Provides an interface for spectral risk measures. More...

#include <ROL_SpectralRisk.hpp>

Inheritance diagram for ROL::SpectralRisk< Real >:

Public Member Functions
	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) override
void	setHessVecStorage (const Ptr< ScalarController< Real > > &gradvec_storage, const Ptr< VectorController< Real > > &hessvec_storage) override
void	setSample (const std::vector< Real > &point, const Real weight) override
void	resetStorage (bool flag=true) override
void	resetStorage (UpdateType type) override
void	initialize (const Vector< Real > &x) override
Real	computeStatistic (const Ptr< const std::vector< Real > > &xstat) const override
void	updateValue (Objective< Real > &obj, const Vector< Real > &x, const std::vector< Real > &xstat, Real &tol) override
void	updateGradient (Objective< Real > &obj, const Vector< Real > &x, const std::vector< Real > &xstat, Real &tol) override
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) override
Real	getValue (const Vector< Real > &x, const std::vector< Real > &xstat, SampleGenerator< Real > &sampler) override
void	getGradient (Vector< Real > &g, std::vector< Real > &gstat, const Vector< Real > &x, const std::vector< Real > &xstat, SampleGenerator< Real > &sampler) override
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) override

Protected Member Functions
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

Private Member Functions
void	checkInputs (const ROL::Ptr< Distribution< Real > > &dist=ROL::nullPtr) const

Private Attributes
ROL::Ptr< MixedCVaR< Real > >	mqq_
ROL::Ptr< PlusFunction< Real > >	plusFunction_
std::vector< Real >	wts_
std::vector< Real >	pts_

Detailed Description

template<class Real>
class ROL::SpectralRisk< Real >

Provides an interface for spectral risk measures.

Kusuoka's representation for law-invariant risk measures is

\[ \mathcal{R}(X) = \sup_{\mu\in\mathfrak{M}} \int_0^1 \mathrm{CVaR}_{\alpha}(X)\,\mathrm{d}\mu(\alpha) \]

where the conditional value-at-risk (CVaR) with confidence level \(0\le \alpha < 1\) is

\[ \mathrm{CVaR}_\alpha(X) = \inf_{t\in\mathbb{R}} \left\{ t + \frac{1}{1-\alpha} \mathbb{E}\left[(X-t)_+\right] \right\}, \quad (x)_+ = \max\{0,x\}, \]

and \(\mathfrak{M}\) is a subset of distributions on the interval \([0,1)\). By spectral risk measures, we refer to the case where the set \(\mathfrak{M}\) is a singleton. If the distribution \(\mu\in\mathfrak{M}\) is discrete, then the corresponding risk measure is a mixed quantile quadrangle risk measure.

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-Chebyshev quadrature of the first kind. The corresponding quadrature points and weights are then used to construct a ROL::MixedCVaR risk measure. When using derivative-based optimization, the user can provide a smooth approximation of \((\cdot)_+\) using the ROL::PlusFunction class.

Definition at line 55 of file ROL_SpectralRisk.hpp.

Constructor & Destructor Documentation

◆ SpectralRisk() [1/4]

template<class Real>

ROL::SpectralRisk< Real >::SpectralRisk ( void )

inline

Definition at line 132 of file ROL_SpectralRisk.hpp.

Referenced by ROL::ChebyshevSpectral< Real >::ChebyshevSpectral(), ROL::ChebyshevSpectral< Real >::ChebyshevSpectral(), ROL::SecondOrderCVaR< Real >::SecondOrderCVaR(), and ROL::SecondOrderCVaR< Real >::SecondOrderCVaR().

◆ SpectralRisk() [2/4]

template<class Real>

ROL::SpectralRisk< Real >::SpectralRisk	(	const ROL::Ptr< Distribution< Real > > &	dist,
		const int	nQuad,
		const ROL::Ptr< PlusFunction< Real > > &	pf )

inline

Definition at line 134 of file ROL_SpectralRisk.hpp.

References buildMixedQuantile(), buildQuadFromDist(), and checkInputs().

◆ SpectralRisk() [3/4]

template<class Real>

ROL::SpectralRisk< Real >::SpectralRisk ( ROL::ParameterList & parlist )

inline

Definition at line 147 of file ROL_SpectralRisk.hpp.

