ROL
Public Member Functions | Private Member Functions | Private Attributes | List of all members
ROL::MixedQuantileQuadrangle< Real > Class Template Reference

Provides an interface for a convex combination of conditional value-at-risks. More...

#include <ROL_MixedQuantileQuadrangle.hpp>

+ Inheritance diagram for ROL::MixedQuantileQuadrangle< Real >:

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...
 
- Public Member Functions inherited from ROL::RiskMeasure< Real >
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

- 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::MixedQuantileQuadrangle< Real >

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.

Constructor & Destructor Documentation

◆ MixedQuantileQuadrangle() [1/2]

template<class Real >
ROL::MixedQuantileQuadrangle< Real >::MixedQuantileQuadrangle ( Teuchos::ParameterList &  parlist)
inline

◆ MixedQuantileQuadrangle() [2/2]

template<class Real >
ROL::MixedQuantileQuadrangle< Real >::MixedQuantileQuadrangle ( const std::vector< Real > &  prob,
const std::vector< Real > &  coeff,
const Teuchos::RCP< PlusFunction< Real > > &  pf 
)
inline

Member Function Documentation

◆ checkInputs()

template<class Real >
void ROL::MixedQuantileQuadrangle< Real >::checkInputs ( void  ) const
inlineprivate

◆ initialize()

template<class Real >
void ROL::MixedQuantileQuadrangle< Real >::initialize ( void  )
inlineprivate

◆ reset() [1/2]

template<class Real >
void ROL::MixedQuantileQuadrangle< Real >::reset ( Teuchos::RCP< Vector< Real > > &  x0,
const Vector< Real > &  x 
)
inlinevirtual

Reset internal risk measure storage. Called for value and gradient computation.

Parameters
[out]x0is a user-provided optimization vector
[in]xis 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().

◆ reset() [2/2]

template<class Real >
void ROL::MixedQuantileQuadrangle< Real >::reset ( Teuchos::RCP< Vector< Real > > &  x0,
const Vector< Real > &  x,
Teuchos::RCP< Vector< Real > > &  v0,
const Vector< Real > &  v 
)
inlinevirtual

Reset internal risk measure storage. Called for Hessian-times-a-vector computation.

Parameters
[out]x0is a user-provided optimization vector
[in]xis a (potentially) augmented risk vector
[out]v0is a user-provided direction vector
[in]vis 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_.

◆ update() [1/3]

template<class Real >
void ROL::MixedQuantileQuadrangle< Real >::update ( const Real  val,
const Real  weight 
)
inlinevirtual

Update internal risk measure storage for value computation.

Parameters
[in]valis the value of the random variable objective function at the current sample point
[in]weightis 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_.

◆ getValue()

template<class Real >
Real ROL::MixedQuantileQuadrangle< Real >::getValue ( SampleGenerator< Real > &  sampler)
inlinevirtual

Return risk measure value.

Parameters
[in]sampleris 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_.

◆ update() [2/3]

template<class Real >
void ROL::MixedQuantileQuadrangle< Real >::update ( const Real  val,
const Vector< Real > &  g,
const Real  weight 
)
inlinevirtual

Update internal risk measure storage for gradient computation.

Parameters
[in]valis the value of the random variable objective function at the current sample point
[in]gis the gradient of the random variable objective function at the current sample point
[in]weightis 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_.

◆ getGradient()

template<class Real >
void ROL::MixedQuantileQuadrangle< Real >::getGradient ( Vector< Real > &  g,
SampleGenerator< Real > &  sampler 
)
inlinevirtual

Return risk measure (sub)gradient.

Parameters
[out]gis the (sub)gradient of the risk measure
[in]sampleris 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_.

◆ update() [3/3]

template<class Real >
void ROL::MixedQuantileQuadrangle< Real >::update ( const Real  val,
const Vector< Real > &  g,
const Real  gv,
const Vector< Real > &  hv,
const Real  weight 
)
inlinevirtual

Update internal risk measure storage for Hessian-time-a-vector computation.

Parameters
[in]valis the value of the random variable objective function at the current sample point
[in]gis the gradient of the random variable objective function at the current sample point
[in]gvis the gradient of the random variable objective function at the current sample point applied to the vector v0
[in]hvis the Hessian of the random variable objective function at the current sample point applied to the vector v0
[in]weightis 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_.

◆ getHessVec()

template<class Real >
void ROL::MixedQuantileQuadrangle< Real >::getHessVec ( Vector< Real > &  hv,
SampleGenerator< Real > &  sampler 
)
inlinevirtual

Return risk measure Hessian-times-a-vector.

Parameters
[out]hvis the Hessian-times-a-vector of the risk measure
[in]sampleris 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_.

Member Data Documentation

◆ plusFunction_

template<class Real >
Teuchos::RCP<PlusFunction<Real> > ROL::MixedQuantileQuadrangle< Real >::plusFunction_
private

◆ prob_

template<class Real >
Teuchos::Array<Real> ROL::MixedQuantileQuadrangle< Real >::prob_
private

◆ coeff_

template<class Real >
Teuchos::Array<Real> ROL::MixedQuantileQuadrangle< Real >::coeff_
private

◆ dualVector_

template<class Real >
Teuchos::RCP<Vector<Real> > ROL::MixedQuantileQuadrangle< Real >::dualVector_
private

◆ xvar_

template<class Real >
std::vector<Real> ROL::MixedQuantileQuadrangle< Real >::xvar_
private

◆ vvar_

template<class Real >
std::vector<Real> ROL::MixedQuantileQuadrangle< Real >::vvar_
private

◆ vec_

template<class Real >
std::vector<Real> ROL::MixedQuantileQuadrangle< Real >::vec_
private

◆ size_

template<class Real >
int ROL::MixedQuantileQuadrangle< Real >::size_
private

◆ firstReset_

template<class Real >
bool ROL::MixedQuantileQuadrangle< Real >::firstReset_
private

The documentation for this class was generated from the following file: