[(X-t)_+\right] \right\} \]

where \((x)_+ = \max\{0,x\}\). If the distribution of \(X\) is continuous, then \(\mathrm{CVaR}_{\beta}(X)\) is the conditional expectation of \(X\) exceeding the \(\beta\)-quantile of \(X\) and the optimal \(t\) is the \(\beta\)-quantile. Additionally, \(\mathcal{R}\) is a law-invariant coherent risk measure.

When using derivative-based optimization, the user can provide a smooth approximation of \((\cdot)_+\) using the ROL::PlusFunction class.

Definition at line 54 of file ROL_MixedCVaR.hpp.

Constructor & Destructor Documentation

◆ MixedCVaR() [1/2]

template<class Real>
ROL::MixedCVaR< Real >::MixedCVaR ( ROL::ParameterList & parlist)
inline

Definition at line 102 of file ROL_MixedCVaR.hpp.

References checkInputs(), coeff_, plusFunction_, and prob_.

◆ MixedCVaR() [2/2]

template<class Real>
ROL::MixedCVaR< Real >::MixedCVaR ( const std::vector< Real > & prob,
const std::vector< Real > & coeff,
const ROL::Ptr< PlusFunction< Real > > & pf )
inline

Definition at line 114 of file ROL_MixedCVaR.hpp.

References checkInputs(), coeff_, plusFunction_, and prob_.

Member Function Documentation

◆ initializeMCVAR()

template<class Real>
void ROL::MixedCVaR< Real >::initializeMCVAR ( void )
inlineprivate

Definition at line 76 of file ROL_MixedCVaR.hpp.

References prob_, size_, and vec_.

Referenced by checkInputs().

◆ checkInputs()

template<class Real>
void ROL::MixedCVaR< Real >::checkInputs ( void )
inlineprivate

Definition at line 81 of file ROL_MixedCVaR.hpp.

References coeff_, initializeMCVAR(), plusFunction_, prob_, ROL::ROL_EPSILON(), and zero.

Referenced by MixedCVaR(), and MixedCVaR().

◆ initialize()

template<class Real>
void ROL::MixedCVaR< Real >::initialize ( const Vector< Real > & x)
inlineoverride

Definition at line 121 of file ROL_MixedCVaR.hpp.

References size_, and vec_.

◆ computeStatistic()

template<class Real>
Real ROL::MixedCVaR< Real >::computeStatistic ( const Ptr< const std::vector< Real > > & xstat) const
inlineoverride

Definition at line 126 of file ROL_MixedCVaR.hpp.

References coeff_, and size_.

◆ updateValue()

template<class Real>
void ROL::MixedCVaR< Real >::updateValue ( Objective< Real > & obj,
const Vector< Real > & x,
const std::vector< Real > & xstat,
Real & tol )
inlineoverride

Definition at line 136 of file ROL_MixedCVaR.hpp.

References coeff_, plusFunction_, prob_, and size_.

◆ getValue()

template<class Real>
Real ROL::MixedCVaR< Real >::getValue ( const Vector< Real > & x,
const std::vector< Real > & xstat,
SampleGenerator< Real > & sampler )
inlineoverride

Definition at line 148 of file ROL_MixedCVaR.hpp.

References coeff_, size_, and ROL::SampleGenerator< Real >::sumAll().

◆ updateGradient()

template<class Real>
void ROL::MixedCVaR< Real >::updateGradient ( Objective< Real > & obj,
const Vector< Real > & x,
const std::vector< Real > & xstat,
Real & tol )
inlineoverride

Definition at line 159 of file ROL_MixedCVaR.hpp.

References coeff_, plusFunction_, prob_, ROL::ROL_EPSILON(), size_, and vec_.

◆ getGradient()

template<class Real>
void ROL::MixedCVaR< Real >::getGradient ( Vector< Real > & g,
std::vector< Real > & gstat,
const Vector< Real > & x,
const std::vector< Real > & xstat,
SampleGenerator< Real > & sampler )
inlineoverride

Definition at line 176 of file ROL_MixedCVaR.hpp.

References coeff_, size_, ROL::SampleGenerator< Real >::sumAll(), and vec_.

◆ updateHessVec()

template<class Real>
void ROL::MixedCVaR< Real >::updateHessVec ( Objective< Real > & obj,
const Vector< Real > & v,
const std::vector< Real > & vstat,
const Vector< Real > & x,
const std::vector< Real > & xstat,
Real & tol )
inlineoverride

Definition at line 188 of file ROL_MixedCVaR.hpp.

References coeff_, plusFunction_, prob_, ROL::ROL_EPSILON(), size_, and vec_.

◆ getHessVec()

template<class Real>
void ROL::MixedCVaR< Real >::getHessVec ( Vector< Real > & hv,
std::vector< Real > & hvstat,
const Vector< Real > & v,
const std::vector< Real > & vstat,
const Vector< Real > & x,
const std::vector< Real > & xstat,
SampleGenerator< Real > & sampler )
inlineoverride

Definition at line 213 of file ROL_MixedCVaR.hpp.

References size_, ROL::SampleGenerator< Real >::sumAll(), and vec_.

Member Data Documentation

◆ plusFunction_

template<class Real>
ROL::Ptr<PlusFunction<Real> > ROL::MixedCVaR< Real >::plusFunction_
private

Definition at line 56 of file ROL_MixedCVaR.hpp.

Referenced by checkInputs(), MixedCVaR(), MixedCVaR(), updateGradient(), updateHessVec(), and updateValue().

◆ prob_

template<class Real>
std::vector<Real> ROL::MixedCVaR< Real >::prob_
private

Definition at line 57 of file ROL_MixedCVaR.hpp.

Referenced by checkInputs(), initializeMCVAR(), MixedCVaR(), MixedCVaR(), updateGradient(), updateHessVec(), and updateValue().

◆ coeff_

template<class Real>
std::vector<Real> ROL::MixedCVaR< Real >::coeff_
private

Definition at line 58 of file ROL_MixedCVaR.hpp.

Referenced by checkInputs(), computeStatistic(), getGradient(), getValue(), MixedCVaR(), MixedCVaR(), updateGradient(), updateHessVec(), and updateValue().

◆ vec_

template<class Real>
std::vector<Real> ROL::MixedCVaR< Real >::vec_
private

Definition at line 59 of file ROL_MixedCVaR.hpp.

Referenced by getGradient(), getHessVec(), initialize(), initializeMCVAR(), updateGradient(), and updateHessVec().

◆ size_

template<class Real>
int ROL::MixedCVaR< Real >::size_
private

Definition at line 60 of file ROL_MixedCVaR.hpp.

Referenced by computeStatistic(), getGradient(), getHessVec(), getValue(), initialize(), initializeMCVAR(), updateGradient(), updateHessVec(), and updateValue().

The documentation for this class was generated from the following file:
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