Provides the interface to implement any functional that maps a random variable to a (extended) real number. More...

#include <ROL_RandVarFunctional.hpp>

Inheritance diagram for ROL::RandVarFunctional< Real >:

Public Member Functions
virtual	~RandVarFunctional ()

	RandVarFunctional (void)

	weight_ (0)

void	useStorage (bool storage)

void	useHessVecStorage (bool storage)

virtual void	setStorage (const Ptr< SampledScalar< Real >> &value_storage, const Ptr< SampledVector< Real >> &gradient_storage)

virtual void	setHessVecStorage (const Ptr< SampledScalar< Real >> &gradvec_storage, const Ptr< SampledVector< Real >> &hessvec_storage)

virtual void	resetStorage (bool flag=true)
	Reset internal storage. More...

virtual void	initialize (const Vector< Real > &x)
	Initialize temporary variables. More...

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

virtual Real	computeStatistic (const Ptr< const std::vector< Real >> &xstat) const
	Compute statistic. More...

virtual void	updateValue (Objective< Real > &obj, const Vector< Real > &x, const std::vector< Real > &xstat, Real &tol)
	Update internal storage for value computation. More...

virtual 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...

virtual 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...

virtual Real	getValue (const Vector< Real > &x, const std::vector< Real > &xstat, SampleGenerator< Real > &sampler)
	Return risk measure value. More...

virtual 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...

virtual 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...

Protected Member Functions
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
Real	val_

Real	gv_

Ptr< Vector< Real > >	g_

Ptr< Vector< Real > >	hv_

Ptr< Vector< Real > >	dualVector_

bool	firstReset_

std::vector< Real >	point_

Real	weight_

Private Attributes
bool	storage_

bool	storage_hessvec_

Ptr< SampledScalar< Real > >	value_storage_

Ptr< SampledVector< Real > >	gradient_storage_

Ptr< SampledScalar< Real > >	gradvec_storage_

Ptr< SampledVector< Real > >	hessvec_storage_

Detailed Description

template<class Real>
class ROL::RandVarFunctional< Real >

Provides the interface to implement any functional that maps a random variable to a (extended) real number.

Let \((\Omega,\mathcal{F},\mathbb{P})\) be a probability space. Here, \(\Omega\) is the set of outcomes, \(\mathcal{F}\subseteq 2^\Omega\) is a \(\sigma\)-algebra of events and \(\mathbb{P}:\mathcal{F}\to[0,1]\) is a probability measure. Moreover, let \(\mathcal{X}\) be a class of random variables. A ``random variable functional'' is an extended real-valued functional that associates numerical values to random variables, i.e., \(\mathcal{R}:\mathcal{X}\to\mathbb{R}\cup\{+\infty\}\). In most cases, \(\mathcal{X} = L^p(\Omega,\mathcal{F},\mathbb{P})\) for some \(1\le p\le \infty\).

ROL's random variable functional base class is written in a way to exploit parallel sampling. General risk measures may depend on global information such as the expected value of a random variable, \(\mathbb{E}[X]\). Thus, ROL::RandVarFunctional contains functions to update intermediate information and to compute desired quantities such as values, gradients and Hessians applied to vectors.

Definition at line 79 of file ROL_RandVarFunctional.hpp.

Constructor & Destructor Documentation

template<class Real >

virtual ROL::RandVarFunctional< Real >::~RandVarFunctional ( )

inlinevirtual

Definition at line 170 of file ROL_RandVarFunctional.hpp.

template<class Real >

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

inline

Definition at line 172 of file ROL_RandVarFunctional.hpp.

Member Function Documentation

template<class Real >

Real ROL::RandVarFunctional< Real >::computeValue	(	Objective< Real > &	obj,
		const Vector< Real > &	x,
		Real &	tol
	)

inlineprotected

Definition at line 100 of file ROL_RandVarFunctional.hpp.

References ROL::RandVarFunctional< Real >::point_, ROL::Objective< Real >::setParameter(), ROL::RandVarFunctional< Real >::storage_, ROL::Objective< Real >::value(), and ROL::RandVarFunctional< Real >::value_storage_.

template<class Real >

void ROL::RandVarFunctional< Real >::computeGradient	(	Vector< Real > &	g,
		Objective< Real > &	obj,
		const Vector< Real > &	x,
		Real &	tol
	)

inlineprotected

Definition at line 118 of file ROL_RandVarFunctional.hpp.

