ROL
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Provides an interface for the Kullback-Leibler distributionally robust expectation. More...
#include <ROL_KLDivergence.hpp>
Public Member Functions | |
KLDivergence (const Real eps=1.e-2) | |
Constructor. More... | |
KLDivergence (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) | |
Private Member Functions | |
void | checkInputs (void) const |
Real | exponential (const Real arg1, const Real arg2) const |
Real | exponential (const Real arg) const |
Real | power (const Real arg, const Real pow) const |
Private Attributes | |
Real | eps_ |
Real | gval_ |
Real | gvval_ |
Real | hval_ |
Teuchos::RCP< Vector< Real > > | scaledGradient_ |
Teuchos::RCP< Vector< Real > > | scaledHessVec_ |
Teuchos::RCP< Vector< Real > > | dualVector1_ |
Teuchos::RCP< Vector< Real > > | dualVector2_ |
Real | xstat_ |
Real | vstat_ |
bool | firstReset_ |
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 Kullback-Leibler 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 Kullback-Leibler divergence, i.e.,
\[ \mathfrak{A} = \{\vartheta\in\mathcal{X}^*\,:\, \mathbb{E}[\vartheta] = 1,\; \vartheta \ge 0,\;\text{and}\; \mathbb{E}[\vartheta\log(\vartheta)] \le \epsilon\}. \]
\(\mathcal{R}\) is a law-invariant, coherent risk measure. Moreover, by a duality argument, \(\mathcal{R}\) can be reformulated as
\[ \mathcal{R}(X) = \inf_{\lambda > 0}\left\{ \lambda \epsilon + \lambda\mathbb{E}\left[\exp\left( \frac{X}{\lambda}\right)\right]\right\}. \]
ROL implements this by augmenting the optimization vector \(x_0\) with the parameter \(\lambda\), then minimizes jointly for \((x_0,\lambda)\).
Definition at line 81 of file ROL_KLDivergence.hpp.
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Constructor.
[in] | eps | is the tolerance for the KL divergence constraint |
Definition at line 109 of file ROL_KLDivergence.hpp.
References ROL::KLDivergence< Real >::checkInputs().
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Constructor.
[in] | parlist | is a parameter list specifying inputs |
parlist should contain sublists "SOL"->"Risk Measure"->"KL Divergence" and within the "KL Divergence" sublist should have the following parameters
Definition at line 122 of file ROL_KLDivergence.hpp.
References ROL::KLDivergence< Real >::checkInputs(), and ROL::KLDivergence< Real >::eps_.
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Definition at line 98 of file ROL_KLDivergence.hpp.
References ROL::KLDivergence< Real >::eps_.
Referenced by ROL::KLDivergence< Real >::KLDivergence().
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Reset internal risk measure storage. Called for value and gradient computation.
[out] | x0 | is a user-provided optimization vector |
[in] | x | is a (potentially) augmented risk vector On input, \form#56 carries \form#323 and any statistics (scalars) associated with the risk measure. |
Reimplemented from ROL::RiskMeasure< Real >.
Definition at line 130 of file ROL_KLDivergence.hpp.
References ROL::KLDivergence< Real >::dualVector1_, ROL::KLDivergence< Real >::dualVector2_, ROL::KLDivergence< Real >::firstReset_, ROL::KLDivergence< Real >::gval_, ROL::KLDivergence< Real >::gvval_, ROL::KLDivergence< Real >::hval_, ROL::RiskMeasure< Real >::reset(), ROL::KLDivergence< Real >::scaledGradient_, ROL::KLDivergence< Real >::scaledHessVec_, and ROL::KLDivergence< Real >::xstat_.
Referenced by ROL::KLDivergence< Real >::reset().
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Reset internal risk measure storage. Called for Hessian-times-a-vector computation.
[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, \form#56 carries \form#323 and any statistics (scalars) associated with the risk measure. Similarly, \form#37 carries\(v_0\) and any statistics (scalars) associated with the risk measure. |
Reimplemented from ROL::RiskMeasure< Real >.
Definition at line 146 of file ROL_KLDivergence.hpp.
References ROL::KLDivergence< Real >::reset(), and ROL::KLDivergence< Real >::vstat_.
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Update internal risk measure storage for value computation.
[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 153 of file ROL_KLDivergence.hpp.
References ROL::KLDivergence< Real >::eps_, ROL::KLDivergence< Real >::exponential(), and ROL::KLDivergence< Real >::xstat_.
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Return risk measure value.
[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 158 of file ROL_KLDivergence.hpp.
References ROL::KLDivergence< Real >::eps_, ROL::SampleGenerator< Real >::sumAll(), and ROL::KLDivergence< Real >::xstat_.
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Update internal risk measure storage for gradient computation.
[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 167 of file ROL_KLDivergence.hpp.
