Provides a general interface for the F-divergence distributionally robust expectation. More...
#include <ROL_FDivergence.hpp>
Inheritance diagram for ROL::FDivergence< Real >:
Public Member Functions | |
| FDivergence (const Real thresh) | |
| Constructor. More... | |
| FDivergence (Teuchos::ParameterList &parlist) | |
| Constructor. More... | |
| virtual Real | Fprimal (Real x, int deriv=0)=0 |
| Implementation of the scalar primal F function. More... | |
| virtual Real | Fdual (Real x, int deriv=0)=0 |
| Implementation of the scalar dual F 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... | |
| 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... | |
| Public Member Functions inherited from ROL::RiskMeasure< Real > | |
| virtual | ~RiskMeasure () |
| RiskMeasure (void) | |
Private Member Functions | |
| void | checkInputs (void) const |
Private Attributes | |
| Real | thresh_ |
| Teuchos::RCP< Vector< Real > > | dualVector_ |
| Real | xlam_ |
| Real | xmu_ |
| Real | vlam_ |
| Real | vmu_ |
| Real | valLam_ |
| Real | valLam2_ |
| Real | valMu_ |
| Real | valMu2_ |
| bool | firstReset_ |
Additional Inherited Members | |
| Protected Attributes inherited from ROL::RiskMeasure< Real > | |
| Real | val_ |
| Real | gv_ |
| Teuchos::RCP< Vector< Real > > | g_ |
| Teuchos::RCP< Vector< Real > > | hv_ |
| Teuchos::RCP< Vector< Real > > | dualVector_ |
| bool | firstReset_ |
Detailed Description
template<class Real>
class ROL::FDivergence< Real >
Provides a general interface for the F-divergence distributionally robust expectation.
This class defines a risk measure \(\mathcal{R}\) which 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 F-divergence, i.e.,
\[ \mathfrak{A} = \{\vartheta\in\mathcal{X}^*\,:\, \mathbb{E}[\vartheta] = 1,\; \vartheta \ge 0,\;\text{and}\; \mathbb{E}[F(\vartheta)] \le \epsilon\} \]
where \(F:\mathbb{R}\to[0,\infty]\) convex, lower semicontinuous and satisfies \(F(1) = 1\) and \(F(x) = \infty\) for \(x < 0\). \(\mathcal{R}\) is a law-invariant, coherent risk measure. Moreover, by a duality argument, \(\mathcal{R}\) can be reformulated as
\[ \mathcal{R}(X) = \inf_{\lambda > 0,\,\mu}\left\{ \lambda \epsilon + \mu + \mathbb{E}\left[ (\lambda F)^*(X-\mu)\right]\right\}. \]
Here, \((\lambda F)^*\) denotes the Legendre-Fenchel transformation of \((\lambda F)\). ROL implements this by augmenting the optimization vector \(x_0\) with the parameter \((\lambda,\mu)\), then minimizes jointly for \((x_0,\lambda,\mu)\).
Definition at line 88 of file ROL_FDivergence.hpp.
Constructor & Destructor Documentation
◆ FDivergence() [1/2]
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inline |
Constructor.
- Parameters
-
[in] eps is the tolerance for the F-divergence constraint
Definition at line 118 of file ROL_FDivergence.hpp.
References ROL::FDivergence< Real >::checkInputs().
◆ FDivergence() [2/2]
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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 132 of file ROL_FDivergence.hpp.
References ROL::FDivergence< Real >::checkInputs(), ROL::FDivergence< Real >::Fdual(), and ROL::FDivergence< Real >::Fprimal().
Member Function Documentation
◆ checkInputs()
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inlineprivate |
Definition at line 107 of file ROL_FDivergence.hpp.
Referenced by ROL::FDivergence< Real >::FDivergence().
◆ Fprimal()
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pure virtual |
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 \(F(x)\).
Implemented in ROL::Chi2Divergence< Real >.
Referenced by ROL::FDivergence< Real >::FDivergence().
◆ Fdual()
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pure virtual |
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.,
\[ F^*(y) = \sup_{x\in\mathbb{R}}\{xy - F(x)\}. \]
Implemented in ROL::Chi2Divergence< Real >.
Referenced by ROL::FDivergence< Real >::FDivergence(), and ROL::FDivergence< Real >::update().
◆ reset() [1/2]
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inlinevirtual |
Reset internal risk measure storage. Called for value and gradient computation.
- Parameters
-
[out] x0 is a user-provided optimization vector [in] x is a (potentially) augmented risk vector
On input, \(x\) carries \(x_0\) and any statistics (scalars) associated with the risk measure.
Reimplemented from ROL::RiskMeasure< Real >.
Definition at line 164 of file ROL_FDivergence.hpp.
References ROL::RiskMeasure< Real >::reset().
Referenced by ROL::FDivergence< Real >::reset().
◆ reset() [2/2]
|
inlinevirtual |
Reset internal risk measure storage. Called for Hessian-times-a-vector computation.
- Parameters
-
[out] x0 is a user-provided optimization vector [in] x is a (potentially) augmented risk vector [out] v0 is a user-provided direction vector [in] v is a (potentially) augmented risk vector
On input, \(x\) carries \(x_0\) and any statistics (scalars) associated with the risk measure. Similarly, \(v\) carries \(v_0\) and any statistics (scalars) associated with the risk measure.
Reimplemented from ROL::RiskMeasure< Real >.
Definition at line 176 of file ROL_FDivergence.hpp.
