ROL
Public Member Functions | Private Member Functions | Private Attributes | List of all members
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. 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 47 of file ROL_LogExponentialQuadrangle.hpp.

Constructor & Destructor Documentation

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

Constructor.

Parameters
[in]coeffis the scale parameter \(\lambda\)

Definition at line 80 of file ROL_LogExponentialQuadrangle.hpp.

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

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

Constructor.

Parameters
[in]parlistis 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 ROL::LogExponentialQuadrangle< Real >::checkInputs(), and ROL::LogExponentialQuadrangle< Real >::parseParameterList().

Member Function Documentation

template<class Real >
void ROL::LogExponentialQuadrangle< Real >::parseParameterList ( ROL::ParameterList &  parlist)
inlineprivate
template<class Real >
void ROL::LogExponentialQuadrangle< Real >::checkInputs ( void  ) const
inlineprivate
template<class Real >
Real ROL::LogExponentialQuadrangle< 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 99 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]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 113 of file ROL_LogExponentialQuadrangle.hpp.

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

Member Data Documentation

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

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