Provides a general interface for the F-divergence distributionally robust expectation. More...

#include <ROL_FDivergence.hpp>

Inheritance diagram for ROL::FDivergence< Real >:

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

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

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

virtual Real	Fdual (Real x, int deriv=0) const =0
	Implementation of the scalar dual F function. 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< 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	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
Real	thresh_

Real	valLam_

Real	valLam2_

Real	valMu_

Real	valMu2_

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::FDivergence< Real >

Provides a general interface for the F-divergence distributionally robust expectation.

This class defines a risk measure \(\mathcal{R}\) which 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 F-divergence, i.e.,

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

where \(F:\mathbb{R}\to[0,\infty]\) convex, lower semicontinuous and satisfies \(F(1) = 1\) and \(F(x) = \infty\) for \(x < 0\). \(\mathcal{R}\) is a law-invariant, coherent risk measure. Moreover, by a duality argument, \(\mathcal{R}\) can be reformulated as

\[ \mathcal{R}(X) = \inf_{\lambda > 0,\,\mu}\left\{ \lambda \epsilon + \mu + \mathbb{E}\left[ (\lambda F)^*(X-\mu)\right]\right\}. \]

Here, \((\lambda F)^*\) denotes the Legendre-Fenchel transformation of \((\lambda F)\). ROL implements this by augmenting the optimization vector \(x_0\) with the parameter \((\lambda,\mu)\), then minimizes jointly for \((x_0,\lambda,\mu)\).

Definition at line 53 of file ROL_FDivergence.hpp.

Constructor & Destructor Documentation

template<class Real >

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

inline

Constructor.

Parameters

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

Definition at line 87 of file ROL_FDivergence.hpp.

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

template<class Real >

ROL::FDivergence< Real >::FDivergence ( 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 100 of file ROL_FDivergence.hpp.

References ROL::FDivergence< Real >::checkInputs(), and ROL::FDivergence< Real >::thresh_.

Member Function Documentation

template<class Real >

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

inlineprivate

Definition at line 76 of file ROL_FDivergence.hpp.

References ROL::FDivergence< Real >::thresh_, and zero.

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

template<class Real >

virtual Real ROL::FDivergence< Real >::Fprimal	(	Real	x,
		int	deriv = `0`
	)		const

pure virtual

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 \(F(x)\).

Implemented in ROL::Chi2Divergence< Real >.

Referenced by ROL::FDivergence< Real >::check().

template<class Real >

virtual Real ROL::FDivergence< Real >::Fdual	(	Real	x,
		int	deriv = `0`
	)		const

pure virtual

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.,

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

Implemented in ROL::Chi2Divergence< Real >.

Referenced by ROL::FDivergence< Real >::check(), ROL::FDivergence< Real >::updateGradient(), ROL::FDivergence< Real >::updateHessVec(), and ROL::FDivergence< Real >::updateValue().

template<class Real >

bool ROL::FDivergence< Real >::check ( std::ostream & outStream = std::cout ) const

inline

Definition at line 131 of file ROL_FDivergence.hpp.

References ROL::FDivergence< Real >::Fdual(), and ROL::FDivergence< Real >::Fprimal().

template<class Real >

void ROL::FDivergence< Real >::initialize ( const Vector< Real > & x )

inlinevirtual

Initialize temporary variables.

Parameters

[in] x is a vector used for initializing storage

Reimplemented from ROL::RandVarFunctional< Real >.

Definition at line 174 of file ROL_FDivergence.hpp.

References ROL::RandVarFunctional< Real >::initialize(), ROL::FDivergence< Real >::valLam2_, ROL::FDivergence< Real >::valLam_, ROL::FDivergence< Real >::valMu2_, and ROL::FDivergence< Real >::valMu_.

template<class Real >

void ROL::FDivergence< 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 180 of file ROL_FDivergence.hpp.

References ROL::RandVarFunctional< Real >::computeValue(), ROL::FDivergence< Real >::Fdual(), ROL::RandVarFunctional< Real >::val_, and ROL::RandVarFunctional< Real >::weight_.

template<class Real >

Real ROL::FDivergence< 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 191 of file ROL_FDivergence.hpp.

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

template<class Real >

void ROL::FDivergence< 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 202 of file ROL_FDivergence.hpp.

References ROL::RandVarFunctional< Real >::computeGradient(), ROL::RandVarFunctional< Real >::computeValue(), ROL::RandVarFunctional< Real >::dualVector_, ROL::FDivergence< Real >::Fdual(), ROL::RandVarFunctional< Real >::g_, ROL::RandVarFunctional< Real >::val_, ROL::FDivergence< Real >::valLam_, ROL::FDivergence< Real >::valMu_, and ROL::RandVarFunctional< Real >::weight_.

template<class Real >

void ROL::FDivergence< 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 223 of file ROL_FDivergence.hpp.

References ROL::RandVarFunctional< Real >::g_, ROL::SampleGenerator< Real >::sumAll(), ROL::FDivergence< Real >::thresh_, ROL::RandVarFunctional< Real >::val_, ROL::FDivergence< Real >::valLam_, and ROL::FDivergence< Real >::valMu_.

template<class Real >

void ROL::FDivergence< 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 240 of file ROL_FDivergence.hpp.

References ROL::RandVarFunctional< Real >::computeGradVec(), ROL::RandVarFunctional< Real >::computeHessVec(), ROL::RandVarFunctional< Real >::computeValue(), ROL::RandVarFunctional< Real >::dualVector_, ROL::FDivergence< Real >::Fdual(), ROL::RandVarFunctional< Real >::hv_, ROL::RandVarFunctional< Real >::val_, ROL::FDivergence< Real >::valLam2_, ROL::FDivergence< Real >::valLam_, ROL::FDivergence< Real >::valMu2_, ROL::FDivergence< Real >::valMu_, and ROL::RandVarFunctional< Real >::weight_.

template<class Real >

void ROL::FDivergence< 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 268 of file ROL_FDivergence.hpp.

References ROL::RandVarFunctional< Real >::hv_, ROL::SampleGenerator< Real >::sumAll(), ROL::RandVarFunctional< Real >::val_, ROL::FDivergence< Real >::valLam2_, ROL::FDivergence< Real >::valLam_, ROL::FDivergence< Real >::valMu2_, and ROL::FDivergence< Real >::valMu_.