Provides an interface for spectral risk measures. More...

#include <ROL_SpectralRisk.hpp>

Inheritance diagram for ROL::SpectralRisk< Real >:

Public Member Functions
	SpectralRisk (void)

	SpectralRisk (const Teuchos::RCP< Distribution< Real > > &dist, const int nQuad, const Teuchos::RCP< PlusFunction< Real > > &pf)

	SpectralRisk (Teuchos::ParameterList &parlist)

	SpectralRisk (const std::vector< Real > &pts, const std::vector< Real > &wts, const Teuchos::RCP< PlusFunction< Real > > &pf)

Real	computeStatistic (const Vector< Real > &x) const

void	reset (Teuchos::RCP< Vector< Real > > &x0, const Vector< Real > &x)
	Reset internal risk measure storage. Called for value and gradient computation. More...

void	reset (Teuchos::RCP< Vector< Real > > &x0, const Vector< Real > &x, Teuchos::RCP< Vector< Real > > &v0, const Vector< Real > &v)
	Reset internal risk measure storage. Called for Hessian-times-a-vector computation. More...

void	update (const Real val, const Real weight)
	Update internal risk measure storage for value computation. More...

void	update (const Real val, const Vector< Real > &g, const Real weight)
	Update internal risk measure storage for gradient computation. More...

void	update (const Real val, const Vector< Real > &g, const Real gv, const Vector< Real > &hv, const Real weight)
	Update internal risk measure storage for Hessian-time-a-vector computation. More...

Real	getValue (SampleGenerator< Real > &sampler)
	Return risk measure value. More...

void	getGradient (Vector< Real > &g, SampleGenerator< Real > &sampler)
	Return risk measure (sub)gradient. More...

void	getHessVec (Vector< Real > &hv, SampleGenerator< Real > &sampler)
	Return risk measure Hessian-times-a-vector. More...

Public Member Functions inherited from ROL::RiskMeasure< Real >
virtual	~RiskMeasure ()

	RiskMeasure (void)

Protected Member Functions
void	buildMixedQuantile (const std::vector< Real > &pts, const std::vector< Real > &wts, const Teuchos::RCP< PlusFunction< Real > > &pf)

void	buildQuadFromDist (std::vector< Real > &pts, std::vector< Real > &wts, const int nQuad, const Teuchos::RCP< Distribution< Real > > &dist) const

void	printQuad (const std::vector< Real > &pts, const std::vector< Real > &wts, const bool print=false) const

Private Member Functions
void	checkInputs (Teuchos::RCP< Distribution< Real > > &dist=Teuchos::null) const

Private Attributes
Teuchos::RCP< MixedQuantileQuadrangle< Real > >	mqq_

Teuchos::RCP< PlusFunction< Real > >	plusFunction_

std::vector< Real >	wts_

std::vector< Real >	pts_

Additional Inherited Members
Protected Attributes inherited from ROL::RiskMeasure< Real >
Real	val_

Real	gv_

Teuchos::RCP< Vector< Real > >	g_

Teuchos::RCP< Vector< Real > >	hv_

Teuchos::RCP< Vector< Real > >	dualVector_

bool	firstReset_

Detailed Description

template<class Real>
class ROL::SpectralRisk< Real >

Provides an interface for spectral risk measures.

Kusuoka's representation for law-invariant risk measures is

\[ \mathcal{R}(X) = \sup_{\mu\in\mathfrak{M}} \int_0^1 \mathrm{CVaR}_{\alpha}(X)\,\mathrm{d}\mu(\alpha) \]

where the conditional value-at-risk (CVaR) with confidence level \(0\le \alpha < 1\) is

\[ \mathrm{CVaR}_\alpha(X) = \inf_{t\in\mathbb{R}} \left\{ t + \frac{1}{1-\alpha} \mathbb{E}\left[(X-t)_+\right] \right\}, \quad (x)_+ = \max\{0,x\}, \]

and \(\mathfrak{M}\) is a subset of distributions on the interval \([0,1)\). By spectral risk measures, we refer to the case where the set \(\mathfrak{M}\) is a singleton. If the distribution \(\mu\in\mathfrak{M}\) is discrete, then the corresponding risk measure is a mixed quantile quadrangle risk measure.

If the distribution of \(X\) is continuous, then \(\mathrm{CVaR}_{\alpha}(X)\) is the conditional expectation of \(X\) exceeding the \(\alpha\)-quantile of \(X\) and the optimal \(t\) is the \(\alpha\)-quantile. Additionally, \(\mathcal{R}\) is a law-invariant coherent risk measure.

