ROL::LogExponentialQuadrangle< Real > Class Template Reference

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.
	LogExponentialQuadrangle (ROL::ParameterList &parlist)
	Constructor.
Real	error (Real x, int deriv=0)
	Evaluate the scalar error function at x.
Real	regret (Real x, int deriv=0)
	Evaluate the scalar regret function at x.
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.

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 47 of file ROL_LogExponentialQuadrangle.hpp.

Constructor & Destructor Documentation

LogExponentialQuadrangle() [1/2]

template<class Real>

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

inline

Constructor.

Parameters

[in]

coeff

is the scale parameter \(\lambda\)

Definition at line 80 of file ROL_LogExponentialQuadrangle.hpp.

References checkInputs(), coeff_, and ROL::ExpectationQuad< Real >::ExpectationQuad().

LogExponentialQuadrangle() [2/2]

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 93 of file ROL_LogExponentialQuadrangle.hpp.

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

Member Function Documentation

parseParameterList()

template<class Real>

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

inlineprivate

Definition at line 51 of file ROL_LogExponentialQuadrangle.hpp.

References coeff_.

Referenced by LogExponentialQuadrangle().

checkInputs()

template<class Real>

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

inlineprivate

Definition at line 69 of file ROL_LogExponentialQuadrangle.hpp.

References coeff_, and zero.

Referenced by LogExponentialQuadrangle(), and LogExponentialQuadrangle().

error()

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 99 of file ROL_LogExponentialQuadrangle.hpp.

References coeff_.

Referenced by regret().

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 113 of file ROL_LogExponentialQuadrangle.hpp.

References error(), and zero.

Member Data Documentation

coeff_

template<class Real>

Real ROL::LogExponentialQuadrangle< Real >::coeff_

private

Definition at line 49 of file ROL_LogExponentialQuadrangle.hpp.

Referenced by checkInputs(), error(), LogExponentialQuadrangle(), and parseParameterList().

---

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

• ROL_LogExponentialQuadrangle.hpp