ROL
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Provides an interface for the chi-squared-divergence distributionally robust expectation. More...
#include <ROL_Chi2Divergence.hpp>
Public Member Functions | |
Chi2Divergence (const Real thresh) | |
Constructor. More... | |
Chi2Divergence (Teuchos::ParameterList &parlist) | |
Constructor. More... | |
Real | Fprimal (Real x, int deriv=0) |
Implementation of the scalar primal F function. More... | |
Real | Fdual (Real x, int deriv=0) |
Implementation of the scalar dual F function. More... | |
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FDivergence (const Real thresh) | |
Constructor. More... | |
FDivergence (Teuchos::ParameterList &parlist) | |
Constructor. 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... | |
Real | getValue (SampleGenerator< Real > &sampler) |
Return risk measure value. More... | |
void | update (const Real val, const Vector< Real > &g, const Real weight) |
Update internal risk measure storage for gradient computation. More... | |
void | getGradient (Vector< Real > &g, SampleGenerator< Real > &sampler) |
Return risk measure (sub)gradient. 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... | |
void | getHessVec (Vector< Real > &hv, SampleGenerator< Real > &sampler) |
Return risk measure Hessian-times-a-vector. More... | |
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virtual | ~RiskMeasure () |
RiskMeasure (void) | |
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 chi-squared-divergence distributionally robust expectation.
This class defines a risk measure \(\mathcal{R}\) that arises in distributionally robust stochastic programming. \(\mathcal{R}\) is given by
\[ \mathcal{R}(X) = \sup_{\vartheta\in\mathfrak{A}} \mathbb{E}[\vartheta X] \]
where \(\mathfrak{A}\) is called the ambiguity (or uncertainty) set and is defined by a constraint on the \(\chi^2\)-divergence, i.e.,
\[ \mathfrak{A} = \left\{\vartheta\in\mathcal{X}^*\,:\, \mathbb{E}[\vartheta] = 1,\; \vartheta \ge 0,\;\text{and}\; \frac{1}{2}\mathbb{E}[(\vartheta-1)^2] \le \epsilon\right\}. \]
\(\mathcal{R}\) is a law-invariant, coherent risk measure.
Definition at line 73 of file ROL_Chi2Divergence.hpp.
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inline |
Constructor.
[in] | thresh | is the tolerance for the F-divergence constraint |
Definition at line 80 of file ROL_Chi2Divergence.hpp.
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inline |
Constructor.
[in] | parlist | is a parameter list specifying inputs |
parlist should contain sublists "SOL"->"Risk Measure"->"F-Divergence" and within the "F-Divergence" sublist should have the following parameters
Definition at line 90 of file ROL_Chi2Divergence.hpp.
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inlinevirtual |
Implementation of the scalar primal F function.
[in] | x | is a scalar input |
[in] | deriv | is the derivative order |
Upon return, Fprimal returns \(F(x)\) or a derivative of \(F(x)\).
Implements ROL::FDivergence< Real >.
Definition at line 92 of file ROL_Chi2Divergence.hpp.
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inlinevirtual |
Implementation of the scalar dual F function.
[in] | x | is a scalar input |
[in] | deriv | is the derivative order |
Upon return, Fdual returns \(F^*(x)\) or a derivative of \(F^*(x)\). Here, \(F^*\) denotes the Legendre-Fenchel transformation of \(F\), i.e.,
\[ F^*(y) = \sup_{x\in\mathbb{R}}\{xy - F(x)\}. \]
Implements ROL::FDivergence< Real >.
Definition at line 110 of file ROL_Chi2Divergence.hpp.