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 (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... | |
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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... | |
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virtual | ~RiskMeasure () |
RiskMeasure (void) | |
Private Member Functions | |
void | checkInputs (void) const |
Private Attributes | |
Real | coeff_ |
Additional Inherited Members | |
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Real | val_ |
Real | gv_ |
Teuchos::RCP< Vector< Real > > | g_ |
Teuchos::RCP< Vector< Real > > | hv_ |
Teuchos::RCP< Vector< Real > > | dualVector_ |
bool | firstReset_ |
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.
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inline |
Constructor.
[in] | coeff | is the scale parameter \(\lambda\) |
Definition at line 96 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 109 of file ROL_LogExponentialQuadrangle.hpp.
References ROL::LogExponentialQuadrangle< Real >::checkInputs(), and ROL::LogExponentialQuadrangle< Real >::coeff_.
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inlineprivate |
Definition at line 85 of file ROL_LogExponentialQuadrangle.hpp.
References ROL::LogExponentialQuadrangle< Real >::coeff_.
Referenced by ROL::LogExponentialQuadrangle< Real >::LogExponentialQuadrangle().
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inline |
Definition at line 117 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 131 of file ROL_LogExponentialQuadrangle.hpp.
References ROL::LogExponentialQuadrangle< Real >::error().
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private |
Definition at line 83 of file ROL_LogExponentialQuadrangle.hpp.
Referenced by ROL::LogExponentialQuadrangle< Real >::checkInputs(), ROL::LogExponentialQuadrangle< Real >::error(), and ROL::LogExponentialQuadrangle< Real >::LogExponentialQuadrangle().