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

#include <ROL_MeanVariance.hpp>

Inheritance diagram for ROL::MeanVariance< Real >:

Public Member Functions
	MeanVariance (const Real order, const Real coeff, const Ptr< PositiveFunction< Real > > &pf)
	Constructor. More...

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

	MeanVariance (ROL::ParameterList &parlist)
	Constructor. More...

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

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

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

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

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)

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...

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

Private Member Functions
void	initializeMV (void)

void	checkInputs (void)

Private Attributes
Ptr< PositiveFunction< Real > >	positiveFunction_

std::vector< Real >	order_

std::vector< Real >	coeff_

uint	NumMoments_

Ptr< SampledScalar< Real > >	values_

Ptr< SampledScalar< Real > >	gradvecs_

Ptr< SampledVector< Real > >	gradients_

Ptr< SampledVector< Real > >	hessvecs_

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::MeanVariance< Real >

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

The mean plus variances risk measure is

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

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. When \(\wp(x) = |x|\), \(\mathcal{R}\) also violates monotonicity.

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

Definition at line 78 of file ROL_MeanVariance.hpp.

Member Typedef Documentation

template<class Real >

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

private

Definition at line 79 of file ROL_MeanVariance.hpp.

Constructor & Destructor Documentation

template<class Real >

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

inline

Constructor.

Parameters

[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 risk measure with a single variance.

Definition at line 141 of file ROL_MeanVariance.hpp.

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

template<class Real >

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

inline

Constructor.

Parameters

[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 risk measure with an arbitrary number of variances.

Definition at line 159 of file ROL_MeanVariance.hpp.

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

template<class Real >

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

inline

Constructor.

Parameters

[in] parlist is a parameter list specifying inputs

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

"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 185 of file ROL_MeanVariance.hpp.

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

Member Function Documentation

template<class Real >

void ROL::MeanVariance< Real >::initializeMV ( void )

inlineprivate

Definition at line 105 of file ROL_MeanVariance.hpp.

References ROL::MeanVariance< Real >::gradients_, ROL::MeanVariance< Real >::gradvecs_, ROL::MeanVariance< Real >::hessvecs_, ROL::RandVarFunctional< Real >::setHessVecStorage(), ROL::RandVarFunctional< Real >::setStorage(), and ROL::MeanVariance< Real >::values_.

Referenced by ROL::MeanVariance< Real >::checkInputs().

template<class Real >

void ROL::MeanVariance< Real >::checkInputs ( void )

inlineprivate

Definition at line 115 of file ROL_MeanVariance.hpp.

References ROL::MeanVariance< Real >::coeff_, ROL::MeanVariance< Real >::initializeMV(), ROL::MeanVariance< Real >::order_, ROL::MeanVariance< Real >::positiveFunction_, and zero.

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

template<class Real >

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

inlinevirtual

Reimplemented from ROL::RandVarFunctional< Real >.

Definition at line 209 of file ROL_MeanVariance.hpp.

References ROL::MeanVariance< Real >::gradients_, ROL::RandVarFunctional< Real >::setStorage(), and ROL::MeanVariance< Real >::values_.

template<class Real >

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

inlinevirtual

Reimplemented from ROL::RandVarFunctional< Real >.

Definition at line 216 of file ROL_MeanVariance.hpp.

References ROL::MeanVariance< Real >::gradvecs_, ROL::MeanVariance< Real >::hessvecs_, and ROL::RandVarFunctional< Real >::setHessVecStorage().

template<class Real >

void ROL::MeanVariance< 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 223 of file ROL_MeanVariance.hpp.

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

template<class Real >

Real ROL::MeanVariance< 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 from ROL::RandVarFunctional< Real >.

Definition at line 231 of file ROL_MeanVariance.hpp.

References ROL::MeanVariance< Real >::coeff_, ROL::SampleGenerator< Real >::getMyPoint(), ROL::SampleGenerator< Real >::getMyWeight(), ROL::MeanVariance< Real >::NumMoments_, ROL::SampleGenerator< Real >::numMySamples(), ROL::MeanVariance< Real >::order_, ROL::MeanVariance< Real >::positiveFunction_, ROL::SampleGenerator< Real >::start(), ROL::SampleGenerator< Real >::sumAll(), ROL::RandVarFunctional< Real >::val_, and ROL::MeanVariance< Real >::values_.

template<class Real >

void ROL::MeanVariance< 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 253 of file ROL_MeanVariance.hpp.

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

template<class Real >

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

Definition at line 263 of file ROL_MeanVariance.hpp.

References ROL::MeanVariance< Real >::coeff_, ROL::RandVarFunctional< Real >::dualVector_, ROL::RandVarFunctional< Real >::g_, ROL::SampleGenerator< Real >::getMyPoint(), ROL::SampleGenerator< Real >::getMyWeight(), ROL::MeanVariance< Real >::gradients_, ROL::MeanVariance< Real >::NumMoments_, ROL::SampleGenerator< Real >::numMySamples(), ROL::MeanVariance< Real >::order_, ROL::Vector< Real >::plus(), ROL::MeanVariance< Real >::positiveFunction_, ROL::Vector< Real >::scale(), ROL::SampleGenerator< Real >::start(), ROL::SampleGenerator< Real >::sumAll(), ROL::RandVarFunctional< Real >::val_, ROL::MeanVariance< Real >::values_, and zero.

template<class Real >

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

Definition at line 296 of file ROL_MeanVariance.hpp.

References ROL::RandVarFunctional< Real >::computeGradVec(), ROL::RandVarFunctional< Real >::computeHessVec(), ROL::RandVarFunctional< Real >::computeValue(), ROL::RandVarFunctional< Real >::dualVector_, ROL::RandVarFunctional< Real >::g_, ROL::RandVarFunctional< Real >::gv_, ROL::RandVarFunctional< Real >::hv_, ROL::RandVarFunctional< Real >::val_, and ROL::RandVarFunctional< Real >::weight_.

template<class Real >

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

Definition at line 311 of file ROL_MeanVariance.hpp.