ROL
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Provides an interface for the risk measure associated with the super quantile quadrangle. More...
#include <ROL_SecondOrderCVaR.hpp>
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_ |
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.
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Definition at line 92 of file ROL_SecondOrderCVaR.hpp.
References ROL::SecondOrderCVaR< Real >::alpha_, ROL::SecondOrderCVaR< Real >::checkInputs(), ROL::SecondOrderCVaR< Real >::initializeQuad(), ROL::SecondOrderCVaR< Real >::nQuad_, ROL::SecondOrderCVaR< Real >::plusFunction_, and ROL::SecondOrderCVaR< Real >::useGauss_.
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Definition at line 106 of file ROL_SecondOrderCVaR.hpp.
References ROL::SecondOrderCVaR< Real >::checkInputs(), and ROL::SecondOrderCVaR< Real >::initializeQuad().
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Definition at line 62 of file ROL_SecondOrderCVaR.hpp.
References ROL::SecondOrderCVaR< Real >::plusFunction_.
Referenced by ROL::SecondOrderCVaR< Real >::SecondOrderCVaR().
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Definition at line 69 of file ROL_SecondOrderCVaR.hpp.
References ROL::SecondOrderCVaR< Real >::alpha_, ROL::SpectralRisk< Real >::buildMixedQuantile(), ROL::SecondOrderCVaR< Real >::nQuad_, ROL::SecondOrderCVaR< Real >::plusFunction_, ROL::SecondOrderCVaR< Real >::pts_, ROL::SecondOrderCVaR< Real >::useGauss_, and ROL::SecondOrderCVaR< Real >::wts_.
Referenced by ROL::SecondOrderCVaR< Real >::SecondOrderCVaR().
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Definition at line 53 of file ROL_SecondOrderCVaR.hpp.
Referenced by ROL::SecondOrderCVaR< Real >::checkInputs(), ROL::SecondOrderCVaR< Real >::initializeQuad(), and ROL::SecondOrderCVaR< Real >::SecondOrderCVaR().
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Definition at line 55 of file ROL_SecondOrderCVaR.hpp.
Referenced by ROL::SecondOrderCVaR< Real >::initializeQuad(), and ROL::SecondOrderCVaR< Real >::SecondOrderCVaR().
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Definition at line 56 of file ROL_SecondOrderCVaR.hpp.
Referenced by ROL::SecondOrderCVaR< Real >::initializeQuad(), and ROL::SecondOrderCVaR< Real >::SecondOrderCVaR().
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Definition at line 57 of file ROL_SecondOrderCVaR.hpp.
Referenced by ROL::SecondOrderCVaR< Real >::initializeQuad(), and ROL::SecondOrderCVaR< Real >::SecondOrderCVaR().
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Definition at line 59 of file ROL_SecondOrderCVaR.hpp.
Referenced by ROL::SecondOrderCVaR< Real >::initializeQuad().
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Definition at line 60 of file ROL_SecondOrderCVaR.hpp.
Referenced by ROL::SecondOrderCVaR< Real >::initializeQuad().