References ROL::Objective< Real >::gradient(), ROL::RandVarFunctional< Real >::gradient_storage_, ROL::RandVarFunctional< Real >::point_, ROL::Objective< Real >::setParameter(), and ROL::RandVarFunctional< Real >::storage_.

template<class Real >

Real ROL::RandVarFunctional< Real >::computeGradVec	(	Vector< Real > &	g,
		Objective< Real > &	obj,
		const Vector< Real > &	v,
		const Vector< Real > &	x,
		Real &	tol
	)

inlineprotected

Definition at line 134 of file ROL_RandVarFunctional.hpp.

References ROL::RandVarFunctional< Real >::computeGradient(), ROL::Vector< Real >::dot(), ROL::Vector< Real >::dual(), ROL::RandVarFunctional< Real >::gradvec_storage_, ROL::RandVarFunctional< Real >::point_, and ROL::RandVarFunctional< Real >::storage_hessvec_.

template<class Real >

void ROL::RandVarFunctional< Real >::computeHessVec	(	Vector< Real > &	hv,
		Objective< Real > &	obj,
		const Vector< Real > &	v,
		const Vector< Real > &	x,
		Real &	tol
	)

inlineprotected

Definition at line 153 of file ROL_RandVarFunctional.hpp.

References ROL::Objective< Real >::hessVec(), ROL::RandVarFunctional< Real >::hessvec_storage_, ROL::RandVarFunctional< Real >::point_, ROL::Objective< Real >::setParameter(), and ROL::RandVarFunctional< Real >::storage_hessvec_.

template<class Real >

ROL::RandVarFunctional< Real >::weight_ ( 0 )

inline

Definition at line 178 of file ROL_RandVarFunctional.hpp.

template<class Real >

void ROL::RandVarFunctional< Real >::useStorage ( bool storage )

inline

Definition at line 180 of file ROL_RandVarFunctional.hpp.

References ROL::RandVarFunctional< Real >::gradient_storage_, ROL::RandVarFunctional< Real >::storage_, and ROL::RandVarFunctional< Real >::value_storage_.

Referenced by ROL::RandVarFunctional< Real >::setStorage(), and ROL::RandVarFunctional< Real >::useHessVecStorage().

template<class Real >

void ROL::RandVarFunctional< Real >::useHessVecStorage ( bool storage )

inline

Definition at line 192 of file ROL_RandVarFunctional.hpp.

References ROL::RandVarFunctional< Real >::gradvec_storage_, ROL::RandVarFunctional< Real >::hessvec_storage_, ROL::RandVarFunctional< Real >::storage_hessvec_, and ROL::RandVarFunctional< Real >::useStorage().

Referenced by ROL::RandVarFunctional< Real >::setHessVecStorage().

template<class Real >

virtual void ROL::RandVarFunctional< Real >::setStorage	(	const Ptr< SampledScalar< Real >> &	value_storage,
		const Ptr< SampledVector< Real >> &	gradient_storage
	)

inlinevirtual

Reimplemented in ROL::MeanDeviation< Real >, ROL::SpectralRisk< Real >, ROL::MeanVariance< Real >, and ROL::MeanSemiDeviation< Real >.

Definition at line 205 of file ROL_RandVarFunctional.hpp.

References ROL::RandVarFunctional< Real >::gradient_storage_, ROL::RandVarFunctional< Real >::useStorage(), and ROL::RandVarFunctional< Real >::value_storage_.

Referenced by ROL::ConvexCombinationRiskMeasure< Real >::initializeCCRM(), ROL::MeanVariance< Real >::initializeMV(), ROL::MeanSemiDeviation< Real >::initializeStorage(), ROL::MeanDeviation< Real >::initializeStorage(), ROL::MeanSemiDeviation< Real >::setStorage(), ROL::MeanVariance< Real >::setStorage(), ROL::SpectralRisk< Real >::setStorage(), and ROL::MeanDeviation< Real >::setStorage().

template<class Real >

virtual void ROL::RandVarFunctional< Real >::setHessVecStorage	(	const Ptr< SampledScalar< Real >> &	gradvec_storage,
		const Ptr< SampledVector< Real >> &	hessvec_storage
	)

inlinevirtual

Reimplemented in ROL::MeanDeviation< Real >, ROL::SpectralRisk< Real >, ROL::MeanVariance< Real >, and ROL::MeanSemiDeviation< Real >.