References buildMixedQuantile(), buildQuadFromDist(), checkInputs(), ROL::DistributionFactory(), and printQuad().

◆ SpectralRisk() [4/4]

template<class Real>

ROL::SpectralRisk< Real >::SpectralRisk	(	const std::vector< Real > &	pts,
		const std::vector< Real > &	wts,
		const ROL::Ptr< PlusFunction< Real > > &	pf )

inline

Definition at line 168 of file ROL_SpectralRisk.hpp.

References buildMixedQuantile(), and checkInputs().

Member Function Documentation

◆ checkInputs()

template<class Real>

void ROL::SpectralRisk< Real >::checkInputs ( const ROL::Ptr< Distribution< Real > > & dist = ROL::nullPtr ) const

inlineprivate

Definition at line 63 of file ROL_SpectralRisk.hpp.

References plusFunction_.

Referenced by SpectralRisk(), SpectralRisk(), and SpectralRisk().

◆ buildMixedQuantile()

template<class Real>

void ROL::SpectralRisk< Real >::buildMixedQuantile	(	const std::vector< Real > &	pts,
		const std::vector< Real > &	wts,
		const ROL::Ptr< PlusFunction< Real > > &	pf )

inlineprotected

Definition at line 77 of file ROL_SpectralRisk.hpp.

References mqq_, plusFunction_, pts_, and wts_.

Referenced by ROL::ChebyshevSpectral< Real >::initializeQuad(), ROL::SecondOrderCVaR< Real >::initializeQuad(), SpectralRisk(), SpectralRisk(), and SpectralRisk().

◆ buildQuadFromDist()

template<class Real>

void ROL::SpectralRisk< Real >::buildQuadFromDist	(	std::vector< Real > &	pts,
		std::vector< Real > &	wts,
		const int	nQuad,
		const ROL::Ptr< Distribution< Real > > &	dist ) const

inlineprotected

Definition at line 85 of file ROL_SpectralRisk.hpp.

Referenced by SpectralRisk(), and SpectralRisk().

◆ printQuad()

template<class Real>

void ROL::SpectralRisk< Real >::printQuad	(	const std::vector< Real > &	pts,
		const std::vector< Real > &	wts,
		const bool	print = false ) const

inlineprotected

Definition at line 111 of file ROL_SpectralRisk.hpp.

Referenced by SpectralRisk().

◆ setStorage()

template<class Real>

void ROL::SpectralRisk< Real >::setStorage	(	const Ptr< ScalarController< Real > > &	value_storage,
		const Ptr< VectorController< Real > > &	gradient_storage )

inlineoverride

Definition at line 176 of file ROL_SpectralRisk.hpp.

References mqq_.

◆ setHessVecStorage()

template<class Real>

void ROL::SpectralRisk< Real >::setHessVecStorage	(	const Ptr< ScalarController< Real > > &	gradvec_storage,
		const Ptr< VectorController< Real > > &	hessvec_storage )

inlineoverride

Definition at line 182 of file ROL_SpectralRisk.hpp.

References mqq_.

◆ setSample()

template<class Real>

void ROL::SpectralRisk< Real >::setSample	(	const std::vector< Real > &	point,
		const Real	weight )

inlineoverride

Definition at line 188 of file ROL_SpectralRisk.hpp.

References mqq_.

◆ resetStorage() [1/2]

template<class Real>

void ROL::SpectralRisk< Real >::resetStorage ( bool flag = true )

inlineoverride

Definition at line 193 of file ROL_SpectralRisk.hpp.

References mqq_.

◆ resetStorage() [2/2]

template<class Real>

void ROL::SpectralRisk< Real >::resetStorage ( UpdateType type )

inlineoverride

Definition at line 198 of file ROL_SpectralRisk.hpp.

References mqq_.

◆ initialize()

template<class Real>

void ROL::SpectralRisk< Real >::initialize ( const Vector< Real > & x )

inlineoverride

Definition at line 203 of file ROL_SpectralRisk.hpp.

References mqq_.

◆ computeStatistic()

template<class Real>

Real ROL::SpectralRisk< Real >::computeStatistic ( const Ptr< const std::vector< Real > > & xstat ) const

inlineoverride

Definition at line 208 of file ROL_SpectralRisk.hpp.