ROL implements \(\mathcal{R}\) by approximating the integral with Gauss-Chebyshev quadrature of the first kind. The corresponding quadrature points and weights are then used to construct a ROL::MixedQuantileQuadrangle risk measure. When using derivative-based optimization, the user can provide a smooth approximation of \((\cdot)_+\) using the ROL::PlusFunction class.

Definition at line 89 of file ROL_SpectralRisk.hpp.

Constructor & Destructor Documentation

◆ SpectralRisk() [1/4]

template<class Real>

ROL::SpectralRisk< Real >::SpectralRisk ( void )

inline

Definition at line 165 of file ROL_SpectralRisk.hpp.

◆ SpectralRisk() [2/4]

template<class Real>

ROL::SpectralRisk< Real >::SpectralRisk	(	const Teuchos::RCP< Distribution< Real > > &	dist,
		const int	nQuad,
		const Teuchos::RCP< PlusFunction< Real > > &	pf
	)

inline

Definition at line 167 of file ROL_SpectralRisk.hpp.

References ROL::SpectralRisk< Real >::buildMixedQuantile(), ROL::SpectralRisk< Real >::buildQuadFromDist(), and ROL::SpectralRisk< Real >::checkInputs().

◆ SpectralRisk() [3/4]

template<class Real>

ROL::SpectralRisk< Real >::SpectralRisk ( Teuchos::ParameterList & parlist )

inline

Definition at line 180 of file ROL_SpectralRisk.hpp.

References ROL::SpectralRisk< Real >::buildMixedQuantile(), ROL::SpectralRisk< Real >::buildQuadFromDist(), ROL::SpectralRisk< Real >::checkInputs(), and ROL::SpectralRisk< Real >::printQuad().

◆ SpectralRisk() [4/4]

template<class Real>

ROL::SpectralRisk< Real >::SpectralRisk	(	const std::vector< Real > &	pts,
		const std::vector< Real > &	wts,
		const Teuchos::RCP< PlusFunction< Real > > &	pf
	)

inline

Definition at line 201 of file ROL_SpectralRisk.hpp.

References ROL::SpectralRisk< Real >::buildMixedQuantile(), and ROL::SpectralRisk< Real >::checkInputs().

Member Function Documentation

◆ checkInputs()

template<class Real>

void ROL::SpectralRisk< Real >::checkInputs ( Teuchos::RCP< Distribution< Real > > & dist = Teuchos::null ) const

inlineprivate

Definition at line 97 of file ROL_SpectralRisk.hpp.

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

◆ buildMixedQuantile()

template<class Real>

void ROL::SpectralRisk< Real >::buildMixedQuantile	(	const std::vector< Real > &	pts,
		const std::vector< Real > &	wts,
		const Teuchos::RCP< PlusFunction< Real > > &	pf
	)

inlineprotected

Definition at line 111 of file ROL_SpectralRisk.hpp.

Referenced by ROL::SuperQuantileQuadrangle< Real >::initialize(), ROL::ChebyshevKusuoka< Real >::initialize(), and ROL::SpectralRisk< Real >::SpectralRisk().

◆ buildQuadFromDist()

template<class Real>

void ROL::SpectralRisk< Real >::buildQuadFromDist	(	std::vector< Real > &	pts,
		std::vector< Real > &	wts,
		const int	nQuad,
		const Teuchos::RCP< Distribution< Real > > &	dist
	)		const

inlineprotected

Definition at line 119 of file ROL_SpectralRisk.hpp.

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

◆ printQuad()

template<class Real>

void ROL::SpectralRisk< Real >::printQuad	(	const std::vector< Real > &	pts,
		const std::vector< Real > &	wts,
		const bool	print = `false`
	)		const

inlineprotected

Definition at line 145 of file ROL_SpectralRisk.hpp.

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

◆ computeStatistic()

template<class Real>

Real ROL::SpectralRisk< Real >::computeStatistic ( const Vector< Real > & x ) const

inline

Definition at line 209 of file ROL_SpectralRisk.hpp.

Referenced by ROL::StochasticProblem< Real >::getSolutionStatistic().

◆ reset() [1/2]

template<class Real>

void ROL::SpectralRisk< Real >::reset	(	Teuchos::RCP< Vector< Real > > &	x0,
		const Vector< Real > &	x
	)

inlinevirtual

Reset internal risk measure storage. Called for value and gradient computation.

Parameters

[out]	x0	is a user-provided optimization vector
[in]	x	is a (potentially) augmented risk vector

On input, \(x\) carries \(x_0\) and any statistics (scalars) associated with the risk measure.

