Provides an interface for the mean plus a sum of arbitrary order variances from targets. More...

#include <ROL_MeanVarianceFromTarget.hpp>

Inheritance diagram for ROL::MeanVarianceFromTarget< Real >:

Public Member Functions
	MeanVarianceFromTarget (const Real target, const Real order, const Real coeff, const ROL::Ptr< PositiveFunction< Real > > &pf)
	Constructor. More...

	MeanVarianceFromTarget (const std::vector< Real > &target, const std::vector< Real > &order, const std::vector< Real > &coeff, const ROL::Ptr< PositiveFunction< Real > > &pf)
	Constructor. More...

	MeanVarianceFromTarget (ROL::ParameterList &parlist)
	Constructor. 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...

Public Member Functions inherited from ROL::RandVarFunctional< Real >
virtual	~RandVarFunctional ()

	RandVarFunctional (void)

	weight_ (0)

void	useStorage (bool storage)

void	useHessVecStorage (bool storage)

virtual void	setStorage (const Ptr< ScalarController< Real >> &value_storage, const Ptr< VectorController< Real >> &gradient_storage)

virtual void	setHessVecStorage (const Ptr< ScalarController< Real >> &gradvec_storage, const Ptr< VectorController< Real >> &hessvec_storage)

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

virtual void	resetStorage (UpdateType type)

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 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...

Private Types
typedef std::vector< Real > ::size_type	uint

Private Member Functions
void	checkInputs (void) const

Private Attributes
ROL::Ptr< PositiveFunction < Real > >	positiveFunction_

std::vector< Real >	target_

std::vector< Real >	order_

std::vector< Real >	coeff_

uint	NumMoments_

Additional Inherited Members
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_

Detailed Description

template<class Real>
class ROL::MeanVarianceFromTarget< Real >

Provides an interface for the mean plus a sum of arbitrary order variances from targets.

The mean plus variances from targets risk measure is

\[ \mathcal{R}(X) = \mathbb{E}[X] + \sum_{k=1}^n c_k \mathbb{E}[\wp(X-t_k)^{p_k}] \]

where \(\wp:\mathbb{R}\to[0,\infty)\) is either the absolute value or \((x)_+ = \max\{0,x\}\), \(c_k > 0\) and \(p_k\in\mathbb{N}\). \(\mathcal{R}\) is law-invariant, but not coherent since it violates positive homogeneity and translation equivariance.

When using derivative-based optimization, the user can provide a smooth approximation of \((\cdot)_+\) using the ROL::PositiveFunction class.

Definition at line 43 of file ROL_MeanVarianceFromTarget.hpp.

Member Typedef Documentation

template<class Real >

typedef std::vector<Real>::size_type ROL::MeanVarianceFromTarget< Real >::uint

private

Definition at line 44 of file ROL_MeanVarianceFromTarget.hpp.

Constructor & Destructor Documentation

template<class Real >

ROL::MeanVarianceFromTarget< Real >::MeanVarianceFromTarget	(	const Real	target,
		const Real	order,
		const Real	coeff,
		const ROL::Ptr< PositiveFunction< Real > > &	pf
	)

inline

Constructor.

Parameters

[in]	target	is the scalar target
[in]	order	is the variance order
[in]	coeff	is the weight for variance term
[in]	pf	is the plus function or an approximation

This constructor produces a mean plus variance from target risk measure with a single variance.

Definition at line 92 of file ROL_MeanVarianceFromTarget.hpp.

References ROL::MeanVarianceFromTarget< Real >::checkInputs(), ROL::MeanVarianceFromTarget< Real >::coeff_, ROL::MeanVarianceFromTarget< Real >::NumMoments_, ROL::MeanVarianceFromTarget< Real >::order_, and ROL::MeanVarianceFromTarget< Real >::target_.

template<class Real >

ROL::MeanVarianceFromTarget< Real >::MeanVarianceFromTarget	(	const std::vector< Real > &	target,
		const std::vector< Real > &	order,
		const std::vector< Real > &	coeff,
		const ROL::Ptr< PositiveFunction< Real > > &	pf
	)

inline

Constructor.

