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.
	MeanVariance (const std::vector< Real > &order, const std::vector< Real > &coeff, const Ptr< PositiveFunction< Real > > &pf)
	Constructor.
	MeanVariance (ROL::ParameterList &parlist)
	Constructor.
void	setStorage (const Ptr< ScalarController< Real > > &value_storage, const Ptr< VectorController< Real > > &gradient_storage)
void	setHessVecStorage (const Ptr< ScalarController< Real > > &gradvec_storage, const Ptr< VectorController< Real > > &hessvec_storage)
void	updateValue (Objective< Real > &obj, const Vector< Real > &x, const std::vector< Real > &xstat, Real &tol)
Real	getValue (const Vector< Real > &x, const std::vector< Real > &xstat, SampleGenerator< Real > &sampler)
void	updateGradient (Objective< Real > &obj, const Vector< Real > &x, const std::vector< Real > &xstat, Real &tol)
void	getGradient (Vector< Real > &g, std::vector< Real > &gstat, const Vector< Real > &x, const std::vector< Real > &xstat, SampleGenerator< Real > &sampler)
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)
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)

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< ScalarController< Real > >	values_
Ptr< ScalarController< Real > >	gradvecs_
Ptr< VectorController< Real > >	gradients_
Ptr< VectorController< Real > >	hessvecs_

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 44 of file ROL_MeanVariance.hpp.

Member Typedef Documentation

◆ uint

template<class Real>

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

private

Definition at line 45 of file ROL_MeanVariance.hpp.

Constructor & Destructor Documentation

◆ MeanVariance() [1/3]

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 107 of file ROL_MeanVariance.hpp.

References checkInputs(), coeff_, NumMoments_, order_, and positiveFunction_.

◆ MeanVariance() [2/3]

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 125 of file ROL_MeanVariance.hpp.

References checkInputs(), coeff_, NumMoments_, order_, and positiveFunction_.

◆ MeanVariance() [3/3]

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 151 of file ROL_MeanVariance.hpp.

References checkInputs(), coeff_, NumMoments_, order_, and positiveFunction_.

Member Function Documentation

◆ initializeMV()

template<class Real>

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

inlineprivate

Definition at line 71 of file ROL_MeanVariance.hpp.

References gradients_, gradvecs_, hessvecs_, and values_.

Referenced by checkInputs().

◆ checkInputs()

template<class Real>

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

inlineprivate

Definition at line 81 of file ROL_MeanVariance.hpp.

References coeff_, initializeMV(), order_, positiveFunction_, and zero.

Referenced by MeanVariance(), MeanVariance(), and MeanVariance().

◆ setStorage()

template<class Real>

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

inline

Definition at line 175 of file ROL_MeanVariance.hpp.

References gradients_, and values_.

◆ setHessVecStorage()

template<class Real>

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

inline

Definition at line 182 of file ROL_MeanVariance.hpp.

References gradvecs_, and hessvecs_.

◆ updateValue()

template<class Real>

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

inline

Definition at line 189 of file ROL_MeanVariance.hpp.

◆ getValue()

template<class Real>

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

inline

Definition at line 197 of file ROL_MeanVariance.hpp.

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

◆ updateGradient()

template<class Real>

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

inline

Definition at line 219 of file ROL_MeanVariance.hpp.

◆ getGradient()

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 )

inline

Definition at line 229 of file ROL_MeanVariance.hpp.

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

◆ updateHessVec()

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 )

inline

Definition at line 262 of file ROL_MeanVariance.hpp.

◆ getHessVec()

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 )