Reimplemented from ROL::RiskMeasure< Real >.

Definition at line 220 of file ROL_SpectralRisk.hpp.

◆ reset() [2/2]

template<class Real>

void ROL::SpectralRisk< Real >::reset	(	Teuchos::RCP< Vector< Real > > &	x0,
		const Vector< Real > &	x,
		Teuchos::RCP< Vector< Real > > &	v0,
		const Vector< Real > &	v
	)

inlinevirtual

Reset internal risk measure storage. Called for Hessian-times-a-vector computation.

Parameters

[out]	x0	is a user-provided optimization vector
[in]	x	is a (potentially) augmented risk vector
[out]	v0	is a user-provided direction vector
[in]	v	is a (potentially) augmented risk vector

On input, \(x\) carries \(x_0\) and any statistics (scalars) associated with the risk measure. Similarly, \(v\) carries \(v_0\) and any statistics (scalars) associated with the risk measure.

Reimplemented from ROL::RiskMeasure< Real >.

Definition at line 224 of file ROL_SpectralRisk.hpp.

◆ update() [1/3]

template<class Real>

void ROL::SpectralRisk< Real >::update	(	const Real	val,
		const Real	weight
	)

inlinevirtual

Update internal risk measure 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::RiskMeasure< Real >.

Definition at line 229 of file ROL_SpectralRisk.hpp.

◆ update() [2/3]

template<class Real>

void ROL::SpectralRisk< Real >::update	(	const Real	val,
		const Vector< Real > &	g,
		const Real	weight
	)

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::RiskMeasure< Real >.

Definition at line 233 of file ROL_SpectralRisk.hpp.

◆ update() [3/3]

template<class Real>

void ROL::SpectralRisk< Real >::update	(	const Real	val,
		const Vector< Real > &	g,
		const Real	gv,
		const Vector< Real > &	hv,
		const Real	weight
	)

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::RiskMeasure< Real >.

Definition at line 237 of file ROL_SpectralRisk.hpp.

◆ getValue()

template<class Real>

Real ROL::SpectralRisk< Real >::getValue ( 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::RiskMeasure< Real >.

Definition at line 242 of file ROL_SpectralRisk.hpp.

◆ getGradient()

template<class Real>

void ROL::SpectralRisk< Real >::getGradient	(	Vector< Real > &	g,
		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::RiskMeasure< Real >.

Definition at line 246 of file ROL_SpectralRisk.hpp.

◆ getHessVec()

template<class Real>

void ROL::SpectralRisk< Real >::getHessVec	(	Vector< Real > &	hv,
		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::RiskMeasure< Real >.

Definition at line 250 of file ROL_SpectralRisk.hpp.

Member Data Documentation

◆ mqq_

template<class Real>

Teuchos::RCP<MixedQuantileQuadrangle<Real> > ROL::SpectralRisk< Real >::mqq_

private

Definition at line 91 of file ROL_SpectralRisk.hpp.

◆ plusFunction_

template<class Real>

Teuchos::RCP<PlusFunction<Real> > ROL::SpectralRisk< Real >::plusFunction_

private

Definition at line 92 of file ROL_SpectralRisk.hpp.

◆ wts_

template<class Real>

std::vector<Real> ROL::SpectralRisk< Real >::wts_

private

Definition at line 94 of file ROL_SpectralRisk.hpp.

◆ pts_

template<class Real>

std::vector<Real> ROL::SpectralRisk< Real >::pts_

private

Definition at line 95 of file ROL_SpectralRisk.hpp.

The documentation for this class was generated from the following file:

ROL_SpectralRisk.hpp

Public Member Functions

Protected Member Functions

Private Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

template<class Real> class ROL::SpectralRisk< Real >

Constructor & Destructor Documentation

◆ SpectralRisk() [1/4]

◆ SpectralRisk() [2/4]

◆ SpectralRisk() [3/4]

◆ SpectralRisk() [4/4]

Member Function Documentation

◆ checkInputs()

◆ buildMixedQuantile()

◆ buildQuadFromDist()

◆ printQuad()

◆ computeStatistic()

◆ reset() [1/2]

◆ reset() [2/2]

◆ update() [1/3]

◆ update() [2/3]

◆ update() [3/3]

◆ getValue()

◆ getGradient()

◆ getHessVec()

Member Data Documentation

◆ mqq_

◆ plusFunction_

◆ wts_

◆ pts_

template<class Real>
class ROL::SpectralRisk< Real >