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 76 of file ROL_LogQuantileQuadrangle.hpp.
Constructor & Destructor Documentation
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inline |
Constructor.
- Parameters
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[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 128 of file ROL_LogQuantileQuadrangle.hpp.
References ROL::LogQuantileQuadrangle< Real >::checkInputs().
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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 145 of file ROL_LogQuantileQuadrangle.hpp.
References ROL::LogQuantileQuadrangle< Real >::checkInputs(), and ROL::LogQuantileQuadrangle< Real >::parseParameterList().
Member Function Documentation
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inlineprivate |
Definition at line 85 of file ROL_LogQuantileQuadrangle.hpp.
References ROL::LogQuantileQuadrangle< Real >::alpha_, ROL::LogQuantileQuadrangle< Real >::eps_, ROL::LogQuantileQuadrangle< Real >::pf_, and ROL::LogQuantileQuadrangle< Real >::rate_.
Referenced by ROL::LogQuantileQuadrangle< Real >::LogQuantileQuadrangle().
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inlineprivate |
Definition at line 108 of file ROL_LogQuantileQuadrangle.hpp.
References ROL::LogQuantileQuadrangle< Real >::alpha_, ROL::LogQuantileQuadrangle< Real >::eps_, ROL::LogQuantileQuadrangle< Real >::pf_, ROL::LogQuantileQuadrangle< Real >::rate_, and zero.
Referenced by ROL::LogQuantileQuadrangle< Real >::LogQuantileQuadrangle().
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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 151 of file ROL_LogQuantileQuadrangle.hpp.
References ROL::LogQuantileQuadrangle< Real >::regret(), and zero.
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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 162 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().
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inlinevirtual |
Run default derivative tests for the scalar regret function.
Reimplemented from ROL::ExpectationQuad< Real >.
Definition at line 178 of file ROL_LogQuantileQuadrangle.hpp.
References ROL::ExpectationQuad< Real >::check(), ROL::LogQuantileQuadrangle< Real >::eps_, ROL::LogQuantileQuadrangle< Real >::regret(), and zero.
Member Data Documentation
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private |
Definition at line 79 of file ROL_LogQuantileQuadrangle.hpp.
Referenced by ROL::LogQuantileQuadrangle< Real >::checkInputs(), ROL::LogQuantileQuadrangle< Real >::parseParameterList(), and ROL::LogQuantileQuadrangle< Real >::regret().
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private |
Definition at line 81 of file ROL_LogQuantileQuadrangle.hpp.
Referenced by ROL::LogQuantileQuadrangle< Real >::checkInputs(), ROL::LogQuantileQuadrangle< Real >::parseParameterList(), and ROL::LogQuantileQuadrangle< Real >::regret().
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private |
Definition at line 82 of file ROL_LogQuantileQuadrangle.hpp.
Referenced by ROL::LogQuantileQuadrangle< Real >::checkInputs(), ROL::LogQuantileQuadrangle< Real >::parseParameterList(), and ROL::LogQuantileQuadrangle< Real >::regret().
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private |
Definition at line 83 of file ROL_LogQuantileQuadrangle.hpp.
Referenced by ROL::LogQuantileQuadrangle< Real >::check(), ROL::LogQuantileQuadrangle< Real >::checkInputs(), and ROL::LogQuantileQuadrangle< Real >::parseParameterList().
The documentation for this class was generated from the following file:
