ROL
Public Member Functions | Private Member Functions | Private Attributes | List of all members
ROL::SecondOrderCVaR< Real > Class Template Reference
Algorithmic Extensions » Stochastic Optimization » Risk Measures

Provides an interface for the risk measure associated with the super quantile quadrangle. More...

#include <ROL_SecondOrderCVaR.hpp>

Inheritance diagram for ROL::SecondOrderCVaR< Real >:

Public Member Functions

 SecondOrderCVaR (ROL::ParameterList &parlist)
 SecondOrderCVaR (const Real alpha, const int nQuad, const ROL::Ptr< PlusFunction< Real > > &pf, const bool useGauss=true)
Public Member Functions inherited from ROL::SpectralRisk< Real >
 SpectralRisk (void)
 SpectralRisk (const ROL::Ptr< Distribution< Real > > &dist, const int nQuad, const ROL::Ptr< PlusFunction< Real > > &pf)
 SpectralRisk (ROL::ParameterList &parlist)
 SpectralRisk (const std::vector< Real > &pts, const std::vector< Real > &wts, const ROL::Ptr< PlusFunction< Real > > &pf)
void setStorage (const Ptr< ScalarController< Real > > &value_storage, const Ptr< VectorController< Real > > &gradient_storage) override
void setHessVecStorage (const Ptr< ScalarController< Real > > &gradvec_storage, const Ptr< VectorController< Real > > &hessvec_storage) override
void setSample (const std::vector< Real > &point, const Real weight) override
void resetStorage (bool flag=true) override
void resetStorage (UpdateType type) override
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
void updateGradient (Objective< Real > &obj, const Vector< Real > &x, const std::vector< Real > &xstat, Real &tol) 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
Real getValue (const Vector< Real > &x, const std::vector< Real > &xstat, SampleGenerator< Real > &sampler) override
void getGradient (Vector< Real > &g, std::vector< Real > &gstat, const Vector< Real > &x, const std::vector< Real > &xstat, SampleGenerator< Real > &sampler) 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 checkInputs (void) const
void initializeQuad (void)

Private Attributes

ROL::Ptr< PlusFunction< Real > > plusFunction_
Real alpha_
int nQuad_
bool useGauss_
std::vector< Real > wts_
std::vector< Real > pts_

Additional Inherited Members

Protected Member Functions inherited from ROL::SpectralRisk< Real >
void buildMixedQuantile (const std::vector< Real > &pts, const std::vector< Real > &wts, const ROL::Ptr< PlusFunction< Real > > &pf)
void buildQuadFromDist (std::vector< Real > &pts, std::vector< Real > &wts, const int nQuad, const ROL::Ptr< Distribution< Real > > &dist) const
void printQuad (const std::vector< Real > &pts, const std::vector< Real > &wts, const bool print=false) const

Detailed Description

template<class Real>
class ROL::SecondOrderCVaR< Real >

Provides an interface for the risk measure associated with the super quantile quadrangle.

The risk measure associated with the super quantile quadrangle is defined as

\[ \mathcal{R}(X) = \frac{1}{1-\beta}\int_\beta^1\mathrm{CVaR}_{\alpha}(X) \,\mathrm{d}\alpha \]

where \(0 \le \beta < 1\) and the conditional value-at-risk (CVaR) with confidence level \(0\le \alpha < 1\) is

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

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

ROL implements \(\mathcal{R}\) by approximating the integral with Gauss-Legendre or Fejer 2 quadrature. The corresponding quadrature points and weights are then used to construct a ROL::MixedQuantileQuadrangle risk measure. When using derivative-based optimization, the user can provide a smooth approximation of \((\cdot)_+\) using the ROL::PlusFunction class.

Definition at line 51 of file ROL_SecondOrderCVaR.hpp.

Constructor & Destructor Documentation

◆ SecondOrderCVaR() [1/2]

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

Definition at line 92 of file ROL_SecondOrderCVaR.hpp.

References alpha_, checkInputs(), initializeQuad(), nQuad_, plusFunction_, ROL::SpectralRisk< Real >::SpectralRisk(), and useGauss_.

◆ SecondOrderCVaR() [2/2]

template<class Real>
ROL::SecondOrderCVaR< Real >::SecondOrderCVaR ( const Real alpha,
const int nQuad,
const ROL::Ptr< PlusFunction< Real > > & pf,
const bool useGauss = true )
inline

Definition at line 106 of file ROL_SecondOrderCVaR.hpp.

References alpha_, checkInputs(), initializeQuad(), nQuad_, plusFunction_, ROL::SpectralRisk< Real >::SpectralRisk(), and useGauss_.

Member Function Documentation

◆ checkInputs()

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

Definition at line 62 of file ROL_SecondOrderCVaR.hpp.

References alpha_, and plusFunction_.

Referenced by SecondOrderCVaR(), and SecondOrderCVaR().

◆ initializeQuad()

template<class Real>
void ROL::SecondOrderCVaR< Real >::initializeQuad ( void )
inlineprivate

Definition at line 69 of file ROL_SecondOrderCVaR.hpp.

References alpha_, ROL::SpectralRisk< Real >::buildMixedQuantile(), nQuad_, plusFunction_, pts_, useGauss_, and wts_.

Referenced by SecondOrderCVaR(), and SecondOrderCVaR().

Member Data Documentation

◆ plusFunction_

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

Definition at line 53 of file ROL_SecondOrderCVaR.hpp.

Referenced by checkInputs(), initializeQuad(), SecondOrderCVaR(), and SecondOrderCVaR().

◆ alpha_

template<class Real>
Real ROL::SecondOrderCVaR< Real >::alpha_
private

Definition at line 55 of file ROL_SecondOrderCVaR.hpp.

Referenced by checkInputs(), initializeQuad(), SecondOrderCVaR(), and SecondOrderCVaR().

◆ nQuad_

template<class Real>
int ROL::SecondOrderCVaR< Real >::nQuad_
private

Definition at line 56 of file ROL_SecondOrderCVaR.hpp.

Referenced by initializeQuad(), SecondOrderCVaR(), and SecondOrderCVaR().

◆ useGauss_

template<class Real>
bool ROL::SecondOrderCVaR< Real >::useGauss_
private

Definition at line 57 of file ROL_SecondOrderCVaR.hpp.

Referenced by initializeQuad(), SecondOrderCVaR(), and SecondOrderCVaR().

◆ wts_

template<class Real>
std::vector<Real> ROL::SecondOrderCVaR< Real >::wts_
private

Definition at line 59 of file ROL_SecondOrderCVaR.hpp.

Referenced by initializeQuad().

◆ pts_

template<class Real>
std::vector<Real> ROL::SecondOrderCVaR< Real >::pts_
private

Definition at line 60 of file ROL_SecondOrderCVaR.hpp.

Referenced by initializeQuad().

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