ROL
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Provides an interface for a convex combination of conditional value-at-risks. More...
#include <ROL_MixedQuantileQuadrangle.hpp>
Public Member Functions | |
MixedQuantileQuadrangle (Teuchos::ParameterList &parlist) | |
MixedQuantileQuadrangle (const std::vector< Real > &prob, const std::vector< Real > &coeff, const Teuchos::RCP< PlusFunction< Real > > &pf) | |
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 |
void | initialize (void) |
Private Attributes | |
Teuchos::RCP< PlusFunction< Real > > | plusFunction_ |
Teuchos::Array< Real > | prob_ |
Teuchos::Array< Real > | coeff_ |
Teuchos::RCP< Vector< Real > > | dualVector_ |
std::vector< Real > | xvar_ |
std::vector< Real > | vvar_ |
std::vector< Real > | vec_ |
int | size_ |
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 a convex combination of conditional value-at-risks.
The risk measure associated with the mixed-quantile quadrangle is defined as
\[ \mathcal{R}(X) = \lambda_1 \mathrm{CVaR}_{\beta_1}(X) + \ldots + \lambda_n \mathrm{CVaR}_{\beta_n}(X) \]
where \(0 \le \beta_1 \le \cdots \le \beta_n < 1\) and \(0 \le \lambda_i\), \(i=1,\ldots,n\), satisfies
\[ \lambda_1 + \ldots + \lambda_n = 1. \]
Here, the conditional value-at-risk (CVaR) with confidence level \(0\le \beta < 1\) is
\[ \mathrm{CVaR}_\beta(X) = \inf_{t\in\mathbb{R}} \left\{ t + \frac{1}{1-\beta} \mathbb{E}\left[(X-t)_+\right] \right\} \]
where \((x)_+ = \max\{0,x\}\). If the distribution of \(X\) is continuous, then \(\mathrm{CVaR}_{\beta}(X)\) is the conditional expectation of \(X\) exceeding the \(\beta\)-quantile of \(X\) and the optimal \(t\) is the \(\beta\)-quantile. Additionally, \(\mathcal{R}\) is a law-invariant coherent risk measure.
When using derivative-based optimization, the user can provide a smooth approximation of \((\cdot)_+\) using the ROL::PlusFunction class.
Definition at line 90 of file ROL_MixedQuantileQuadrangle.hpp.
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Definition at line 136 of file ROL_MixedQuantileQuadrangle.hpp.
References ROL::MixedQuantileQuadrangle< Real >::checkInputs(), ROL::MixedQuantileQuadrangle< Real >::coeff_, ROL::MixedQuantileQuadrangle< Real >::initialize(), ROL::MixedQuantileQuadrangle< Real >::plusFunction_, and ROL::MixedQuantileQuadrangle< Real >::prob_.
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Definition at line 149 of file ROL_MixedQuantileQuadrangle.hpp.
References ROL::MixedQuantileQuadrangle< Real >::checkInputs(), and ROL::MixedQuantileQuadrangle< Real >::initialize().
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Definition at line 107 of file ROL_MixedQuantileQuadrangle.hpp.
References ROL::MixedQuantileQuadrangle< Real >::coeff_, ROL::MixedQuantileQuadrangle< Real >::plusFunction_, and ROL::MixedQuantileQuadrangle< Real >::prob_.
Referenced by ROL::MixedQuantileQuadrangle< Real >::MixedQuantileQuadrangle().
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Definition at line 125 of file ROL_MixedQuantileQuadrangle.hpp.
References ROL::MixedQuantileQuadrangle< Real >::prob_, ROL::MixedQuantileQuadrangle< Real >::size_, ROL::MixedQuantileQuadrangle< Real >::vec_, ROL::MixedQuantileQuadrangle< Real >::vvar_, and ROL::MixedQuantileQuadrangle< Real >::xvar_.
Referenced by ROL::MixedQuantileQuadrangle< Real >::MixedQuantileQuadrangle().
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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 157 of file ROL_MixedQuantileQuadrangle.hpp.
References ROL::MixedQuantileQuadrangle< Real >::dualVector_, ROL::MixedQuantileQuadrangle< Real >::firstReset_, ROL::RiskMeasure< Real >::reset(), ROL::MixedQuantileQuadrangle< Real >::size_, ROL::MixedQuantileQuadrangle< Real >::vec_, and ROL::MixedQuantileQuadrangle< Real >::xvar_.
Referenced by ROL::MixedQuantileQuadrangle< 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 168 of file ROL_MixedQuantileQuadrangle.hpp.
References ROL::MixedQuantileQuadrangle< Real >::reset(), and ROL::MixedQuantileQuadrangle< Real >::vvar_.
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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 175 of file ROL_MixedQuantileQuadrangle.hpp.
References ROL::MixedQuantileQuadrangle< Real >::coeff_, ROL::MixedQuantileQuadrangle< Real >::plusFunction_, ROL::MixedQuantileQuadrangle< Real >::prob_, ROL::MixedQuantileQuadrangle< Real >::size_, and ROL::MixedQuantileQuadrangle< Real >::xvar_.
