Provides an interface for a convex combination of the expected value and the conditional value-at-risk. More...

#include <ROL_CVaR.hpp>

Inheritance diagram for ROL::CVaR< Real >:

Public Member Functions
	CVaR (const Real prob, const Real coeff, const Ptr< PlusFunction< Real > > &pf)
	Constructor. More...

	CVaR (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...

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	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...

Private Member Functions
void	checkInputs (void) const

Private Attributes
Ptr< PlusFunction< Real > >	plusFunction_

Real	prob_

Real	coeff_

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::CVaR< Real >

Provides an interface for a convex combination of the expected value and the conditional value-at-risk.

The conditional value-at-risk (also called the average value-at-risk or the expected shortfall) with confidence level \(0\le \beta < 1\) is

\[ \mathcal{R}(X) = \inf_{t\in\mathbb{R}} \left\{ t + \frac{1}{1-\beta} \mathbb{E}\left[(X-t)_+\right] \right\} \]

where \((x)_+ = \max\{0,x\}\). If the distribution of \(X\) is continuous, then \(\mathcal{R}\) is the conditional expectation of \(X\) exceeding the \(\beta\)-quantile of \(X\) and the optimal \(t\) is the \(\beta\)-quantile. Additionally, \(\mathcal{R}\) is a law-invariant coherent risk measure. ROL implements this by augmenting the optimization vector \(x_0\) with the parameter \(t\), then minimizes jointly for \((x_0,t)\).

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

Definition at line 44 of file ROL_CVaR.hpp.

Constructor & Destructor Documentation

template<class Real >

ROL::CVaR< Real >::CVaR	(	const Real	prob,
		const Real	coeff,
		const Ptr< PlusFunction< Real > > &	pf
	)

inline

Constructor.

Parameters

[in]	prob	is the confidence level
[in]	coeff	is the convex combination parameter (coeff=0 corresponds to the expected value whereas coeff=1 corresponds to the conditional value-at-risk)
[in]	pf	is the plus function or an approximation

Definition at line 84 of file ROL_CVaR.hpp.

References ROL::CVaR< Real >::checkInputs().

template<class Real >

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

inline

Constructor.

Parameters

[in] parlist is a parameter list specifying inputs

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

"Confidence Level" (between 0 and 1)
"Convex Combination Parameter" (between 0 and 1)
A sublist for plus function information.

Definition at line 100 of file ROL_CVaR.hpp.

References ROL::CVaR< Real >::checkInputs(), ROL::CVaR< Real >::coeff_, ROL::CVaR< Real >::plusFunction_, and ROL::CVaR< Real >::prob_.

Member Function Documentation

template<class Real >

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

inlineprivate

Definition at line 64 of file ROL_CVaR.hpp.

References ROL::CVaR< Real >::coeff_, ROL::CVaR< Real >::plusFunction_, ROL::CVaR< Real >::prob_, and zero.

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

template<class Real >

void ROL::CVaR< 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 113 of file ROL_CVaR.hpp.

References ROL::CVaR< Real >::coeff_, ROL::RandVarFunctional< Real >::computeValue(), ROL::CVaR< Real >::plusFunction_, ROL::CVaR< Real >::prob_, ROL::RandVarFunctional< Real >::val_, and ROL::RandVarFunctional< Real >::weight_.

template<class Real >

void ROL::CVaR< 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 123 of file ROL_CVaR.hpp.

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

template<class Real >

void ROL::CVaR< 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 138 of file ROL_CVaR.hpp.

References ROL::CVaR< Real >::coeff_, ROL::RandVarFunctional< Real >::computeGradVec(), ROL::RandVarFunctional< Real >::computeHessVec(), ROL::RandVarFunctional< Real >::computeValue(), ROL::RandVarFunctional< Real >::dualVector_, ROL::RandVarFunctional< Real >::hv_, ROL::CVaR< Real >::plusFunction_, ROL::CVaR< Real >::prob_, ROL::RandVarFunctional< Real >::val_, and ROL::RandVarFunctional< Real >::weight_.

template<class Real >

Real ROL::CVaR< 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 162 of file ROL_CVaR.hpp.

References ROL::CVaR< Real >::coeff_, ROL::SampleGenerator< Real >::sumAll(), and ROL::RandVarFunctional< Real >::val_.

template<class Real >

void ROL::CVaR< 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 171 of file ROL_CVaR.hpp.

References ROL::CVaR< Real >::coeff_, ROL::RandVarFunctional< Real >::g_, ROL::CVaR< Real >::prob_, ROL::SampleGenerator< Real >::sumAll(), and ROL::RandVarFunctional< Real >::val_.

template<class Real >

void ROL::CVaR< 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 184 of file ROL_CVaR.hpp.

References ROL::CVaR< Real >::coeff_, ROL::RandVarFunctional< Real >::hv_, ROL::CVaR< Real >::prob_, ROL::SampleGenerator< Real >::sumAll(), and ROL::RandVarFunctional< Real >::val_.