ROL
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Provides an interface for the Chebyshev-Kusuoka risk measure. More...
#include <ROL_ChebyshevKusuoka.hpp>
Public Member Functions | |
ChebyshevKusuoka (Teuchos::ParameterList &parlist) | |
Constructor. More... | |
ChebyshevKusuoka (const Real lower, const Real upper, const int nQuad, const int wType, const Teuchos::RCP< PlusFunction< Real > > &pf) | |
Constructor. More... | |
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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 | lower_ |
Real | upper_ |
int | nQuad_ |
int | wType_ |
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 Chebyshev-Kusuoka risk measure.
The Chebyshev-Kusuoka 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 97 of file ROL_ChebyshevKusuoka.hpp.
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Constructor.
[in] | parlist | is a parameter list specifying inputs |
parlist should contain sublists "SOL"->"Risk Measure"->"Chebyshev-Kusuoka" and the "Chebyshev-Kusuoka" sublist should have the following parameters
Definition at line 158 of file ROL_ChebyshevKusuoka.hpp.
References ROL::ChebyshevKusuoka< Real >::checkInputs(), ROL::ChebyshevKusuoka< Real >::initialize(), ROL::ChebyshevKusuoka< Real >::lower_, ROL::ChebyshevKusuoka< Real >::nQuad_, ROL::ChebyshevKusuoka< Real >::plusFunction_, ROL::ChebyshevKusuoka< Real >::upper_, and ROL::ChebyshevKusuoka< 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 181 of file ROL_ChebyshevKusuoka.hpp.
References ROL::ChebyshevKusuoka< Real >::checkInputs(), and ROL::ChebyshevKusuoka< Real >::initialize().
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Definition at line 108 of file ROL_ChebyshevKusuoka.hpp.
References ROL::ChebyshevKusuoka< Real >::lower_, ROL::ChebyshevKusuoka< Real >::plusFunction_, and ROL::ChebyshevKusuoka< Real >::upper_.
Referenced by ROL::ChebyshevKusuoka< Real >::ChebyshevKusuoka().
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Definition at line 121 of file ROL_ChebyshevKusuoka.hpp.
References ROL::SpectralRisk< Real >::buildMixedQuantile(), ROL::ChebyshevKusuoka< Real >::lower_, ROL::ChebyshevKusuoka< Real >::nQuad_, ROL::ChebyshevKusuoka< Real >::plusFunction_, ROL::ChebyshevKusuoka< Real >::pts_, ROL::ChebyshevKusuoka< Real >::upper_, ROL::ChebyshevKusuoka< Real >::wts_, and ROL::ChebyshevKusuoka< Real >::wType_.
Referenced by ROL::ChebyshevKusuoka< Real >::ChebyshevKusuoka().
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Definition at line 99 of file ROL_ChebyshevKusuoka.hpp.
Referenced by ROL::ChebyshevKusuoka< Real >::ChebyshevKusuoka(), ROL::ChebyshevKusuoka< Real >::checkInputs(), and ROL::ChebyshevKusuoka< Real >::initialize().
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Definition at line 101 of file ROL_ChebyshevKusuoka.hpp.
Referenced by ROL::ChebyshevKusuoka< Real >::ChebyshevKusuoka(), ROL::ChebyshevKusuoka< Real >::checkInputs(), and ROL::ChebyshevKusuoka< Real >::initialize().
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Definition at line 101 of file ROL_ChebyshevKusuoka.hpp.
Referenced by ROL::ChebyshevKusuoka< Real >::ChebyshevKusuoka(), ROL::ChebyshevKusuoka< Real >::checkInputs(), and ROL::ChebyshevKusuoka< Real >::initialize().
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Definition at line 102 of file ROL_ChebyshevKusuoka.hpp.
Referenced by ROL::ChebyshevKusuoka< Real >::ChebyshevKusuoka(), and ROL::ChebyshevKusuoka< Real >::initialize().
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Definition at line 103 of file ROL_ChebyshevKusuoka.hpp.
Referenced by ROL::ChebyshevKusuoka< Real >::ChebyshevKusuoka(), and ROL::ChebyshevKusuoka< Real >::initialize().
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Definition at line 105 of file ROL_ChebyshevKusuoka.hpp.
Referenced by ROL::ChebyshevKusuoka< Real >::initialize().
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Definition at line 106 of file ROL_ChebyshevKusuoka.hpp.
Referenced by ROL::ChebyshevKusuoka< Real >::initialize().