Parameters

[in]	target	is a vector of targets
[in]	order	is a vector of variance orders
[in]	coeff	is a vector of weights for the variance terms
[in]	pf	is the plus function or an approximation

This constructor produces a mean plus variance from target risk measure with an arbitrary number of variances.

Definition at line 112 of file ROL_MeanVarianceFromTarget.hpp.

References ROL::MeanVarianceFromTarget< Real >::checkInputs(), ROL::MeanVarianceFromTarget< Real >::coeff_, ROL::MeanVarianceFromTarget< Real >::NumMoments_, ROL::MeanVarianceFromTarget< Real >::order_, and ROL::MeanVarianceFromTarget< Real >::target_.

template<class Real >

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

inline

Constructor.

Parameters

[in] parlist is a parameter list specifying inputs

parlist should contain sublists "SOL"->"Risk Measure"->"Mean Plus Variance From Target" and within the "Mean Plus Variance From Target" sublist should have the following parameters

"Targets" (array of scalars)
"Orders" (array of unsigned integers)
"Coefficients" (array of positive scalars)
"Deviation Type" (eighter "Upper" or "Absolute")
A sublist for positive function information.

Definition at line 143 of file ROL_MeanVarianceFromTarget.hpp.

References ROL::MeanVarianceFromTarget< Real >::checkInputs(), ROL::MeanVarianceFromTarget< Real >::coeff_, ROL::MeanVarianceFromTarget< Real >::NumMoments_, ROL::MeanVarianceFromTarget< Real >::order_, ROL::MeanVarianceFromTarget< Real >::positiveFunction_, and ROL::MeanVarianceFromTarget< Real >::target_.

Member Function Documentation

template<class Real >

void ROL::MeanVarianceFromTarget< Real >::checkInputs ( void ) const

inlineprivate

Definition at line 66 of file ROL_MeanVarianceFromTarget.hpp.

References ROL::MeanVarianceFromTarget< Real >::coeff_, ROL::MeanVarianceFromTarget< Real >::order_, ROL::MeanVarianceFromTarget< Real >::positiveFunction_, and zero.

Referenced by ROL::MeanVarianceFromTarget< Real >::MeanVarianceFromTarget().

template<class Real >

void ROL::MeanVarianceFromTarget< 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 from ROL::RandVarFunctional< Real >.

Definition at line 169 of file ROL_MeanVarianceFromTarget.hpp.

References ROL::MeanVarianceFromTarget< Real >::coeff_, ROL::RandVarFunctional< Real >::computeValue(), ROL::MeanVarianceFromTarget< Real >::NumMoments_, ROL::MeanVarianceFromTarget< Real >::order_, ROL::MeanVarianceFromTarget< Real >::positiveFunction_, ROL::MeanVarianceFromTarget< Real >::target_, ROL::RandVarFunctional< Real >::val_, and ROL::RandVarFunctional< Real >::weight_.

template<class Real >

void ROL::MeanVarianceFromTarget< 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 from ROL::RandVarFunctional< Real >.

Definition at line 183 of file ROL_MeanVarianceFromTarget.hpp.

References ROL::MeanVarianceFromTarget< Real >::coeff_, ROL::RandVarFunctional< Real >::computeGradient(), ROL::RandVarFunctional< Real >::computeValue(), ROL::RandVarFunctional< Real >::dualVector_, ROL::RandVarFunctional< Real >::g_, ROL::MeanVarianceFromTarget< Real >::NumMoments_, ROL::MeanVarianceFromTarget< Real >::order_, ROL::MeanVarianceFromTarget< Real >::positiveFunction_, ROL::MeanVarianceFromTarget< Real >::target_, and ROL::RandVarFunctional< Real >::weight_.

template<class Real >

void ROL::MeanVarianceFromTarget< 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