ROL
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ROL::MeanVarianceQuadrangle< Real > Class Template Reference

Provides an interface for the mean plus variance risk measure using the expectation risk quadrangle. More...

#include <ROL_MeanVarianceQuadrangle.hpp>

+ Inheritance diagram for ROL::MeanVarianceQuadrangle< Real >:

Public Member Functions

 MeanVarianceQuadrangle (const Real coeff=1)
 Constructor. More...
 
 MeanVarianceQuadrangle (ROL::ParameterList &parlist)
 Constructor. More...
 
Real error (Real x, int deriv=0)
 Evaluate the scalar error function at x. More...
 
Real regret (Real x, int deriv=0)
 Evaluate the scalar regret function at x. More...
 
- Public Member Functions inherited from ROL::ExpectationQuad< Real >
virtual ~ExpectationQuad (void)
 
 ExpectationQuad (void)
 
virtual void check (void)
 Run default derivative tests for the scalar regret function. More...
 

Private Member Functions

void parseParameterList (ROL::ParameterList &parlist)
 
void checkInputs (void) const
 

Private Attributes

Real coeff_
 

Detailed Description

template<class Real>
class ROL::MeanVarianceQuadrangle< Real >

Provides an interface for the mean plus variance risk measure using the expectation risk quadrangle.

The mean plus variances risk measure is

\[ \mathcal{R}(X) = \mathbb{E}[X] + c \mathbb{E}[|X-\mathbb{E}[X]|^2] \]

where \(c \ge 0\). \(\mathcal{R}\) is law-invariant, but not coherent since it violates positive homogeneity. The associated scalar regret function is

\[ v(x) = c x^2 + x \]

and the mean-plus-variance risk measure is computed as

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

ROL implements this by augmenting the optimization vector \(x_0\) with the parameter \(t\), then minimizes jointly for \((x_0,t)\).

Definition at line 44 of file ROL_MeanVarianceQuadrangle.hpp.

Constructor & Destructor Documentation

template<class Real >
ROL::MeanVarianceQuadrangle< Real >::MeanVarianceQuadrangle ( const Real  coeff = 1)
inline

Constructor.

Parameters
[in]coeffis the weight for variance term

Definition at line 75 of file ROL_MeanVarianceQuadrangle.hpp.

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

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

Constructor.

Parameters
[in]parlistis a parameter list specifying inputs

parlist should contain sublists "SOL"->"Risk Measure"->"Mean-Variance Quadrangle" and within the "Mean-Variance Quadrangle" sublist should have the following parameters

  • "Coefficient" (array of positive scalars).

Definition at line 88 of file ROL_MeanVarianceQuadrangle.hpp.

References ROL::MeanVarianceQuadrangle< Real >::checkInputs(), and ROL::MeanVarianceQuadrangle< Real >::parseParameterList().

Member Function Documentation

template<class Real >
void ROL::MeanVarianceQuadrangle< Real >::parseParameterList ( ROL::ParameterList &  parlist)
inlineprivate
template<class Real >
void ROL::MeanVarianceQuadrangle< Real >::checkInputs ( void  ) const
inlineprivate
template<class Real >
Real ROL::MeanVarianceQuadrangle< Real >::error ( Real  x,
int  deriv = 0 
)
inlinevirtual

Evaluate the scalar error function at x.

Parameters
[in]xis the scalar input
[in]derivis the derivative order

This function returns \(e(x)\) or a derivative of \(e(x)\).

Reimplemented from ROL::ExpectationQuad< Real >.

Definition at line 94 of file ROL_MeanVarianceQuadrangle.hpp.

References ROL::MeanVarianceQuadrangle< Real >::coeff_.

Referenced by ROL::MeanVarianceQuadrangle< Real >::regret().

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

Evaluate the scalar regret function at x.

Parameters
[in]xis the scalar input
[in]derivis the derivative order

This function returns \(v(x)\) or a derivative of \(v(x)\).

Implements ROL::ExpectationQuad< Real >.

Definition at line 108 of file ROL_MeanVarianceQuadrangle.hpp.

References ROL::MeanVarianceQuadrangle< Real >::error(), and zero.

Member Data Documentation

template<class Real >
Real ROL::MeanVarianceQuadrangle< Real >::coeff_
private

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