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

#include <ROL_MeanDeviation.hpp>

Inheritance diagram for ROL::MeanDeviation< Real >:

Public Member Functions
	MeanDeviation (const Real order, const Real coeff, const Ptr< PositiveFunction< Real > > &pf)
	Constructor.
	MeanDeviation (const std::vector< Real > &order, const std::vector< Real > &coeff, const Ptr< PositiveFunction< Real > > &pf)
	Constructor.
	MeanDeviation (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	initialize (const Vector< Real > &x)
void	updateValue (Objective< Real > &obj, const Vector< Real > &x, const std::vector< Real > &xstat, Real &tol)
void	updateGradient (Objective< Real > &obj, const Vector< Real > &x, const std::vector< Real > &xstat, Real &tol)
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)
Real	getValue (const Vector< Real > &x, const std::vector< Real > &xstat, SampleGenerator< Real > &sampler)
void	getGradient (Vector< Real > &g, std::vector< Real > &gstat, const Vector< Real > &x, const std::vector< Real > &xstat, SampleGenerator< Real > &sampler)
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	initializeStorage (void)
void	clear (void)
void	checkInputs (void)

Private Attributes
Ptr< PositiveFunction< Real > >	positiveFunction_
std::vector< Real >	order_
std::vector< Real >	coeff_
uint	NumMoments_
std::vector< Real >	dev0_
std::vector< Real >	dev1_
std::vector< Real >	dev2_
std::vector< Real >	dev3_
std::vector< Real >	des0_
std::vector< Real >	des1_
std::vector< Real >	des2_
std::vector< Real >	des3_
std::vector< Real >	devp_
std::vector< Real >	gvp1_
std::vector< Real >	gvp2_
std::vector< Real >	gvp3_
std::vector< Real >	gvs1_
std::vector< Real >	gvs2_
std::vector< Real >	gvs3_
Ptr< ScalarController< Real > >	values_
Ptr< ScalarController< Real > >	gradvecs_
Ptr< VectorController< Real > >	gradients_
Ptr< VectorController< Real > >	hessvecs_

Detailed Description

template<class Real>
class ROL::MeanDeviation< Real >

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

The mean plus deviations risk measure is

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

where \(\wp:\mathbb{R}\to[0,\infty)\) is either the absolute value or \((x)_+ = \max\{0,x\}\), \(c_k > 0\) and \(p_k\in\mathbb{N}\). In general, \(\mathcal{R}\) is law-invariant, but not coherent. In the specific case that \(\wp(x) = (x)_+\) and \(c_k\in[0,1]\), \(\mathcal{R}\) is coherent. On the other hand, the common mean-plus-standard-deviation risk measure (i.e., \(\wp(x) = |x|\), \(n=1\) and \(p_1 = 2\)) is not coherent since it violates monotonicity.

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

Definition at line 46 of file ROL_MeanDeviation.hpp.

Member Typedef Documentation

◆ uint

template<class Real>

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

private

Definition at line 47 of file ROL_MeanDeviation.hpp.

Constructor & Destructor Documentation

◆ MeanDeviation() [1/3]

template<class Real>

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

inline

Constructor.

Parameters

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

This constructor produces a mean plus deviation risk measure with a single deviation.

Definition at line 159 of file ROL_MeanDeviation.hpp.

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

◆ MeanDeviation() [2/3]

template<class Real>

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

inline

Constructor.

Parameters

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

This constructor produces a mean plus deviation risk measure with an arbitrary number of deviations.

Definition at line 176 of file ROL_MeanDeviation.hpp.

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

◆ MeanDeviation() [3/3]

template<class Real>

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

inline

Constructor.

Parameters

[in] parlist is a parameter list specifying inputs

parlist should contain sublists "SOL"->"Risk Measure"->"Mean Plus Deviation" and within the "Mean Plus Deviation" 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 201 of file ROL_MeanDeviation.hpp.

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

Member Function Documentation

◆ initializeStorage()

template<class Real>

void ROL::MeanDeviation< Real >::initializeStorage ( void )

inlineprivate

Definition at line 89 of file ROL_MeanDeviation.hpp.

References des0_, des1_, des2_, des3_, dev0_, dev1_, dev2_, dev3_, devp_, gradients_, gradvecs_, gvp1_, gvp2_, gvp3_, gvs1_, gvs2_, gvs3_, hessvecs_, NumMoments_, order_, and values_.

Referenced by checkInputs().

◆ clear()

template<class Real>

void ROL::MeanDeviation< Real >::clear ( void )

inlineprivate

Definition at line 117 of file ROL_MeanDeviation.hpp.

References des0_, des1_, des2_, des3_, dev0_, dev1_, dev2_, dev3_, devp_, gradvecs_, gvp1_, gvp2_, gvp3_, gvs1_, gvs2_, gvs3_, hessvecs_, NumMoments_, and zero.

Referenced by initialize().

◆ checkInputs()

template<class Real>

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

inlineprivate

Definition at line 133 of file ROL_MeanDeviation.hpp.

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

Referenced by MeanDeviation(), MeanDeviation(), and MeanDeviation().

◆ setStorage()

template<class Real>

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

inline

Definition at line 227 of file ROL_MeanDeviation.hpp.

References gradients_, and values_.

◆ setHessVecStorage()

template<class Real>

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

inline

Definition at line 234 of file ROL_MeanDeviation.hpp.

References gradvecs_, and hessvecs_.

◆ initialize()

template<class Real>

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

inline

Definition at line 241 of file ROL_MeanDeviation.hpp.

References clear().

◆ updateValue()

template<class Real>

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

inline

Definition at line 246 of file ROL_MeanDeviation.hpp.

◆ updateGradient()

template<class Real>

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

inline

Definition at line 254 of file ROL_MeanDeviation.hpp.

◆ updateHessVec()

template<class Real>

void ROL::MeanDeviation< 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 264 of file ROL_MeanDeviation.hpp.

◆ getValue()

template<class Real>

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

inline

Definition at line 279 of file ROL_MeanDeviation.hpp.

References coeff_, des0_, dev0_, 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_.

◆ getGradient()

template<class Real>

void ROL::MeanDeviation< 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 304 of file ROL_MeanDeviation.hpp.

References coeff_, des0_, des1_, dev0_, dev1_, ROL::SampleGenerator< Real >::getMyPoint(), ROL::SampleGenerator< Real >::getMyWeight(), gradients_, NumMoments_, ROL::SampleGenerator< Real >::numMySamples(), order_, positiveFunction_, ROL::SampleGenerator< Real >::start(), ROL::SampleGenerator< Real >::sumAll(), values_, and zero.

◆ getHessVec()

template<class Real>

void ROL::MeanDeviation< 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 )