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. More...

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

	MeanDeviation (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	initialize (const Vector< Real > &x)
	Initialize temporary variables. 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...

Real	getValue (const Vector< Real > &x, const std::vector< Real > &xstat, SampleGenerator< Real > &sampler)
	Return risk measure value. 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	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	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	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< 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::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 80 of file ROL_MeanDeviation.hpp.

Member Typedef Documentation

template<class Real >

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

private

Definition at line 81 of file ROL_MeanDeviation.hpp.

Constructor & Destructor Documentation

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 193 of file ROL_MeanDeviation.hpp.

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

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 210 of file ROL_MeanDeviation.hpp.

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

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 235 of file ROL_MeanDeviation.hpp.

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

Member Function Documentation

template<class Real >

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

inlineprivate

Definition at line 123 of file ROL_MeanDeviation.hpp.

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

template<class Real >

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

inlineprivate

template<class Real >

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

inlineprivate

Definition at line 167 of file ROL_MeanDeviation.hpp.

References ROL::MeanDeviation< Real >::coeff_, ROL::MeanDeviation< Real >::initializeStorage(), ROL::MeanDeviation< Real >::order_, ROL::MeanDeviation< Real >::positiveFunction_, and zero.

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

template<class Real >

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

inlinevirtual

Reimplemented from ROL::RandVarFunctional< Real >.

Definition at line 261 of file ROL_MeanDeviation.hpp.

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

template<class Real >

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

inlinevirtual

Reimplemented from ROL::RandVarFunctional< Real >.

Definition at line 268 of file ROL_MeanDeviation.hpp.

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

template<class Real >

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

inlinevirtual

Initialize temporary variables.

Parameters

[in] x is a vector used for initializing storage

Reimplemented from ROL::RandVarFunctional< Real >.

Definition at line 275 of file ROL_MeanDeviation.hpp.

References ROL::MeanDeviation< Real >::clear(), and ROL::RandVarFunctional< Real >::initialize().

template<class Real >

void ROL::MeanDeviation< 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 280 of file ROL_MeanDeviation.hpp.

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

template<class Real >

void ROL::MeanDeviation< 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 288 of file ROL_MeanDeviation.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::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
	)

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 298 of file ROL_MeanDeviation.hpp.

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

template<class Real >

Real ROL::MeanDeviation< 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 313 of file ROL_MeanDeviation.hpp.

References ROL::MeanDeviation< Real >::coeff_, ROL::MeanDeviation< Real >::des0_, ROL::MeanDeviation< Real >::dev0_, ROL::SampleGenerator< Real >::getMyPoint(), ROL::SampleGenerator< Real >::getMyWeight(), ROL::MeanDeviation< Real >::NumMoments_, ROL::SampleGenerator< Real >::numMySamples(), ROL::MeanDeviation< Real >::order_, ROL::MeanDeviation< Real >::positiveFunction_, ROL::SampleGenerator< Real >::start(), ROL::SampleGenerator< Real >::sumAll(), ROL::RandVarFunctional< Real >::val_, and ROL::MeanDeviation< Real >::values_.

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
	)

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 338 of file ROL_MeanDeviation.hpp.

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
	)

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 384 of file ROL_MeanDeviation.hpp.