Definition at line 212 of file ROL_RandVarFunctional.hpp.

References ROL::RandVarFunctional< Real >::gradvec_storage_, ROL::RandVarFunctional< Real >::hessvec_storage_, and ROL::RandVarFunctional< Real >::useHessVecStorage().

Referenced by ROL::ConvexCombinationRiskMeasure< Real >::initializeCCRM(), ROL::MeanVariance< Real >::initializeMV(), ROL::MeanSemiDeviation< Real >::initializeStorage(), ROL::MeanDeviation< Real >::initializeStorage(), ROL::MeanSemiDeviation< Real >::setHessVecStorage(), ROL::MeanVariance< Real >::setHessVecStorage(), ROL::SpectralRisk< Real >::setHessVecStorage(), and ROL::MeanDeviation< Real >::setHessVecStorage().

template<class Real >

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

inlinevirtual

Reset internal storage.

Parameters

[in] x is a vector used for initializing storage

Reimplemented in ROL::SpectralRisk< Real >, and ROL::ConvexCombinationRiskMeasure< Real >.

Definition at line 223 of file ROL_RandVarFunctional.hpp.

References ROL::RandVarFunctional< Real >::gradient_storage_, ROL::RandVarFunctional< Real >::gradvec_storage_, ROL::RandVarFunctional< Real >::hessvec_storage_, ROL::RandVarFunctional< Real >::storage_, ROL::RandVarFunctional< Real >::storage_hessvec_, and ROL::RandVarFunctional< Real >::value_storage_.

Referenced by ROL::ConvexCombinationRiskMeasure< Real >::resetStorage(), and ROL::SpectralRisk< Real >::resetStorage().

template<class Real >

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

inlinevirtual

Initialize temporary variables.

Parameters

[in] x is a vector used for initializing storage

Reimplemented in ROL::MeanDeviation< Real >, ROL::SpectralRisk< Real >, ROL::MeanDeviationFromTarget< Real >, ROL::FDivergence< Real >, ROL::HMCR< Real >, ROL::ConvexCombinationRiskMeasure< Real >, ROL::MeanSemiDeviation< Real >, ROL::MixedCVaR< Real >, ROL::KLDivergence< Real >, ROL::QuantileRadius< Real >, ROL::BPOE< Real >, and ROL::CoherentEntropicRisk< Real >.

Definition at line 240 of file ROL_RandVarFunctional.hpp.

References ROL::Vector< Real >::dual(), ROL::RandVarFunctional< Real >::dualVector_, ROL::RandVarFunctional< Real >::firstReset_, ROL::RandVarFunctional< Real >::g_, ROL::RandVarFunctional< Real >::gradvec_storage_, ROL::RandVarFunctional< Real >::gv_, ROL::RandVarFunctional< Real >::hessvec_storage_, ROL::RandVarFunctional< Real >::hv_, ROL::RandVarFunctional< Real >::storage_hessvec_, ROL::RandVarFunctional< Real >::val_, and zero.

template<class Real >

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

inlinevirtual

Reimplemented in ROL::SpectralRisk< Real >, and ROL::ConvexCombinationRiskMeasure< Real >.

Definition at line 258 of file ROL_RandVarFunctional.hpp.

References ROL::RandVarFunctional< Real >::point_, and ROL::RandVarFunctional< Real >::weight_.

Referenced by ROL::ConvexCombinationRiskMeasure< Real >::setSample(), and ROL::SpectralRisk< Real >::setSample().

template<class Real >

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

inlinevirtual

Compute statistic.

Parameters

[in] xstat is a ROL::Ptr to a std::vector containing the statistic vector

Definition at line 268 of file ROL_RandVarFunctional.hpp.

template<class Real >

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

inlinevirtual

Update internal storage for value computation.

Parameters

[in]	val	is the value of the random variable objective function at the current sample point
[in]	weight	is the weight associated with the current sample point

Reimplemented in ROL::MeanDeviation< Real >, ROL::SpectralRisk< Real >, ROL::MeanDeviationFromTarget< Real >, ROL::MeanVariance< Real >, ROL::FDivergence< Real >, ROL::MeanVarianceFromTarget< Real >, ROL::HMCR< Real >, ROL::ConvexCombinationRiskMeasure< Real >, ROL::MeanSemiDeviation< Real >, ROL::MixedCVaR< Real >, ROL::KLDivergence< Real >, ROL::CVaR< Real >, ROL::MeanSemiDeviationFromTarget< Real >, ROL::QuantileRadius< Real >, ROL::ExpectationQuadDeviation< Real >, ROL::ExpectationQuadError< Real >, ROL::ExpectationQuadRegret< Real >, ROL::ExpectationQuadRisk< Real >, ROL::EntropicRisk< Real >, ROL::BPOE< Real >, ROL::SmoothedPOE< Real >, and ROL::CoherentEntropicRisk< Real >.

