ROL
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ROL::LogQuantileQuadrangle< Real > Class Template Reference

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

#include <ROL_LogQuantileQuadrangle.hpp>

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

Public Member Functions

 LogQuantileQuadrangle (Real alpha, Real rate, Real eps, ROL::Ptr< PlusFunction< Real > > &pf)
 Constructor. More...
 
 LogQuantileQuadrangle (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...
 
void check (void)
 Run default derivative tests for the scalar regret function. More...
 
- Public Member Functions inherited from ROL::ExpectationQuad< Real >
virtual ~ExpectationQuad (void)
 
 ExpectationQuad (void)
 

Private Member Functions

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

Private Attributes

ROL::Ptr< PlusFunction< Real > > pf_
 
Real alpha_
 
Real rate_
 
Real eps_
 

Detailed Description

template<class Real>
class ROL::LogQuantileQuadrangle< Real >

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

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

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

for \(\lambda > 0\) and \(0 \le \alpha < 1\). The entropic risk measure is then implemented as

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

The conditional entropic risk is convex, translation equivariant and monotonic. ROL implements this by augmenting the optimization vector \(x_0\) with the parameter \(t\), then minimizes jointly for \((x_0,t)\).

Definition at line 42 of file ROL_LogQuantileQuadrangle.hpp.

Constructor & Destructor Documentation

template<class Real >
ROL::LogQuantileQuadrangle< Real >::LogQuantileQuadrangle ( Real  alpha,
Real  rate,
Real  eps,
ROL::Ptr< PlusFunction< Real > > &  pf 
)
inline

Constructor.

Parameters
[in]alphais the scale parameter for the negative branch of the scalar regret
[in]rateis the rate parameter for the positive branch of the scalar regret
[in]epsis the smoothing parameter for the approximate plus function
[in]pfis the plus function or an approximation

Definition at line 94 of file ROL_LogQuantileQuadrangle.hpp.

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

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

Constructor.

Parameters
[in]parlistis a parameter list specifying inputs

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

  • "Slope for Linear Growth" (between 0 and 1)
  • "Rate for Exponential Growth" (must be positive)
  • "Smoothing Parameter" (must be positive)
  • A sublist for plus function information.

Definition at line 111 of file ROL_LogQuantileQuadrangle.hpp.

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

Member Function Documentation

template<class Real >
void ROL::LogQuantileQuadrangle< Real >::parseParameterList ( ROL::ParameterList &  parlist)
inlineprivate
template<class Real >
void ROL::LogQuantileQuadrangle< Real >::checkInputs ( void  ) const
inlineprivate
template<class Real >
Real ROL::LogQuantileQuadrangle< 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 117 of file ROL_LogQuantileQuadrangle.hpp.

References ROL::LogQuantileQuadrangle< Real >::regret(), and zero.

template<class Real >
Real ROL::LogQuantileQuadrangle< 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 128 of file ROL_LogQuantileQuadrangle.hpp.

References ROL::LogQuantileQuadrangle< Real >::alpha_, ROL::LogQuantileQuadrangle< Real >::pf_, ROL::LogQuantileQuadrangle< Real >::rate_, and zero.

Referenced by ROL::LogQuantileQuadrangle< Real >::check(), and ROL::LogQuantileQuadrangle< Real >::error().

template<class Real >
void ROL::LogQuantileQuadrangle< Real >::check ( void  )
inlinevirtual

Run default derivative tests for the scalar regret function.

Reimplemented from ROL::ExpectationQuad< Real >.

Definition at line 144 of file ROL_LogQuantileQuadrangle.hpp.

References ROL::ExpectationQuad< Real >::check(), ROL::LogQuantileQuadrangle< Real >::eps_, ROL::LogQuantileQuadrangle< Real >::regret(), and zero.

Member Data Documentation

template<class Real >
ROL::Ptr<PlusFunction<Real> > ROL::LogQuantileQuadrangle< Real >::pf_
private
template<class Real >
Real ROL::LogQuantileQuadrangle< Real >::alpha_
private
template<class Real >
Real ROL::LogQuantileQuadrangle< Real >::rate_
private
template<class Real >
Real ROL::LogQuantileQuadrangle< Real >::eps_
private

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