References mqq_.

◆ updateValue()

template<class Real>

void ROL::SpectralRisk< Real >::updateValue	(	Objective< Real > &	obj,
		const Vector< Real > &	x,
		const std::vector< Real > &	xstat,
		Real &	tol )

inlineoverride

Definition at line 212 of file ROL_SpectralRisk.hpp.

References mqq_.

◆ updateGradient()

template<class Real>

void ROL::SpectralRisk< Real >::updateGradient	(	Objective< Real > &	obj,
		const Vector< Real > &	x,
		const std::vector< Real > &	xstat,
		Real &	tol )

inlineoverride

Definition at line 219 of file ROL_SpectralRisk.hpp.

References mqq_.

◆ updateHessVec()

template<class Real>

void ROL::SpectralRisk< Real >::updateHessVec	(	Objective< Real > &	obj,
		const Vector< Real > &	v,
		const std::vector< Real > &	vstat,
		const Vector< Real > &	x,
		const std::vector< Real > &	xstat,
		Real &	tol )

inlineoverride

Definition at line 226 of file ROL_SpectralRisk.hpp.

References mqq_.

◆ getValue()

template<class Real>

Real ROL::SpectralRisk< Real >::getValue	(	const Vector< Real > &	x,
		const std::vector< Real > &	xstat,
		SampleGenerator< Real > &	sampler )

inlineoverride

Definition at line 235 of file ROL_SpectralRisk.hpp.

References mqq_.

◆ getGradient()

template<class Real>

void ROL::SpectralRisk< Real >::getGradient	(	Vector< Real > &	g,
		std::vector< Real > &	gstat,
		const Vector< Real > &	x,
		const std::vector< Real > &	xstat,
		SampleGenerator< Real > &	sampler )

inlineoverride

Definition at line 241 of file ROL_SpectralRisk.hpp.

References mqq_.

◆ getHessVec()

template<class Real>

void ROL::SpectralRisk< Real >::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 )

inlineoverride

Definition at line 249 of file ROL_SpectralRisk.hpp.

References mqq_.

Member Data Documentation

◆ mqq_

template<class Real>

ROL::Ptr<MixedCVaR<Real> > ROL::SpectralRisk< Real >::mqq_

private

Definition at line 57 of file ROL_SpectralRisk.hpp.

Referenced by buildMixedQuantile(), computeStatistic(), getGradient(), getHessVec(), getValue(), initialize(), resetStorage(), resetStorage(), setHessVecStorage(), setSample(), setStorage(), updateGradient(), updateHessVec(), and updateValue().

◆ plusFunction_

template<class Real>

ROL::Ptr<PlusFunction<Real> > ROL::SpectralRisk< Real >::plusFunction_

private

Definition at line 58 of file ROL_SpectralRisk.hpp.

Referenced by buildMixedQuantile(), and checkInputs().

◆ wts_

template<class Real>

std::vector<Real> ROL::SpectralRisk< Real >::wts_

private

Definition at line 60 of file ROL_SpectralRisk.hpp.

Referenced by buildMixedQuantile().

◆ pts_

template<class Real>

std::vector<Real> ROL::SpectralRisk< Real >::pts_

private

Definition at line 61 of file ROL_SpectralRisk.hpp.

Referenced by buildMixedQuantile().

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

ROL_SpectralRisk.hpp

Public Member Functions

Protected Member Functions

Private Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ SpectralRisk() [1/4]

◆ SpectralRisk() [2/4]

◆ SpectralRisk() [3/4]

◆ SpectralRisk() [4/4]

Member Function Documentation

◆ checkInputs()

◆ buildMixedQuantile()

◆ buildQuadFromDist()

◆ printQuad()

◆ setStorage()

◆ setHessVecStorage()

◆ setSample()

◆ resetStorage() [1/2]

◆ resetStorage() [2/2]

◆ initialize()

◆ computeStatistic()

◆ updateValue()

◆ updateGradient()

◆ updateHessVec()

◆ getValue()

◆ getGradient()

◆ getHessVec()

Member Data Documentation

◆ mqq_

◆ plusFunction_

◆ wts_

◆ pts_