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 (Teuchos::ParameterList &parlist)
 Constructor. More...
 
Real error (Real x, int deriv=0)
 
Real regret (Real x, int deriv=0)
 Evaluate the scalar regret function at x. More...
 
- Public Member Functions inherited from ROL::ExpectationQuad< Real >
 ExpectationQuad (void)
 
virtual void checkRegret (void)
 Run default derivative tests for the scalar regret function. 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...
 
void update (const Real val, const Vector< Real > &g, const Real weight)
 Update internal risk measure storage for gradient computation. 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...
 
Real getValue (SampleGenerator< Real > &sampler)
 Return risk measure value. More...
 
void getGradient (Vector< Real > &g, SampleGenerator< Real > &sampler)
 Return risk measure (sub)gradient. 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)
 

Private Member Functions

void checkInputs (void) const
 

Private Attributes

Real coeff_
 

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::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

◆ LogExponentialQuadrangle() [1/2]

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

Constructor.

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

Definition at line 96 of file ROL_LogExponentialQuadrangle.hpp.

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

◆ LogExponentialQuadrangle() [2/2]

template<class Real >
ROL::LogExponentialQuadrangle< Real >::LogExponentialQuadrangle ( Teuchos::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 109 of file ROL_LogExponentialQuadrangle.hpp.

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

Member Function Documentation

◆ checkInputs()

template<class Real >
void ROL::LogExponentialQuadrangle< Real >::checkInputs ( void  ) const
inlineprivate

◆ error()

template<class Real >
Real ROL::LogExponentialQuadrangle< Real >::error ( Real  x,
int  deriv = 0 
)
inline

◆ 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 131 of file ROL_LogExponentialQuadrangle.hpp.

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

Member Data Documentation

◆ coeff_

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

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