ROL: ROL::LogQuantileQuadrangle< Real > Class Template Reference

ROL

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.
	LogQuantileQuadrangle (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.
void	check (void)
	Run default derivative tests for the scalar regret function.
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

◆ LogQuantileQuadrangle() [1/2]

template<class Real>

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

inline

Constructor.

Parameters

[in]	alpha	is the scale parameter for the negative branch of the scalar regret
[in]	rate	is the rate parameter for the positive branch of the scalar regret
[in]	eps	is the smoothing parameter for the approximate plus function
[in]	pf	is the plus function or an approximation

Definition at line 94 of file ROL_LogQuantileQuadrangle.hpp.

References alpha_, checkInputs(), eps_, ROL::ExpectationQuad< Real >::ExpectationQuad(), pf_, and rate_.

◆ LogQuantileQuadrangle() [2/2]

template<class Real>

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

inline

Constructor.

Parameters

[in] parlist is 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 checkInputs(), ROL::ExpectationQuad< Real >::ExpectationQuad(), and parseParameterList().

Member Function Documentation

◆ parseParameterList()

template<class Real>

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

inlineprivate

Definition at line 51 of file ROL_LogQuantileQuadrangle.hpp.

References alpha_, eps_, pf_, and rate_.

Referenced by LogQuantileQuadrangle().

◆ checkInputs()

template<class Real>

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

inlineprivate

Definition at line 74 of file ROL_LogQuantileQuadrangle.hpp.

References alpha_, eps_, pf_, rate_, and zero.

Referenced by LogQuantileQuadrangle(), and LogQuantileQuadrangle().

◆ error()

template<class Real>

Real ROL::LogQuantileQuadrangle< 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 117 of file ROL_LogQuantileQuadrangle.hpp.

References regret(), and zero.

◆ regret()

template<class Real>

Real ROL::LogQuantileQuadrangle< 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 128 of file ROL_LogQuantileQuadrangle.hpp.

References alpha_, pf_, rate_, and zero.

Referenced by check(), and error().

◆ check()

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(), eps_, regret(), and zero.

Member Data Documentation

◆ pf_

template<class Real>

ROL::Ptr<PlusFunction<Real> > ROL::LogQuantileQuadrangle< Real >::pf_

private

Definition at line 45 of file ROL_LogQuantileQuadrangle.hpp.

Referenced by checkInputs(), LogQuantileQuadrangle(), parseParameterList(), and regret().

◆ alpha_

template<class Real>

Real ROL::LogQuantileQuadrangle< Real >::alpha_

private

Definition at line 47 of file ROL_LogQuantileQuadrangle.hpp.

Referenced by checkInputs(), LogQuantileQuadrangle(), parseParameterList(), and regret().

◆ rate_

template<class Real>

Real ROL::LogQuantileQuadrangle< Real >::rate_

private

Definition at line 48 of file ROL_LogQuantileQuadrangle.hpp.

Referenced by checkInputs(), LogQuantileQuadrangle(), parseParameterList(), and regret().

◆ eps_

template<class Real>

Real ROL::LogQuantileQuadrangle< Real >::eps_

private

Definition at line 49 of file ROL_LogQuantileQuadrangle.hpp.

Referenced by check(), checkInputs(), LogQuantileQuadrangle(), and parseParameterList().

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

ROL_LogQuantileQuadrangle.hpp