References ROL::FDivergence< Real >::reset().
◆ update() [1/3]
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inlinevirtual |
Update internal risk measure storage for value computation.
- Parameters
-
[in] val is the value of the random variable objective function at the current sample point [in] weight is the weight associated with the current sample point
Reimplemented from ROL::RiskMeasure< Real >.
Definition at line 186 of file ROL_FDivergence.hpp.
References ROL::FDivergence< Real >::Fdual().
◆ getValue()
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inlinevirtual |
Return risk measure value.
- Parameters
-
[in] sampler is the ROL::SampleGenerator used to sample the objective function
Upon return, getValue returns \(\mathcal{R}(f(x_0))\) where \(f(x_0)\) denotes the random variable objective function evaluated at \(x_0\).
Reimplemented from ROL::RiskMeasure< Real >.
Definition at line 191 of file ROL_FDivergence.hpp.
References ROL::SampleGenerator< Real >::sumAll().
◆ update() [2/3]
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inlinevirtual |
Update internal risk measure storage for gradient computation.
- Parameters
-
[in] val is the value of the random variable objective function at the current sample point [in] g is the gradient of the random variable objective function at the current sample point [in] weight is the weight associated with the current sample point
Reimplemented from ROL::RiskMeasure< Real >.
Definition at line 198 of file ROL_FDivergence.hpp.
References ROL::FDivergence< Real >::Fdual(), and ROL::FDivergence< Real >::xmu_.
◆ getGradient()
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inlinevirtual |
Return risk measure (sub)gradient.
- Parameters
-
[out] g is the (sub)gradient of the risk measure [in] sampler is the ROL::SampleGenerator used to sample the objective function
Upon return, getGradient returns \(\theta\in\partial\mathcal{R}(f(x_0))\) where \(f(x_0)\) denotes the random variable objective function evaluated at \(x_0\) and \(\partial\mathcal{R}(X)\) denotes the subdifferential of \(\mathcal{R}\) at \(X\).
Reimplemented from ROL::RiskMeasure< Real >.
Definition at line 209 of file ROL_FDivergence.hpp.
References ROL::RiskVector< Real >::setStatistic(), ROL::RiskVector< Real >::setVector(), ROL::SampleGenerator< Real >::sumAll(), ROL::FDivergence< Real >::valLam_, and ROL::FDivergence< Real >::valMu_.
◆ update() [3/3]
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inlinevirtual |
Update internal risk measure storage for Hessian-time-a-vector computation.
- Parameters
-
[in] val is the value of the random variable objective function at the current sample point [in] g is the gradient of the random variable objective function at the current sample point [in] gv is the gradient of the random variable objective function at the current sample point applied to the vector v0 [in] hv is the Hessian of the random variable objective function at the current sample point applied to the vector v0 [in] weight is the weight associated with the current sample point
Reimplemented from ROL::RiskMeasure< Real >.
Definition at line 227 of file ROL_FDivergence.hpp.
References ROL::FDivergence< Real >::Fdual(), and ROL::FDivergence< Real >::xmu_.
◆ getHessVec()
|
inlinevirtual |
Return risk measure Hessian-times-a-vector.
- Parameters
-
[out] hv is the Hessian-times-a-vector of the risk measure [in] sampler is the ROL::SampleGenerator used to sample the objective function
Upon return, getHessVec returns \(\nabla^2 \mathcal{R}(f(x_0))v_0\) (if available) where \(f(x_0)\) denotes the random variable objective function evaluated at \(x_0\).
Reimplemented from ROL::RiskMeasure< Real >.
Definition at line 240 of file ROL_FDivergence.hpp.
References ROL::RiskVector< Real >::setStatistic(), ROL::RiskVector< Real >::setVector(), ROL::SampleGenerator< Real >::sumAll(), ROL::FDivergence< Real >::valLam2_, ROL::FDivergence< Real >::valLam_, ROL::FDivergence< Real >::valMu2_, and ROL::FDivergence< Real >::valMu_.
Member Data Documentation
◆ thresh_
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private |
Definition at line 91 of file ROL_FDivergence.hpp.
◆ dualVector_
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private |
Definition at line 93 of file ROL_FDivergence.hpp.
◆ xlam_
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private |
Definition at line 95 of file ROL_FDivergence.hpp.
◆ xmu_
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private |
Definition at line 96 of file ROL_FDivergence.hpp.
Referenced by ROL::FDivergence< Real >::update().
◆ vlam_
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private |
Definition at line 97 of file ROL_FDivergence.hpp.
◆ vmu_
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private |
Definition at line 98 of file ROL_FDivergence.hpp.
◆ valLam_
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private |
Definition at line 100 of file ROL_FDivergence.hpp.
Referenced by ROL::FDivergence< Real >::getGradient(), and ROL::FDivergence< Real >::getHessVec().
◆ valLam2_
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private |
Definition at line 101 of file ROL_FDivergence.hpp.
Referenced by ROL::FDivergence< Real >::getHessVec().
◆ valMu_
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private |
Definition at line 102 of file ROL_FDivergence.hpp.
Referenced by ROL::FDivergence< Real >::getGradient(), and ROL::FDivergence< Real >::getHessVec().
◆ valMu2_
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private |
Definition at line 103 of file ROL_FDivergence.hpp.
Referenced by ROL::FDivergence< Real >::getHessVec().
◆ firstReset_
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private |
Definition at line 105 of file ROL_FDivergence.hpp.
The documentation for this class was generated from the following file:
