Provides an interface for the chi-squared-divergence distributionally robust expectation. More...
#include <ROL_Chi2Divergence.hpp>
Inheritance diagram for ROL::Chi2Divergence< Real >:
Public Member Functions | |
| Chi2Divergence (const Real thresh) | |
| Constructor. More... | |
| Chi2Divergence (ROL::ParameterList &parlist) | |
| Constructor. More... | |
| Real | Fprimal (Real x, int deriv=0) const |
| Implementation of the scalar primal F function. More... | |
| Real | Fdual (Real x, int deriv=0) const |
| Implementation of the scalar dual F function. More... | |
| Public Member Functions inherited from ROL::FDivergence< Real > | |
| FDivergence (const Real thresh) | |
| Constructor. More... | |
| FDivergence (ROL::ParameterList &parlist) | |
| Constructor. More... | |
| bool | check (std::ostream &outStream=std::cout) const |
| void | initialize (const Vector< Real > &x) |
| Initialize temporary variables. More... | |
| void | updateValue (Objective< Real > &obj, const Vector< Real > &x, const std::vector< Real > &xstat, Real &tol) |
| Update internal storage for value computation. More... | |
| Real | getValue (const Vector< Real > &x, const std::vector< Real > &xstat, SampleGenerator< Real > &sampler) |
| Return risk measure value. More... | |
| void | updateGradient (Objective< Real > &obj, const Vector< Real > &x, const std::vector< Real > &xstat, Real &tol) |
| Update internal risk measure storage for gradient computation. More... | |
| void | getGradient (Vector< Real > &g, std::vector< Real > &gstat, const Vector< Real > &x, const std::vector< Real > &xstat, SampleGenerator< Real > &sampler) |
| Return risk measure (sub)gradient. More... | |
| void | updateHessVec (Objective< Real > &obj, const Vector< Real > &v, const std::vector< Real > &vstat, const Vector< Real > &x, const std::vector< Real > &xstat, Real &tol) |
| Update internal risk measure storage for Hessian-time-a-vector computation. More... | |
| void | getHessVec (Vector< Real > &hv, std::vector< Real > &hvstat, const Vector< Real > &v, const std::vector< Real > &vstat, const Vector< Real > &x, const std::vector< Real > &xstat, SampleGenerator< Real > &sampler) |
| Return risk measure Hessian-times-a-vector. More... | |
| Public Member Functions inherited from ROL::RandVarFunctional< Real > | |
| virtual | ~RandVarFunctional () |
| RandVarFunctional (void) | |
| weight_ (0) | |
| void | useStorage (bool storage) |
| void | useHessVecStorage (bool storage) |
| virtual void | setStorage (const Ptr< ScalarController< Real >> &value_storage, const Ptr< VectorController< Real >> &gradient_storage) |
| virtual void | setHessVecStorage (const Ptr< ScalarController< Real >> &gradvec_storage, const Ptr< VectorController< Real >> &hessvec_storage) |
| virtual void | resetStorage (bool flag=true) |
| Reset internal storage. More... | |
| virtual void | resetStorage (UpdateType type) |
| virtual void | setSample (const std::vector< Real > &point, const Real weight) |
| virtual Real | computeStatistic (const Ptr< const std::vector< Real >> &xstat) const |
| Compute statistic. More... | |
Additional Inherited Members | |
| Protected Member Functions inherited from ROL::RandVarFunctional< Real > | |
| Real | computeValue (Objective< Real > &obj, const Vector< Real > &x, Real &tol) |
| void | computeGradient (Vector< Real > &g, Objective< Real > &obj, const Vector< Real > &x, Real &tol) |
| Real | computeGradVec (Vector< Real > &g, Objective< Real > &obj, const Vector< Real > &v, const Vector< Real > &x, Real &tol) |
| void | computeHessVec (Vector< Real > &hv, Objective< Real > &obj, const Vector< Real > &v, const Vector< Real > &x, Real &tol) |
| Protected Attributes inherited from ROL::RandVarFunctional< Real > | |
| Real | val_ |
| Real | gv_ |
| Ptr< Vector< Real > > | g_ |
| Ptr< Vector< Real > > | hv_ |
| Ptr< Vector< Real > > | dualVector_ |
| bool | firstReset_ |
| std::vector< Real > | point_ |
| Real | weight_ |
Detailed Description
template<class Real>
class ROL::Chi2Divergence< Real >
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 39 of file ROL_Chi2Divergence.hpp.
Constructor & Destructor Documentation
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inline |
Constructor.
- Parameters
-
[in] thresh is the tolerance for the F-divergence constraint
Definition at line 46 of file ROL_Chi2Divergence.hpp.
|
inline |
Constructor.
- Parameters
-
[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
- "Threshold" (greater than 0)
Definition at line 56 of file ROL_Chi2Divergence.hpp.
Member Function Documentation
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inlinevirtual |
Implementation of the scalar primal F function.
- Parameters
-
[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 58 of file ROL_Chi2Divergence.hpp.
References zero.
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inlinevirtual |
Implementation of the scalar dual F function.
- Parameters
-
[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 76 of file ROL_Chi2Divergence.hpp.
References zero.
The documentation for this class was generated from the following file:
