ROL
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ROL::SuperQuantileQuadrangle< Real > Class Template Reference

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

#include <ROL_SuperQuantileQuadrangle.hpp>

+ Inheritance diagram for ROL::SuperQuantileQuadrangle< Real >:

Public Member Functions

 SuperQuantileQuadrangle (Teuchos::ParameterList &parlist)
 
 SuperQuantileQuadrangle (const Real alpha, const int nQuad, const Teuchos::RCP< PlusFunction< Real > > &pf, const bool useGauss=true)
 
- Public Member Functions inherited from ROL::SpectralRisk< Real >
 SpectralRisk (void)
 
 SpectralRisk (const Teuchos::RCP< Distribution< Real > > &dist, const int nQuad, const Teuchos::RCP< PlusFunction< Real > > &pf)
 
 SpectralRisk (Teuchos::ParameterList &parlist)
 
 SpectralRisk (const std::vector< Real > &pts, const std::vector< Real > &wts, const Teuchos::RCP< PlusFunction< Real > > &pf)
 
Real computeStatistic (const Vector< Real > &x) const
 
void reset (Teuchos::RCP< Vector< Real > > &x0, const Vector< Real > &x)
 Reset internal risk measure storage. Called for value and gradient computation. More...
 
void reset (Teuchos::RCP< Vector< Real > > &x0, const Vector< Real > &x, Teuchos::RCP< Vector< Real > > &v0, const Vector< Real > &v)
 Reset internal risk measure storage. Called for Hessian-times-a-vector computation. More...
 
void update (const Real val, const Real weight)
 Update internal risk measure storage for value computation. More...
 
void update (const Real val, const Vector< Real > &g, const Real weight)
 Update internal risk measure storage for gradient computation. More...
 
void update (const Real val, const Vector< Real > &g, const Real gv, const Vector< Real > &hv, const Real weight)
 Update internal risk measure storage for Hessian-time-a-vector computation. More...
 
Real getValue (SampleGenerator< Real > &sampler)
 Return risk measure value. More...
 
void getGradient (Vector< Real > &g, SampleGenerator< Real > &sampler)
 Return risk measure (sub)gradient. More...
 
void getHessVec (Vector< Real > &hv, SampleGenerator< Real > &sampler)
 Return risk measure Hessian-times-a-vector. More...
 
- Public Member Functions inherited from ROL::RiskMeasure< Real >
virtual ~RiskMeasure ()
 
 RiskMeasure (void)
 

Private Member Functions

void checkInputs (void) const
 
void initialize (void)
 

Private Attributes

Teuchos::RCP< 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 Teuchos::RCP< PlusFunction< Real > > &pf)
 
void buildQuadFromDist (std::vector< Real > &pts, std::vector< Real > &wts, const int nQuad, const Teuchos::RCP< Distribution< Real > > &dist) const
 
void printQuad (const std::vector< Real > &pts, const std::vector< Real > &wts, const bool print=false) const
 
- Protected Attributes inherited from ROL::RiskMeasure< Real >
Real val_
 
Real gv_
 
Teuchos::RCP< Vector< Real > > g_
 
Teuchos::RCP< Vector< Real > > hv_
 
Teuchos::RCP< Vector< Real > > dualVector_
 
bool firstReset_
 

Detailed Description

template<class Real>
class ROL::SuperQuantileQuadrangle< 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 85 of file ROL_SuperQuantileQuadrangle.hpp.

Constructor & Destructor Documentation

◆ SuperQuantileQuadrangle() [1/2]

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

◆ SuperQuantileQuadrangle() [2/2]

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

Member Function Documentation

◆ checkInputs()

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

◆ initialize()

template<class Real>
void ROL::SuperQuantileQuadrangle< Real >::initialize ( void  )
inlineprivate

Member Data Documentation

◆ plusFunction_

template<class Real>
Teuchos::RCP<PlusFunction<Real> > ROL::SuperQuantileQuadrangle< Real >::plusFunction_
private

◆ alpha_

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

◆ nQuad_

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

◆ useGauss_

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

◆ wts_

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

◆ pts_

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

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