Provides a general interface for error measures generated through the expectation risk quadrangle. More...

#include <ROL_ExpectationQuadError.hpp>

Inheritance diagram for ROL::ExpectationQuadError< Real >:

Public Member Functions
	ExpectationQuadError (const Ptr< ExpectationQuad< Real >> &eq)

void	checkRegret (void)
	Run derivative tests for the scalar error function. 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< SampledScalar< Real >> &value_storage, const Ptr< SampledVector< Real >> &gradient_storage)

virtual void	setHessVecStorage (const Ptr< SampledScalar< Real >> &gradvec_storage, const Ptr< SampledVector< Real >> &hessvec_storage)

virtual void	resetStorage (bool flag=true)
	Reset internal storage. More...

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 Attributes
Ptr< ExpectationQuad< Real > >	eq_

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::ExpectationQuadError< Real >

Provides a general interface for error measures generated through the expectation risk quadrangle.

The expectation risk quadrangle is a specialization of the general risk quadrangle that provides a rigorous connection between risk-averse optimization and statistical estimation. The risk quadrangle provides fundamental relationships between measures of risk, regret, error and deviation. An expectation risk quadrangle is defined through scalar regret and error functions. The scalar regret function, \(v:\mathbb{R}\to(-\infty,\infty]\), must be proper, closed, convex and satisfy \(v(0)=0\) and \(v(x) > x\) for all \(x\neq 0\). Similarly, the scalar error function, \(e:\mathbb{R}\to[0,\infty]\), must be proper, closed, convex and satisfy \(e(0)=0\) and \(e(x) > 0\) for all \(x\neq 0\). \(v\) and \(e\) are obtained from one another through the relations

\[ v(x) = e(x) + x \quad\text{and}\quad e(x) = v(x) - x. \]

Given \(v\) (or equivalently \(e\)), the associated risk measure is

\[ \mathcal{R}(X) = \inf_{t\in\mathbb{R}} \left\{ t + \mathbb{E}\left[v(X-t)\right] \right\}. \]

In general, \(\mathcal{R}\) is convex and translation equivariant. Moreover, \(\mathcal{R}\) is monotonic if \(v\) is increasing and \(\mathcal{R}\) is positive homogeneous if \(v\) is. ROL implements this by augmenting the optimization vector \(x_0\) with the parameter \(t\), then minimizes jointly for \((x_0,t)\).

Definition at line 89 of file ROL_ExpectationQuadError.hpp.

Constructor & Destructor Documentation

template<class Real >

ROL::ExpectationQuadError< Real >::ExpectationQuadError ( const Ptr< ExpectationQuad< Real >> & eq )

inline

Definition at line 108 of file ROL_ExpectationQuadError.hpp.

Member Function Documentation

template<class Real >

void ROL::ExpectationQuadError< Real >::checkRegret ( void )

inline

Run derivative tests for the scalar error function.

Definition at line 113 of file ROL_ExpectationQuadError.hpp.

References ROL::ExpectationQuadError< Real >::eq_.

template<class Real >

void ROL::ExpectationQuadError< 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 117 of file ROL_ExpectationQuadError.hpp.

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

template<class Real >

void ROL::ExpectationQuadError< 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 125 of file ROL_ExpectationQuadError.hpp.

References ROL::RandVarFunctional< Real >::computeGradient(), ROL::RandVarFunctional< Real >::computeValue(), ROL::RandVarFunctional< Real >::dualVector_, ROL::ExpectationQuadError< Real >::eq_, ROL::RandVarFunctional< Real >::g_, and ROL::RandVarFunctional< Real >::weight_.

template<class Real >

void ROL::ExpectationQuadError< 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 137 of file ROL_ExpectationQuadError.hpp.

References ROL::RandVarFunctional< Real >::computeGradVec(), ROL::RandVarFunctional< Real >::computeHessVec(), ROL::RandVarFunctional< Real >::computeValue(), ROL::RandVarFunctional< Real >::dualVector_, ROL::ExpectationQuadError< Real >::eq_, ROL::RandVarFunctional< Real >::hv_, and ROL::RandVarFunctional< Real >::weight_.

template<class Real >

Real ROL::ExpectationQuadError< 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 156 of file ROL_ExpectationQuadError.hpp.

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

template<class Real >

void ROL::ExpectationQuadError< 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 164 of file ROL_ExpectationQuadError.hpp.

References ROL::RandVarFunctional< Real >::g_, and ROL::SampleGenerator< Real >::sumAll().

template<class Real >

void ROL::ExpectationQuadError< 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 172 of file ROL_ExpectationQuadError.hpp.

References ROL::RandVarFunctional< Real >::hv_, and ROL::SampleGenerator< Real >::sumAll().