ROL
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Provides an interface for spectral risk measures. More...
#include <ROL_SpectralRisk.hpp>
Public Member Functions | |
SpectralRisk (void) | |
SpectralRisk (const Teuchos::RCP< Distribution< Real > > &dist, const int nQuad, const Teuchos::RCP< PlusFunction< Real > > &pf) | |
SpectralRisk (Teuchos::ParameterList &parlist) | |
SpectralRisk (const std::vector< Real > &pts, const std::vector< Real > &wts, const Teuchos::RCP< PlusFunction< Real > > &pf) | |
Real | computeStatistic (const Vector< Real > &x) const |
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... | |
void | update (const Real val, const Vector< Real > &g, const Real weight) |
Update internal risk measure storage for gradient computation. 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... | |
Real | getValue (SampleGenerator< Real > &sampler) |
Return risk measure value. More... | |
void | getGradient (Vector< Real > &g, SampleGenerator< Real > &sampler) |
Return risk measure (sub)gradient. 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) | |
Protected Member Functions | |
void | buildMixedQuantile (const std::vector< Real > &pts, const std::vector< Real > &wts, const Teuchos::RCP< PlusFunction< Real > > &pf) |
void | buildQuadFromDist (std::vector< Real > &pts, std::vector< Real > &wts, const int nQuad, const Teuchos::RCP< Distribution< Real > > &dist) const |
void | printQuad (const std::vector< Real > &pts, const std::vector< Real > &wts, const bool print=false) const |
Private Member Functions | |
void | checkInputs (Teuchos::RCP< Distribution< Real > > &dist=Teuchos::null) const |
Private Attributes | |
Teuchos::RCP< MixedQuantileQuadrangle< Real > > | mqq_ |
Teuchos::RCP< PlusFunction< Real > > | plusFunction_ |
std::vector< Real > | wts_ |
std::vector< Real > | pts_ |
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 spectral risk measures.
Kusuoka's representation for law-invariant risk measures is
\[ \mathcal{R}(X) = \sup_{\mu\in\mathfrak{M}} \int_0^1 \mathrm{CVaR}_{\alpha}(X)\,\mathrm{d}\mu(\alpha) \]
where the conditional value-at-risk (CVaR) with confidence level \(0\le \alpha < 1\) is
\[ \mathrm{CVaR}_\alpha(X) = \inf_{t\in\mathbb{R}} \left\{ t + \frac{1}{1-\alpha} \mathbb{E}\left[(X-t)_+\right] \right\}, \quad (x)_+ = \max\{0,x\}, \]
and \(\mathfrak{M}\) is a subset of distributions on the interval \([0,1)\). By spectral risk measures, we refer to the case where the set \(\mathfrak{M}\) is a singleton. If the distribution \(\mu\in\mathfrak{M}\) is discrete, then the corresponding risk measure is a mixed quantile quadrangle risk measure.
If the distribution of \(X\) is continuous, then \(\mathrm{CVaR}_{\alpha}(X)\) is the conditional expectation of \(X\) exceeding the \(\alpha\)-quantile of \(X\) and the optimal \(t\) is the \(\alpha\)-quantile. Additionally, \(\mathcal{R}\) is a law-invariant coherent risk measure.
ROL implements \(\mathcal{R}\) by approximating the integral with Gauss-Chebyshev quadrature of the first kind. The corresponding quadrature points and weights are then used to construct a ROL::MixedQuantileQuadrangle risk measure. When using derivative-based optimization, the user can provide a smooth approximation of \((\cdot)_+\) using the ROL::PlusFunction class.
Definition at line 89 of file ROL_SpectralRisk.hpp.
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Definition at line 165 of file ROL_SpectralRisk.hpp.
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Definition at line 167 of file ROL_SpectralRisk.hpp.
References ROL::SpectralRisk< Real >::buildMixedQuantile(), ROL::SpectralRisk< Real >::buildQuadFromDist(), and ROL::SpectralRisk< Real >::checkInputs().
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Definition at line 180 of file ROL_SpectralRisk.hpp.
References ROL::SpectralRisk< Real >::buildMixedQuantile(), ROL::SpectralRisk< Real >::buildQuadFromDist(), ROL::SpectralRisk< Real >::checkInputs(), and ROL::SpectralRisk< Real >::printQuad().
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Definition at line 201 of file ROL_SpectralRisk.hpp.
References ROL::SpectralRisk< Real >::buildMixedQuantile(), and ROL::SpectralRisk< Real >::checkInputs().
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Definition at line 97 of file ROL_SpectralRisk.hpp.
References ROL::SpectralRisk< Real >::plusFunction_.
Referenced by ROL::SpectralRisk< Real >::SpectralRisk().
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Definition at line 111 of file ROL_SpectralRisk.hpp.
References ROL::SpectralRisk< Real >::mqq_, ROL::SpectralRisk< Real >::plusFunction_, ROL::SpectralRisk< Real >::pts_, and ROL::SpectralRisk< Real >::wts_.
Referenced by ROL::SuperQuantileQuadrangle< Real >::initialize(), ROL::ChebyshevKusuoka< Real >::initialize(), and ROL::SpectralRisk< Real >::SpectralRisk().
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Definition at line 119 of file ROL_SpectralRisk.hpp.
Referenced by ROL::SpectralRisk< Real >::SpectralRisk().
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Definition at line 145 of file ROL_SpectralRisk.hpp.
Referenced by ROL::SpectralRisk< Real >::SpectralRisk().
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Definition at line 209 of file ROL_SpectralRisk.hpp.
References ROL::SpectralRisk< Real >::wts_.
Referenced by ROL::StochasticProblem< Real >::getSolutionStatistic().
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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 220 of file ROL_SpectralRisk.hpp.
References ROL::SpectralRisk< Real >::mqq_.
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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 224 of file ROL_SpectralRisk.hpp.
References ROL::SpectralRisk< Real >::mqq_.
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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 229 of file ROL_SpectralRisk.hpp.
References ROL::SpectralRisk< Real >::mqq_.
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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 233 of file ROL_SpectralRisk.hpp.
References ROL::SpectralRisk< Real >::mqq_.
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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 237 of file ROL_SpectralRisk.hpp.
References ROL::SpectralRisk< Real >::mqq_.
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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 242 of file ROL_SpectralRisk.hpp.
References ROL::SpectralRisk< Real >::mqq_.
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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 246 of file ROL_SpectralRisk.hpp.
References ROL::SpectralRisk< Real >::mqq_.
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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 250 of file ROL_SpectralRisk.hpp.
References ROL::SpectralRisk< Real >::mqq_.
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Definition at line 91 of file ROL_SpectralRisk.hpp.
Referenced by ROL::SpectralRisk< Real >::buildMixedQuantile(), ROL::SpectralRisk< Real >::getGradient(), ROL::SpectralRisk< Real >::getHessVec(), ROL::SpectralRisk< Real >::getValue(), ROL::SpectralRisk< Real >::reset(), and ROL::SpectralRisk< Real >::update().
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Definition at line 92 of file ROL_SpectralRisk.hpp.
Referenced by ROL::SpectralRisk< Real >::buildMixedQuantile(), and ROL::SpectralRisk< Real >::checkInputs().
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Definition at line 94 of file ROL_SpectralRisk.hpp.
Referenced by ROL::SpectralRisk< Real >::buildMixedQuantile(), and ROL::SpectralRisk< Real >::computeStatistic().
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Definition at line 95 of file ROL_SpectralRisk.hpp.
Referenced by ROL::SpectralRisk< Real >::buildMixedQuantile().