References ROL::KLDivergence< Real >::eps_, ROL::KLDivergence< Real >::exponential(), ROL::KLDivergence< Real >::gval_, and ROL::KLDivergence< Real >::xstat_.
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Return risk measure (sub)gradient.
[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 174 of file ROL_KLDivergence.hpp.
References ROL::KLDivergence< Real >::dualVector1_, ROL::KLDivergence< Real >::eps_, ROL::KLDivergence< Real >::gval_, ROL::SampleGenerator< Real >::sumAll(), and ROL::KLDivergence< Real >::xstat_.
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Update internal risk measure storage for Hessian-time-a-vector computation.
[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 196 of file ROL_KLDivergence.hpp.
References ROL::KLDivergence< Real >::eps_, ROL::KLDivergence< Real >::exponential(), ROL::KLDivergence< Real >::gval_, ROL::KLDivergence< Real >::gvval_, ROL::KLDivergence< Real >::hval_, ROL::KLDivergence< Real >::scaledGradient_, ROL::KLDivergence< Real >::scaledHessVec_, and ROL::KLDivergence< Real >::xstat_.
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Return risk measure Hessian-times-a-vector.
[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 210 of file ROL_KLDivergence.hpp.
References ROL::KLDivergence< Real >::dualVector1_, ROL::KLDivergence< Real >::dualVector2_, ROL::KLDivergence< Real >::eps_, ROL::KLDivergence< Real >::gval_, ROL::KLDivergence< Real >::gvval_, ROL::KLDivergence< Real >::hval_, ROL::KLDivergence< Real >::scaledGradient_, ROL::KLDivergence< Real >::scaledHessVec_, ROL::SampleGenerator< Real >::sumAll(), ROL::KLDivergence< Real >::vstat_, and ROL::KLDivergence< Real >::xstat_.
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Definition at line 252 of file ROL_KLDivergence.hpp.
References ROL::KLDivergence< Real >::power().
Referenced by ROL::KLDivergence< Real >::update().
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Definition at line 261 of file ROL_KLDivergence.hpp.
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Definition at line 270 of file ROL_KLDivergence.hpp.
Referenced by ROL::KLDivergence< Real >::exponential().
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Definition at line 83 of file ROL_KLDivergence.hpp.
Referenced by ROL::KLDivergence< Real >::checkInputs(), ROL::KLDivergence< Real >::getGradient(), ROL::KLDivergence< Real >::getHessVec(), ROL::KLDivergence< Real >::getValue(), ROL::KLDivergence< Real >::KLDivergence(), and ROL::KLDivergence< Real >::update().
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Definition at line 85 of file ROL_KLDivergence.hpp.
Referenced by ROL::KLDivergence< Real >::getGradient(), ROL::KLDivergence< Real >::getHessVec(), ROL::KLDivergence< Real >::reset(), and ROL::KLDivergence< Real >::update().
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Definition at line 86 of file ROL_KLDivergence.hpp.
Referenced by ROL::KLDivergence< Real >::getHessVec(), ROL::KLDivergence< Real >::reset(), and ROL::KLDivergence< Real >::update().
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Definition at line 87 of file ROL_KLDivergence.hpp.
Referenced by ROL::KLDivergence< Real >::getHessVec(), ROL::KLDivergence< Real >::reset(), and ROL::KLDivergence< Real >::update().
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Definition at line 88 of file ROL_KLDivergence.hpp.
Referenced by ROL::KLDivergence< Real >::getHessVec(), ROL::KLDivergence< Real >::reset(), and ROL::KLDivergence< Real >::update().
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Definition at line 89 of file ROL_KLDivergence.hpp.
Referenced by ROL::KLDivergence< Real >::getHessVec(), ROL::KLDivergence< Real >::reset(), and ROL::KLDivergence< Real >::update().
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Definition at line 90 of file ROL_KLDivergence.hpp.
Referenced by ROL::KLDivergence< Real >::getGradient(), ROL::KLDivergence< Real >::getHessVec(), and ROL::KLDivergence< Real >::reset().
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Definition at line 91 of file ROL_KLDivergence.hpp.
Referenced by ROL::KLDivergence< Real >::getHessVec(), and ROL::KLDivergence< Real >::reset().
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Definition at line 93 of file ROL_KLDivergence.hpp.
Referenced by ROL::KLDivergence< Real >::getGradient(), ROL::KLDivergence< Real >::getHessVec(), ROL::KLDivergence< Real >::getValue(), ROL::KLDivergence< Real >::reset(), and ROL::KLDivergence< Real >::update().
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Definition at line 94 of file ROL_KLDivergence.hpp.
Referenced by ROL::KLDivergence< Real >::getHessVec(), and ROL::KLDivergence< Real >::reset().
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Definition at line 96 of file ROL_KLDivergence.hpp.
Referenced by ROL::KLDivergence< Real >::reset().