ROL
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ROL::Chi2Divergence< Real > Class Template Reference

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 (Teuchos::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 (Teuchos::ParameterList &parlist)
 Constructor. More...
 
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...
 
Real getValue (SampleGenerator< Real > &sampler)
 Return risk measure value. More...
 
void update (const Real val, const Vector< Real > &g, const Real weight)
 Update internal risk measure storage for gradient computation. More...
 
void getGradient (Vector< Real > &g, SampleGenerator< Real > &sampler)
 Return risk measure (sub)gradient. 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...
 
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)
 

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::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

◆ Chi2Divergence() [1/2]

template<class Real >
ROL::Chi2Divergence< Real >::Chi2Divergence ( const Real  thresh)
inline

Constructor.

Parameters
[in]threshis the tolerance for the F-divergence constraint

Definition at line 80 of file ROL_Chi2Divergence.hpp.

◆ Chi2Divergence() [2/2]

template<class Real >
ROL::Chi2Divergence< Real >::Chi2Divergence ( Teuchos::ParameterList &  parlist)
inline

Constructor.

Parameters
[in]parlistis 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

◆ Fprimal()

template<class Real >
Real ROL::Chi2Divergence< Real >::Fprimal ( Real  x,
int  deriv = 0 
)
inlinevirtual

Implementation of the scalar primal F function.

Parameters
[in]xis a scalar input
[in]derivis 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.

◆ Fdual()

template<class Real >
Real ROL::Chi2Divergence< Real >::Fdual ( Real  x,
int  deriv = 0 
)
inlinevirtual

Implementation of the scalar dual F function.

Parameters
[in]xis a scalar input
[in]derivis 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.


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