ROL
Public Member Functions | Private Member Functions | Private Attributes | List of all members
ROL::SecondOrderCVaR< Real > Class Template Reference

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)
 
void setHessVecStorage (const Ptr< ScalarController< Real >> &gradvec_storage, const Ptr< VectorController< Real >> &hessvec_storage)
 
void setSample (const std::vector< Real > &point, const Real weight)
 
void resetStorage (bool flag=true)
 Reset internal storage. More...
 
void resetStorage (UpdateType type)
 
void initialize (const Vector< Real > &x)
 Initialize temporary variables. More...
 
Real computeStatistic (const Ptr< const std::vector< Real >> &xstat) const override
 Compute statistic. More...
 
void updateValue (Objective< Real > &obj, const Vector< Real > &x, const std::vector< Real > &xstat, Real &tol)
 Update internal storage for value computation. More...
 
void updateGradient (Objective< Real > &obj, const Vector< Real > &x, const std::vector< Real > &xstat, Real &tol)
 Update internal risk measure storage for gradient computation. More...
 
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)
 Update internal risk measure storage for Hessian-time-a-vector computation. More...
 
Real getValue (const Vector< Real > &x, const std::vector< Real > &xstat, SampleGenerator< Real > &sampler)
 Return risk measure value. More...
 
void getGradient (Vector< Real > &g, std::vector< Real > &gstat, const Vector< Real > &x, const std::vector< Real > &xstat, SampleGenerator< Real > &sampler)
 Return risk measure (sub)gradient. More...
 
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)
 Return risk measure Hessian-times-a-vector. More...
 
- Public Member Functions inherited from ROL::RandVarFunctional< Real >
virtual ~RandVarFunctional ()
 
 RandVarFunctional (void)
 
 weight_ (0)
 
void useStorage (bool storage)
 
void useHessVecStorage (bool storage)
 

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
 
- Protected Member Functions inherited from ROL::RandVarFunctional< Real >
Real computeValue (Objective< Real > &obj, const Vector< Real > &x, Real &tol)
 
void computeGradient (Vector< Real > &g, Objective< Real > &obj, const Vector< Real > &x, Real &tol)
 
Real computeGradVec (Vector< Real > &g, Objective< Real > &obj, const Vector< Real > &v, const Vector< Real > &x, Real &tol)
 
void computeHessVec (Vector< Real > &hv, Objective< Real > &obj, const Vector< Real > &v, const Vector< Real > &x, Real &tol)
 
- Protected Attributes inherited from ROL::RandVarFunctional< Real >
Real val_
 
Real gv_
 
Ptr< Vector< Real > > g_
 
Ptr< Vector< Real > > hv_
 
Ptr< Vector< Real > > dualVector_
 
bool firstReset_
 
std::vector< Real > point_
 
Real weight_
 

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

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

Member Function Documentation

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

Member Data Documentation

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

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