ROL
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Provides an interface for the risk measure associated with the super quantile quadrangle. More...
#include <ROL_SuperQuantileQuadrangle.hpp>
Public Member Functions | |
SuperQuantileQuadrangle (Teuchos::ParameterList &parlist) | |
SuperQuantileQuadrangle (const Real alpha, const int nQuad, const Teuchos::RCP< PlusFunction< Real > > &pf, const bool useGauss=true) | |
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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... | |
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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 | |
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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 |
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Real | val_ |
Real | gv_ |
Teuchos::RCP< Vector< Real > > | g_ |
Teuchos::RCP< Vector< Real > > | hv_ |
Teuchos::RCP< Vector< Real > > | dualVector_ |
bool | firstReset_ |
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.
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Definition at line 126 of file ROL_SuperQuantileQuadrangle.hpp.
References ROL::SuperQuantileQuadrangle< Real >::alpha_, ROL::SuperQuantileQuadrangle< Real >::checkInputs(), ROL::SuperQuantileQuadrangle< Real >::initialize(), ROL::SuperQuantileQuadrangle< Real >::nQuad_, ROL::SuperQuantileQuadrangle< Real >::plusFunction_, and ROL::SuperQuantileQuadrangle< Real >::useGauss_.
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Definition at line 140 of file ROL_SuperQuantileQuadrangle.hpp.
References ROL::SuperQuantileQuadrangle< Real >::checkInputs(), and ROL::SuperQuantileQuadrangle< Real >::initialize().
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Definition at line 96 of file ROL_SuperQuantileQuadrangle.hpp.
References ROL::SuperQuantileQuadrangle< Real >::plusFunction_.
Referenced by ROL::SuperQuantileQuadrangle< Real >::SuperQuantileQuadrangle().
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Definition at line 103 of file ROL_SuperQuantileQuadrangle.hpp.
References ROL::SuperQuantileQuadrangle< Real >::alpha_, ROL::SpectralRisk< Real >::buildMixedQuantile(), ROL::SuperQuantileQuadrangle< Real >::nQuad_, ROL::SuperQuantileQuadrangle< Real >::plusFunction_, ROL::SuperQuantileQuadrangle< Real >::pts_, ROL::SuperQuantileQuadrangle< Real >::useGauss_, and ROL::SuperQuantileQuadrangle< Real >::wts_.
Referenced by ROL::SuperQuantileQuadrangle< Real >::SuperQuantileQuadrangle().
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Definition at line 87 of file ROL_SuperQuantileQuadrangle.hpp.
Referenced by ROL::SuperQuantileQuadrangle< Real >::checkInputs(), ROL::SuperQuantileQuadrangle< Real >::initialize(), and ROL::SuperQuantileQuadrangle< Real >::SuperQuantileQuadrangle().
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Definition at line 89 of file ROL_SuperQuantileQuadrangle.hpp.
Referenced by ROL::SuperQuantileQuadrangle< Real >::initialize(), and ROL::SuperQuantileQuadrangle< Real >::SuperQuantileQuadrangle().
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Definition at line 90 of file ROL_SuperQuantileQuadrangle.hpp.
Referenced by ROL::SuperQuantileQuadrangle< Real >::initialize(), and ROL::SuperQuantileQuadrangle< Real >::SuperQuantileQuadrangle().
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Definition at line 91 of file ROL_SuperQuantileQuadrangle.hpp.
Referenced by ROL::SuperQuantileQuadrangle< Real >::initialize(), and ROL::SuperQuantileQuadrangle< Real >::SuperQuantileQuadrangle().
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Definition at line 93 of file ROL_SuperQuantileQuadrangle.hpp.
Referenced by ROL::SuperQuantileQuadrangle< Real >::initialize().
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Definition at line 94 of file ROL_SuperQuantileQuadrangle.hpp.
Referenced by ROL::SuperQuantileQuadrangle< Real >::initialize().