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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 183 of file ROL_MixedQuantileQuadrangle.hpp.
References ROL::MixedQuantileQuadrangle< Real >::coeff_, ROL::MixedQuantileQuadrangle< Real >::size_, ROL::SampleGenerator< Real >::sumAll(), and ROL::MixedQuantileQuadrangle< Real >::xvar_.
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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 192 of file ROL_MixedQuantileQuadrangle.hpp.
References ROL::MixedQuantileQuadrangle< Real >::coeff_, ROL::MixedQuantileQuadrangle< Real >::plusFunction_, ROL::MixedQuantileQuadrangle< Real >::prob_, ROL::MixedQuantileQuadrangle< Real >::size_, ROL::MixedQuantileQuadrangle< Real >::vec_, and ROL::MixedQuantileQuadrangle< Real >::xvar_.
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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 202 of file ROL_MixedQuantileQuadrangle.hpp.
References ROL::MixedQuantileQuadrangle< Real >::coeff_, ROL::MixedQuantileQuadrangle< Real >::dualVector_, ROL::RiskVector< Real >::setStatistic(), ROL::RiskVector< Real >::setVector(), ROL::MixedQuantileQuadrangle< Real >::size_, ROL::SampleGenerator< Real >::sumAll(), and ROL::MixedQuantileQuadrangle< Real >::vec_.
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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 215 of file ROL_MixedQuantileQuadrangle.hpp.
References ROL::MixedQuantileQuadrangle< Real >::coeff_, ROL::MixedQuantileQuadrangle< Real >::plusFunction_, ROL::MixedQuantileQuadrangle< Real >::prob_, ROL::MixedQuantileQuadrangle< Real >::size_, ROL::MixedQuantileQuadrangle< Real >::vec_, ROL::MixedQuantileQuadrangle< Real >::vvar_, and ROL::MixedQuantileQuadrangle< Real >::xvar_.
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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 230 of file ROL_MixedQuantileQuadrangle.hpp.
References ROL::MixedQuantileQuadrangle< Real >::dualVector_, ROL::RiskVector< Real >::setStatistic(), ROL::RiskVector< Real >::setVector(), ROL::MixedQuantileQuadrangle< Real >::size_, ROL::SampleGenerator< Real >::sumAll(), and ROL::MixedQuantileQuadrangle< Real >::vec_.
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Definition at line 92 of file ROL_MixedQuantileQuadrangle.hpp.
Referenced by ROL::MixedQuantileQuadrangle< Real >::checkInputs(), ROL::MixedQuantileQuadrangle< Real >::MixedQuantileQuadrangle(), and ROL::MixedQuantileQuadrangle< Real >::update().
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Definition at line 95 of file ROL_MixedQuantileQuadrangle.hpp.
Referenced by ROL::MixedQuantileQuadrangle< Real >::checkInputs(), ROL::MixedQuantileQuadrangle< Real >::getGradient(), ROL::MixedQuantileQuadrangle< Real >::getValue(), ROL::MixedQuantileQuadrangle< Real >::MixedQuantileQuadrangle(), and ROL::MixedQuantileQuadrangle< Real >::update().
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Definition at line 97 of file ROL_MixedQuantileQuadrangle.hpp.
Referenced by ROL::MixedQuantileQuadrangle< Real >::getGradient(), ROL::MixedQuantileQuadrangle< Real >::getHessVec(), and ROL::MixedQuantileQuadrangle< Real >::reset().
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Definition at line 99 of file ROL_MixedQuantileQuadrangle.hpp.
Referenced by ROL::MixedQuantileQuadrangle< Real >::initialize(), ROL::MixedQuantileQuadrangle< Real >::reset(), and ROL::MixedQuantileQuadrangle< Real >::update().
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Definition at line 101 of file ROL_MixedQuantileQuadrangle.hpp.
Referenced by ROL::MixedQuantileQuadrangle< Real >::getGradient(), ROL::MixedQuantileQuadrangle< Real >::getHessVec(), ROL::MixedQuantileQuadrangle< Real >::initialize(), ROL::MixedQuantileQuadrangle< Real >::reset(), and ROL::MixedQuantileQuadrangle< Real >::update().
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Definition at line 103 of file ROL_MixedQuantileQuadrangle.hpp.
Referenced by ROL::MixedQuantileQuadrangle< Real >::getGradient(), ROL::MixedQuantileQuadrangle< Real >::getHessVec(), ROL::MixedQuantileQuadrangle< Real >::getValue(), ROL::MixedQuantileQuadrangle< Real >::initialize(), ROL::MixedQuantileQuadrangle< Real >::reset(), and ROL::MixedQuantileQuadrangle< Real >::update().
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Definition at line 105 of file ROL_MixedQuantileQuadrangle.hpp.
Referenced by ROL::MixedQuantileQuadrangle< Real >::reset().