ROL
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Provides an interface for the entropic risk using the expectation risk quadrangle. More...
#include <ROL_LogExponentialQuadrangle.hpp>
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_ |
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.
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inline |
Constructor.
[in] | coeff | is the scale parameter \(\lambda\) |
Definition at line 80 of file ROL_LogExponentialQuadrangle.hpp.
References ROL::LogExponentialQuadrangle< Real >::checkInputs().
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inline |
Constructor.
[in] | parlist | is a parameter list specifying inputs |
parlist should contain sublists "SOL"->"Risk Measures"->"Log-Exponential Quadrangle" and withing the "Log-Exponential Quadrangle" sublist should have
Definition at line 93 of file ROL_LogExponentialQuadrangle.hpp.
References ROL::LogExponentialQuadrangle< Real >::checkInputs(), and ROL::LogExponentialQuadrangle< Real >::parseParameterList().
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inlineprivate |
Definition at line 51 of file ROL_LogExponentialQuadrangle.hpp.
References ROL::LogExponentialQuadrangle< Real >::coeff_.
Referenced by ROL::LogExponentialQuadrangle< Real >::LogExponentialQuadrangle().
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inlineprivate |
Definition at line 69 of file ROL_LogExponentialQuadrangle.hpp.
References ROL::LogExponentialQuadrangle< Real >::coeff_, and zero.
Referenced by ROL::LogExponentialQuadrangle< Real >::LogExponentialQuadrangle().
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inlinevirtual |
Evaluate the scalar error function at x.
[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 99 of file ROL_LogExponentialQuadrangle.hpp.
References ROL::LogExponentialQuadrangle< Real >::coeff_.
Referenced by ROL::LogExponentialQuadrangle< Real >::regret().
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inlinevirtual |
Evaluate the scalar regret function at x.
[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 113 of file ROL_LogExponentialQuadrangle.hpp.
References ROL::LogExponentialQuadrangle< Real >::error(), and zero.
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private |
Definition at line 49 of file ROL_LogExponentialQuadrangle.hpp.
Referenced by ROL::LogExponentialQuadrangle< Real >::checkInputs(), ROL::LogExponentialQuadrangle< Real >::error(), and ROL::LogExponentialQuadrangle< Real >::parseParameterList().