ROL
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Provides an interface for the Chebyshev-Spectral risk measure. More...
#include <ROL_ChebyshevSpectral.hpp>
Public Member Functions | |
ChebyshevSpectral (ROL::ParameterList &parlist) | |
Constructor. More... | |
ChebyshevSpectral (const Real lower, const Real upper, const int nQuad, const int wType, const ROL::Ptr< PlusFunction< Real > > &pf) | |
Constructor. More... | |
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 | lower_ |
Real | upper_ |
int | nQuad_ |
int | wType_ |
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 Chebyshev-Spectral risk measure.
The Chebyshev-Spectral risk measure is defined as
\[ \mathcal{R}(X) = \int_{\alpha_0}^{\alpha_1} w(\alpha) \mathrm{CVaR}_{\alpha}(X) \,\mathrm{d}\alpha \]
where \(0\le \alpha_0 < \alpha_1 < 1\) and the conditional value-at-risk (CVaR) with confidence level \(0\le \alpha < 1\) is
\[ \mathrm{CVaR}_\alpha(X) = \inf_{t\in\mathbb{R}} \left\{ t + \frac{1}{1-\alpha} \mathbb{E}\left[(X-t)_+\right] \right\}, \quad (x)_+ = \max\{0,x\}. \]
There are three choices of weight functions \(w\): (i) the first weight function generates the Chebyshev polynomials of the first kind and has the specific form
\[ w(x) = \frac{1}{\sqrt{(x-\alpha_0)(\alpha_1-x)}}; \]
(ii) the second weight function generates the Chebyshev polynomials of the second kind and has the specific form
\[ w(x) = \sqrt{(x-\alpha_0)(\alpha_1-x)}; \]
and (iii) the third weight function is related again to the Chebyshev polynomials of the first kind and has the specific form
\[ w(x) = \sqrt{\frac{x-\alpha_0}{\alpha_1-x}}. \]
As defined, \(\mathcal{R}\) is a law-invariant coherent risk measure.
ROL implements \(\mathcal{R}\) by approximating the integral with the appropriate Gauss-Chebyshev quadrature rule. 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 63 of file ROL_ChebyshevSpectral.hpp.
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Constructor.
[in] | parlist | is a parameter list specifying inputs |
parlist should contain sublists "SOL"->"Risk Measure"->"Chebyshev-Spectral" and the "Chebyshev-Spectral" sublist should have the following parameters
Definition at line 124 of file ROL_ChebyshevSpectral.hpp.
References ROL::ChebyshevSpectral< Real >::checkInputs(), ROL::ChebyshevSpectral< Real >::initializeQuad(), ROL::ChebyshevSpectral< Real >::lower_, ROL::ChebyshevSpectral< Real >::nQuad_, ROL::ChebyshevSpectral< Real >::plusFunction_, ROL::ChebyshevSpectral< Real >::upper_, and ROL::ChebyshevSpectral< Real >::wType_.
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Constructor.
[in] | lower | is the lower confidence level (between 0 and 1) |
[in] | upper | is the upper confidence level (between 0 and 1, greater than lower) |
[in] | nQuad | is the number of quadrature points |
[in] | wType | is the weight type (either 1, 2, or 3) |
[in] | pf | is the plus function or an approximation |
Definition at line 147 of file ROL_ChebyshevSpectral.hpp.
References ROL::ChebyshevSpectral< Real >::checkInputs(), and ROL::ChebyshevSpectral< Real >::initializeQuad().
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Definition at line 74 of file ROL_ChebyshevSpectral.hpp.
References ROL::ChebyshevSpectral< Real >::lower_, ROL::ChebyshevSpectral< Real >::plusFunction_, and ROL::ChebyshevSpectral< Real >::upper_.
Referenced by ROL::ChebyshevSpectral< Real >::ChebyshevSpectral().
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Definition at line 87 of file ROL_ChebyshevSpectral.hpp.
References ROL::SpectralRisk< Real >::buildMixedQuantile(), ROL::ChebyshevSpectral< Real >::lower_, ROL::ChebyshevSpectral< Real >::nQuad_, ROL::ChebyshevSpectral< Real >::plusFunction_, ROL::ChebyshevSpectral< Real >::pts_, ROL::ChebyshevSpectral< Real >::upper_, ROL::ChebyshevSpectral< Real >::wts_, and ROL::ChebyshevSpectral< Real >::wType_.
Referenced by ROL::ChebyshevSpectral< Real >::ChebyshevSpectral().
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Definition at line 65 of file ROL_ChebyshevSpectral.hpp.
Referenced by ROL::ChebyshevSpectral< Real >::ChebyshevSpectral(), ROL::ChebyshevSpectral< Real >::checkInputs(), and ROL::ChebyshevSpectral< Real >::initializeQuad().
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Definition at line 67 of file ROL_ChebyshevSpectral.hpp.
Referenced by ROL::ChebyshevSpectral< Real >::ChebyshevSpectral(), ROL::ChebyshevSpectral< Real >::checkInputs(), and ROL::ChebyshevSpectral< Real >::initializeQuad().
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Definition at line 67 of file ROL_ChebyshevSpectral.hpp.
Referenced by ROL::ChebyshevSpectral< Real >::ChebyshevSpectral(), ROL::ChebyshevSpectral< Real >::checkInputs(), and ROL::ChebyshevSpectral< Real >::initializeQuad().
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Definition at line 68 of file ROL_ChebyshevSpectral.hpp.
Referenced by ROL::ChebyshevSpectral< Real >::ChebyshevSpectral(), and ROL::ChebyshevSpectral< Real >::initializeQuad().
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Definition at line 69 of file ROL_ChebyshevSpectral.hpp.
Referenced by ROL::ChebyshevSpectral< Real >::ChebyshevSpectral(), and ROL::ChebyshevSpectral< Real >::initializeQuad().
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Definition at line 71 of file ROL_ChebyshevSpectral.hpp.
Referenced by ROL::ChebyshevSpectral< Real >::initializeQuad().
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Definition at line 72 of file ROL_ChebyshevSpectral.hpp.
Referenced by ROL::ChebyshevSpectral< Real >::initializeQuad().