Definition at line 283 of file ROL_RandVarFunctional.hpp.

References ROL::RandVarFunctional< Real >::computeValue(), ROL::RandVarFunctional< Real >::val_, and ROL::RandVarFunctional< Real >::weight_.

template<class Real >

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

inlinevirtual

Update internal risk measure storage for gradient computation.

Parameters

[in]	val	is the value of the random variable objective function at the current sample point
[in]	g	is the gradient of the random variable objective function at the current sample point
[in]	weight	is the weight associated with the current sample point

Reimplemented in ROL::MeanDeviation< Real >, ROL::MeanDeviationFromTarget< Real >, ROL::SpectralRisk< Real >, ROL::MeanVariance< Real >, ROL::FDivergence< Real >, ROL::MeanVarianceFromTarget< Real >, ROL::HMCR< Real >, ROL::ConvexCombinationRiskMeasure< Real >, ROL::MeanSemiDeviation< Real >, ROL::MixedCVaR< Real >, ROL::KLDivergence< Real >, ROL::CVaR< Real >, ROL::MeanSemiDeviationFromTarget< Real >, ROL::QuantileRadius< Real >, ROL::BPOE< Real >, ROL::SmoothedPOE< Real >, ROL::EntropicRisk< Real >, ROL::ExpectationQuadDeviation< Real >, ROL::ExpectationQuadRisk< Real >, ROL::ExpectationQuadError< Real >, ROL::ExpectationQuadRegret< Real >, and ROL::CoherentEntropicRisk< Real >.

Definition at line 300 of file ROL_RandVarFunctional.hpp.

References ROL::RandVarFunctional< Real >::computeGradient(), ROL::RandVarFunctional< Real >::dualVector_, ROL::RandVarFunctional< Real >::g_, and ROL::RandVarFunctional< Real >::weight_.

template<class Real >

virtual void ROL::RandVarFunctional< 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
	)

inlinevirtual

Update internal risk measure storage for Hessian-time-a-vector computation.

Parameters

[in]	val	is the value of the random variable objective function at the current sample point
[in]	g	is the gradient of the random variable objective function at the current sample point
[in]	gv	is the gradient of the random variable objective function at the current sample point applied to the vector v0
[in]	hv	is the Hessian of the random variable objective function at the current sample point applied to the vector v0
[in]	weight	is the weight associated with the current sample point

Reimplemented in ROL::MeanDeviationFromTarget< Real >, ROL::MeanDeviation< Real >, ROL::MeanVariance< Real >, ROL::FDivergence< Real >, ROL::HMCR< Real >, ROL::SpectralRisk< Real >, ROL::ConvexCombinationRiskMeasure< Real >, ROL::MeanSemiDeviation< Real >, ROL::MeanVarianceFromTarget< Real >, ROL::MixedCVaR< Real >, ROL::KLDivergence< Real >, ROL::BPOE< Real >, ROL::QuantileRadius< Real >, ROL::CVaR< Real >, ROL::MeanSemiDeviationFromTarget< Real >, ROL::SmoothedPOE< Real >, ROL::EntropicRisk< Real >, ROL::CoherentEntropicRisk< Real >, ROL::ExpectationQuadDeviation< Real >, ROL::ExpectationQuadRisk< Real >, ROL::ExpectationQuadError< Real >, and ROL::ExpectationQuadRegret< Real >.

Definition at line 323 of file ROL_RandVarFunctional.hpp.

References ROL::RandVarFunctional< Real >::computeHessVec(), ROL::RandVarFunctional< Real >::dualVector_, ROL::RandVarFunctional< Real >::hv_, and ROL::RandVarFunctional< Real >::weight_.

template<class Real >

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

inlinevirtual

Return risk measure value.

