Provides an interface for the entropic risk using the expectation risk quadrangle. More...

#include <ROL_LogExponentialQuadrangle.hpp>

Inheritance diagram for ROL::LogExponentialQuadrangle< Real >:

Public Member Functions
	LogExponentialQuadrangle (const Real coeff=1)
	Constructor. More...

	LogExponentialQuadrangle (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::LogExponentialQuadrangle< Real >

Provides an interface for the entropic risk using the expectation risk quadrangle.

The entropic risk measure (also called the exponential utility and the log-exponential risk measure) is

\[ \mathcal{R}(X) = \lambda \log\mathbb{E}\left[\exp\left(\frac{X}{\lambda}\right)\right] \]

for \(\lambda > 0\). The entropic risk is convex, translation equivariant and monotonic.

This class defines the entropic risk measure using the framework of the expectation risk quadrangle. In this case, the scalar regret function is

\[ v(x) = \lambda(\exp\left(\frac{x}{\lambda}\right)-1). \]

The entropic risk measure is then implemented 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 81 of file ROL_LogExponentialQuadrangle.hpp.

Constructor & Destructor Documentation

template<class Real >

ROL::LogExponentialQuadrangle< Real >::LogExponentialQuadrangle ( const Real coeff = 1 )

inline

Constructor.

Parameters

[in] coeff is the scale parameter \(\lambda\)

Definition at line 114 of file ROL_LogExponentialQuadrangle.hpp.

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

template<class Real >

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

inline

Constructor.

Parameters

[in] parlist is a parameter list specifying inputs

parlist should contain sublists "SOL"->"Risk Measures"->"Log-Exponential Quadrangle" and withing the "Log-Exponential Quadrangle" sublist should have

"Rate" (greater than 0).

Definition at line 127 of file ROL_LogExponentialQuadrangle.hpp.

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

Member Function Documentation

template<class Real >

void ROL::LogExponentialQuadrangle< Real >::parseParameterList ( ROL::ParameterList & parlist )

inlineprivate

Definition at line 85 of file ROL_LogExponentialQuadrangle.hpp.

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

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

template<class Real >

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

inlineprivate

Definition at line 103 of file ROL_LogExponentialQuadrangle.hpp.

References ROL::LogExponentialQuadrangle< Real >::coeff_, and zero.

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

template<class Real >

Real ROL::LogExponentialQuadrangle< Real >::error	(	Real	x,
		int	deriv = `0`
	)

inlinevirtual

Evaluate the scalar error function at x.

Parameters

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

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

Reimplemented from ROL::ExpectationQuad< Real >.

Definition at line 133 of file ROL_LogExponentialQuadrangle.hpp.

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

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

template<class Real >

Real ROL::LogExponentialQuadrangle< Real >::regret	(	Real	x,
		int	deriv = `0`
	)

inlinevirtual

Evaluate the scalar regret function at x.

Parameters

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

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

Implements ROL::ExpectationQuad< Real >.

Definition at line 147 of file ROL_LogExponentialQuadrangle.hpp.

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

Member Data Documentation

template<class Real >

Real ROL::LogExponentialQuadrangle< Real >::coeff_

private

Definition at line 83 of file ROL_LogExponentialQuadrangle.hpp.

Referenced by ROL::LogExponentialQuadrangle< Real >::checkInputs(), ROL::LogExponentialQuadrangle< Real >::error(), and ROL::LogExponentialQuadrangle< Real >::parseParameterList().

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

ROL_LogExponentialQuadrangle.hpp

Public Member Functions

Private Member Functions

Private Attributes

Detailed Description

template<class Real> class ROL::LogExponentialQuadrangle< Real >

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

template<class Real>
class ROL::LogExponentialQuadrangle< Real >