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.
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 Attributes
Ptr< ExpectationQuad< Real > >	eq_

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 55 of file ROL_ExpectationQuadError.hpp.

Constructor & Destructor Documentation

◆ ExpectationQuadError()

template<class Real>

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

inline

Definition at line 74 of file ROL_ExpectationQuadError.hpp.

References eq_.

Member Function Documentation

◆ checkRegret()

template<class Real>

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

inline

Run derivative tests for the scalar error function.

Definition at line 79 of file ROL_ExpectationQuadError.hpp.

References eq_.

◆ updateValue()

template<class Real>

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

inline

Definition at line 83 of file ROL_ExpectationQuadError.hpp.

References eq_.

◆ updateGradient()

template<class Real>

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

inline

Definition at line 91 of file ROL_ExpectationQuadError.hpp.

References eq_, and ROL::ROL_EPSILON().

◆ updateHessVec()

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 )

inline

Definition at line 103 of file ROL_ExpectationQuadError.hpp.

References eq_, and ROL::ROL_EPSILON().

◆ getValue()

template<class Real>

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

inline

Definition at line 122 of file ROL_ExpectationQuadError.hpp.

References ROL::SampleGenerator< Real >::sumAll().

◆ getGradient()

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 )

inline

Definition at line 130 of file ROL_ExpectationQuadError.hpp.

References ROL::SampleGenerator< Real >::sumAll().

◆ getHessVec()

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 )