Parameters

[in] sampler is the ROL::SampleGenerator used to sample the objective function

Upon return, getValue returns \(\mathcal{R}(f(x_0))\) where \(f(x_0)\) denotes the random variable objective function evaluated at \(x_0\).

Reimplemented in ROL::MeanDeviation< Real >, ROL::SpectralRisk< Real >, ROL::MeanDeviationFromTarget< Real >, ROL::MeanVariance< Real >, ROL::FDivergence< Real >, ROL::HMCR< Real >, ROL::CVaR< Real >, ROL::ConvexCombinationRiskMeasure< Real >, ROL::MixedCVaR< Real >, ROL::MeanSemiDeviation< Real >, ROL::KLDivergence< Real >, ROL::ExpectationQuadDeviation< Real >, ROL::ExpectationQuadRisk< Real >, ROL::ExpectationQuadError< Real >, ROL::ExpectationQuadRegret< Real >, ROL::MeanSemiDeviationFromTarget< Real >, ROL::QuantileRadius< Real >, ROL::BPOE< Real >, ROL::SmoothedPOE< Real >, ROL::EntropicRisk< Real >, and ROL::CoherentEntropicRisk< Real >.

Definition at line 341 of file ROL_RandVarFunctional.hpp.

References ROL::SampleGenerator< Real >::sumAll(), and ROL::RandVarFunctional< Real >::val_.

template<class Real >

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

inlinevirtual

Return risk measure (sub)gradient.

Parameters

[out]	g	is the (sub)gradient of the risk measure
[in]	sampler	is the ROL::SampleGenerator used to sample the objective function

Upon return, getGradient returns \(\theta\in\partial\mathcal{R}(f(x_0))\) where \(f(x_0)\) denotes the random variable objective function evaluated at \(x_0\) and \(\partial\mathcal{R}(X)\) denotes the subdifferential of \(\mathcal{R}\) at \(X\).

Reimplemented in ROL::MeanDeviation< Real >, ROL::MeanDeviationFromTarget< Real >, ROL::SpectralRisk< Real >, ROL::MeanVariance< Real >, ROL::FDivergence< Real >, ROL::HMCR< Real >, ROL::ConvexCombinationRiskMeasure< Real >, ROL::MixedCVaR< Real >, ROL::MeanSemiDeviation< Real >, ROL::CVaR< Real >, ROL::KLDivergence< Real >, ROL::ExpectationQuadRisk< Real >, ROL::ExpectationQuadDeviation< Real >, ROL::ExpectationQuadError< Real >, ROL::ExpectationQuadRegret< Real >, ROL::MeanSemiDeviationFromTarget< Real >, ROL::QuantileRadius< Real >, ROL::BPOE< Real >, ROL::SmoothedPOE< Real >, ROL::EntropicRisk< Real >, and ROL::CoherentEntropicRisk< Real >.

Definition at line 360 of file ROL_RandVarFunctional.hpp.

References ROL::RandVarFunctional< Real >::g_, and ROL::SampleGenerator< Real >::sumAll().

template<class Real >

virtual void ROL::RandVarFunctional< 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
	)

inlinevirtual

Return risk measure Hessian-times-a-vector.

Parameters

[out]	hv	is the Hessian-times-a-vector of the risk measure
[in]	sampler	is the ROL::SampleGenerator used to sample the objective function

Upon return, getHessVec returns \(\nabla^2 \mathcal{R}(f(x_0))v_0\) (if available) where \(f(x_0)\) denotes the random variable objective function evaluated at \(x_0\).

Reimplemented in ROL::MeanDeviation< Real >, ROL::MeanDeviationFromTarget< Real >, ROL::MeanVariance< Real >, ROL::HMCR< Real >, ROL::FDivergence< Real >, ROL::SpectralRisk< Real >, ROL::ConvexCombinationRiskMeasure< Real >, ROL::MeanSemiDeviation< Real >, ROL::MixedCVaR< Real >, ROL::KLDivergence< Real >, ROL::CVaR< Real >, ROL::BPOE< Real >, ROL::QuantileRadius< Real >, ROL::MeanSemiDeviationFromTarget< Real >, ROL::ExpectationQuadRisk< Real >, ROL::ExpectationQuadDeviation< Real >, ROL::SmoothedPOE< Real >, ROL::ExpectationQuadError< Real >, ROL::ExpectationQuadRegret< Real >, ROL::EntropicRisk< Real >, and ROL::CoherentEntropicRisk< Real >.