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

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

#include <ROL_MixedCVaR.hpp>

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

Public Member Functions

 MixedCVaR (ROL::ParameterList &parlist)
 
 MixedCVaR (const std::vector< Real > &prob, const std::vector< Real > &coeff, const ROL::Ptr< PlusFunction< Real > > &pf)
 
void initialize (const Vector< Real > &x)
 Initialize temporary variables. More...
 
Real computeStatistic (const Ptr< const std::vector< Real >> &xstat) const override
 Compute statistic. 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)
 

Private Member Functions

void initializeMCVAR (void)
 
void checkInputs (void)
 

Private Attributes

ROL::Ptr< PlusFunction< Real > > plusFunction_
 
std::vector< Real > prob_
 
std::vector< Real > coeff_
 
std::vector< Real > vec_
 
int size_
 

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::MixedCVaR< 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 54 of file ROL_MixedCVaR.hpp.

Constructor & Destructor Documentation

template<class Real >
ROL::MixedCVaR< Real >::MixedCVaR ( ROL::ParameterList &  parlist)
inline
template<class Real >
ROL::MixedCVaR< Real >::MixedCVaR ( const std::vector< Real > &  prob,
const std::vector< Real > &  coeff,
const ROL::Ptr< PlusFunction< Real > > &  pf 
)
inline

Definition at line 114 of file ROL_MixedCVaR.hpp.

References ROL::MixedCVaR< Real >::checkInputs().

Member Function Documentation

template<class Real >
void ROL::MixedCVaR< Real >::initializeMCVAR ( void  )
inlineprivate
template<class Real >
void ROL::MixedCVaR< Real >::checkInputs ( void  )
inlineprivate
template<class Real >
void ROL::MixedCVaR< Real >::initialize ( const Vector< Real > &  x)
inlinevirtual

Initialize temporary variables.

Parameters
[in]xis a vector used for initializing storage

Reimplemented from ROL::RandVarFunctional< Real >.

Definition at line 121 of file ROL_MixedCVaR.hpp.

References ROL::RandVarFunctional< Real >::initialize(), ROL::MixedCVaR< Real >::size_, and ROL::MixedCVaR< Real >::vec_.

template<class Real >
Real ROL::MixedCVaR< Real >::computeStatistic ( const Ptr< const std::vector< Real >> &  xstat) const
inlineoverridevirtual

Compute statistic.

Parameters
[in]xstatis a ROL::Ptr to a std::vector containing the statistic vector

Reimplemented from ROL::RandVarFunctional< Real >.

Definition at line 126 of file ROL_MixedCVaR.hpp.

References ROL::MixedCVaR< Real >::coeff_, and ROL::MixedCVaR< Real >::size_.

template<class Real >
void ROL::MixedCVaR< Real >::updateValue ( Objective< Real > &  obj,
const Vector< Real > &  x,
const std::vector< Real > &  xstat,
Real &  tol 
)
inlinevirtual

Update internal 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::RandVarFunctional< Real >.

Definition at line 136 of file ROL_MixedCVaR.hpp.

References ROL::MixedCVaR< Real >::coeff_, ROL::RandVarFunctional< Real >::computeValue(), ROL::MixedCVaR< Real >::plusFunction_, ROL::MixedCVaR< Real >::prob_, ROL::MixedCVaR< Real >::size_, ROL::RandVarFunctional< Real >::val_, and ROL::RandVarFunctional< Real >::weight_.

template<class Real >
Real ROL::MixedCVaR< Real >::getValue ( const Vector< Real > &  x,
const std::vector< Real > &  xstat,
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::RandVarFunctional< Real >.

Definition at line 148 of file ROL_MixedCVaR.hpp.

References ROL::MixedCVaR< Real >::coeff_, ROL::MixedCVaR< Real >::size_, ROL::SampleGenerator< Real >::sumAll(), and ROL::RandVarFunctional< Real >::val_.

template<class Real >
void ROL::MixedCVaR< Real >::updateGradient ( Objective< Real > &  obj,
const Vector< Real > &  x,
const std::vector< Real > &  xstat,
Real &  tol 
)
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::RandVarFunctional< Real >.

Definition at line 159 of file ROL_MixedCVaR.hpp.

References ROL::MixedCVaR< Real >::coeff_, ROL::RandVarFunctional< Real >::computeGradient(), ROL::RandVarFunctional< Real >::computeValue(), ROL::RandVarFunctional< Real >::dualVector_, ROL::RandVarFunctional< Real >::g_, ROL::MixedCVaR< Real >::plusFunction_, ROL::MixedCVaR< Real >::prob_, ROL::MixedCVaR< Real >::size_, ROL::MixedCVaR< Real >::vec_, and ROL::RandVarFunctional< Real >::weight_.

template<class Real >
void ROL::MixedCVaR< Real >::getGradient ( Vector< Real > &  g,
std::vector< Real > &  gstat,
const Vector< Real > &  x,
const std::vector< Real > &  xstat,
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::RandVarFunctional< Real >.

Definition at line 176 of file ROL_MixedCVaR.hpp.

References ROL::MixedCVaR< Real >::coeff_, ROL::RandVarFunctional< Real >::g_, ROL::MixedCVaR< Real >::size_, ROL::SampleGenerator< Real >::sumAll(), and ROL::MixedCVaR< Real >::vec_.

template<class Real >
void ROL::MixedCVaR< Real >::updateHessVec ( Objective< Real > &  obj,
const Vector< Real > &  v,
const std::vector< Real > &  vstat,
const Vector< Real > &  x,
const std::vector< Real > &  xstat,
Real &  tol 
)
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::RandVarFunctional< Real >.

Definition at line 188 of file ROL_MixedCVaR.hpp.

References ROL::MixedCVaR< Real >::coeff_, ROL::RandVarFunctional< Real >::computeGradVec(), ROL::RandVarFunctional< Real >::computeHessVec(), ROL::RandVarFunctional< Real >::computeValue(), ROL::RandVarFunctional< Real >::dualVector_, ROL::RandVarFunctional< Real >::hv_, ROL::MixedCVaR< Real >::plusFunction_, ROL::MixedCVaR< Real >::prob_, ROL::MixedCVaR< Real >::size_, ROL::MixedCVaR< Real >::vec_, and ROL::RandVarFunctional< Real >::weight_.

template<class Real >
void ROL::MixedCVaR< Real >::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 
)
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::RandVarFunctional< Real >.

Definition at line 213 of file ROL_MixedCVaR.hpp.

References ROL::RandVarFunctional< Real >::hv_, ROL::MixedCVaR< Real >::size_, ROL::SampleGenerator< Real >::sumAll(), and ROL::MixedCVaR< Real >::vec_.

Member Data Documentation

template<class Real >
ROL::Ptr<PlusFunction<Real> > ROL::MixedCVaR< Real >::plusFunction_
private
template<class Real >
std::vector<Real> ROL::MixedCVaR< Real >::prob_
private
template<class Real >
std::vector<Real> ROL::MixedCVaR< Real >::coeff_
private
template<class Real >
std::vector<Real> ROL::MixedCVaR< Real >::vec_
private
template<class Real >
int ROL::MixedCVaR< Real >::size_
private

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