Provides an interface for the chi-squared-divergence distributionally robust expectation. More...

#include <ROL_Chi2Divergence.hpp>

Inheritance diagram for ROL::Chi2Divergence< Real >:

Public Member Functions
	Chi2Divergence (const Real thresh)
	Constructor. More...

	Chi2Divergence (ROL::ParameterList &parlist)
	Constructor. More...

Real	Fprimal (Real x, int deriv=0)
	Implementation of the scalar primal F function. More...

Real	Fdual (Real x, int deriv=0)
	Implementation of the scalar dual F function. More...

Public Member Functions inherited from ROL::FDivergence< Real >
	FDivergence (const Real thresh)
	Constructor. More...

	FDivergence (ROL::ParameterList &parlist)
	Constructor. More...

bool	check (std::ostream &outStream=std::cout) const

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...

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

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	setSample (const std::vector< Real > &point, const Real weight)

virtual Real	computeStatistic (const Ptr< const std::vector< Real >> &xstat) const
	Compute statistic. More...

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::Chi2Divergence< Real >

Provides an interface for the chi-squared-divergence distributionally robust expectation.

This class defines a risk measure \(\mathcal{R}\) that arises in distributionally robust stochastic programming. \(\mathcal{R}\) is given by

\[ \mathcal{R}(X) = \sup_{\vartheta\in\mathfrak{A}} \mathbb{E}[\vartheta X] \]

where \(\mathfrak{A}\) is called the ambiguity (or uncertainty) set and is defined by a constraint on the \(\chi^2\)-divergence, i.e.,

\[ \mathfrak{A} = \left\{\vartheta\in\mathcal{X}^*\,:\, \mathbb{E}[\vartheta] = 1,\; \vartheta \ge 0,\;\text{and}\; \frac{1}{2}\mathbb{E}[(\vartheta-1)^2] \le \epsilon\right\}. \]

\(\mathcal{R}\) is a law-invariant, coherent risk measure.

Definition at line 73 of file ROL_Chi2Divergence.hpp.

Constructor & Destructor Documentation

template<class Real >

ROL::Chi2Divergence< Real >::Chi2Divergence ( const Real thresh )

inline

Constructor.

Parameters

[in] thresh is the tolerance for the F-divergence constraint

Definition at line 80 of file ROL_Chi2Divergence.hpp.

template<class Real >

ROL::Chi2Divergence< Real >::Chi2Divergence ( ROL::ParameterList & parlist )

inline

Constructor.

Parameters

[in] parlist is a parameter list specifying inputs

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

"Threshold" (greater than 0)

Definition at line 90 of file ROL_Chi2Divergence.hpp.

Member Function Documentation

template<class Real >

Real ROL::Chi2Divergence< Real >::Fprimal	(	Real	x,
		int	deriv = `0`
	)

inlinevirtual

Implementation of the scalar primal F function.

Parameters

[in]	x	is a scalar input
[in]	deriv	is the derivative order

Upon return, Fprimal returns \(F(x)\) or a derivative of \(F(x)\).

Implements ROL::FDivergence< Real >.

Definition at line 92 of file ROL_Chi2Divergence.hpp.

References zero.

template<class Real >

Real ROL::Chi2Divergence< Real >::Fdual	(	Real	x,
		int	deriv = `0`
	)

inlinevirtual

Implementation of the scalar dual F function.

Parameters

[in]	x	is a scalar input
[in]	deriv	is the derivative order

Upon return, Fdual returns \(F^*(x)\) or a derivative of \(F^*(x)\). Here, \(F^*\) denotes the Legendre-Fenchel transformation of \(F\), i.e.,

\[ F^*(y) = \sup_{x\in\mathbb{R}}\{xy - F(x)\}. \]

Implements ROL::FDivergence< Real >.

Definition at line 110 of file ROL_Chi2Divergence.hpp.

References zero.

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

ROL_Chi2Divergence.hpp

Public Member Functions

Additional Inherited Members

Detailed Description

template<class Real> class ROL::Chi2Divergence< Real >

Constructor & Destructor Documentation

Member Function Documentation

template<class Real>
class ROL::Chi2Divergence< Real >