libtrilinos-rol-dev 12.10.1-3 / usr / include / trilinos / ROL_SpectralRisk.hpp

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#ifndef ROL_SPECTRALRISK_HPP
#define ROL_SPECTRALRISK_HPP

#include "ROL_MixedQuantileQuadrangle.hpp"
#include "ROL_DistributionFactory.hpp"

/** @ingroup risk_group
    \class ROL::SpectralRisk
    \brief Provides an interface for spectral risk measures.

    Kusuoka's representation for law-invariant risk measures is
    \f[
       \mathcal{R}(X) = \sup_{\mu\in\mathfrak{M}}
          \int_0^1 \mathrm{CVaR}_{\alpha}(X)\,\mathrm{d}\mu(\alpha)
    \f]
    where the conditional value-at-risk (CVaR) with confidence level
    \f$0\le \alpha < 1\f$ is
    \f[
       \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\},
    \f]
    and \f$\mathfrak{M}\f$ is a subset of distributions on the interval
    \f$[0,1)\f$.  By spectral risk measures, we refer to the case where the set
    \f$\mathfrak{M}\f$ is a singleton.  If the distribution
    \f$\mu\in\mathfrak{M}\f$ is discrete, then the corresponding risk measure
    is a mixed quantile quadrangle risk measure.

    If the distribution of \f$X\f$ is continuous, then
    \f$\mathrm{CVaR}_{\alpha}(X)\f$ is the conditional
    expectation of \f$X\f$ exceeding the \f$\alpha\f$-quantile of \f$X\f$ and
    the optimal \f$t\f$ is the \f$\alpha\f$-quantile.
    Additionally, \f$\mathcal{R}\f$ is a law-invariant coherent risk measure.

    ROL implements \f$\mathcal{R}\f$ 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 \f$(\cdot)_+\f$ using the ROL::PlusFunction class.
*/

namespace ROL {

template<class Real>
class SpectralRisk : public RiskMeasure<Real> {
private:
  Teuchos::RCP<MixedQuantileQuadrangle<Real> > mqq_;
  Teuchos::RCP<PlusFunction<Real> > plusFunction_;

  std::vector<Real> wts_;
  std::vector<Real> pts_;

  void checkInputs(Teuchos::RCP<Distribution<Real> > &dist = Teuchos::null) const {
    TEUCHOS_TEST_FOR_EXCEPTION(plusFunction_ == Teuchos::null, std::invalid_argument,
      ">>> ERROR (ROL::SpectralRisk): PlusFunction pointer is null!");
    if ( dist != Teuchos::null) {
      Real lb = dist->lowerBound();
      Real ub = dist->upperBound();
      TEUCHOS_TEST_FOR_EXCEPTION(lb < static_cast<Real>(0), std::invalid_argument,
        ">>> ERROR (ROL::SpectralRisk): Distribution lower bound less than zero!");
      TEUCHOS_TEST_FOR_EXCEPTION(ub > static_cast<Real>(1), std::invalid_argument,
        ">>> ERROR (ROL::SpectralRisk): Distribution upper bound greater than one!");
    }
  }

protected:
  void buildMixedQuantile(const std::vector<Real> &pts, const std::vector<Real> &wts,
                          const Teuchos::RCP<PlusFunction<Real> > &pf) {
     pts_.clear(); pts_.assign(pts.begin(),pts.end());
     wts_.clear(); wts_.assign(wts.begin(),wts.end());
     plusFunction_ = pf;
     mqq_ = Teuchos::rcp(new MixedQuantileQuadrangle<Real>(pts,wts,pf));
  }

  void buildQuadFromDist(std::vector<Real> &pts, std::vector<Real> &wts,
                   const int nQuad, const Teuchos::RCP<Distribution<Real> > &dist) const {
    const Real lo = dist->lowerBound(), hi = dist->upperBound();
    const Real half(0.5), one(1), N(nQuad);
    wts.clear(); wts.resize(nQuad);
    pts.clear(); pts.resize(nQuad);
    if ( hi >= one ) {
      wts[0] = half/(N-half);
      pts[0] = lo;
      for (int i = 1; i < nQuad; ++i) {
        wts[i] = one/(N-half);
        pts[i] = dist->invertCDF(static_cast<Real>(i)/N);
      }
    }
    else {
      wts[0] = half/(N-one);
      pts[0] = lo;
      for (int i = 1; i < nQuad-1; ++i) {
        wts[i] = one/(N-one);
        pts[i] = dist->invertCDF(static_cast<Real>(i)/N);
      }
      wts[nQuad-1] = half/(N-one);
      pts[nQuad-1] = hi;
    }
  }

  void printQuad(const std::vector<Real> &pts,
                 const std::vector<Real> &wts,
                 const bool print = false) const {
    if ( print ) {
      const int nQuad = wts.size();
      std::cout << std::endl;
      std::cout << std::scientific << std::setprecision(15);
      std::cout << std::setw(25) << std::left << "Points"
                << std::setw(25) << std::left << "Weights"
                << std::endl;
      for (int i = 0; i < nQuad; ++i) {
        std::cout << std::setw(25) << std::left << pts[i]
                  << std::setw(25) << std::left << wts[i]
                  << std::endl;
      }
      std::cout << std::endl;
    }
  }

public:
  SpectralRisk(void) : RiskMeasure<Real>() {}

  SpectralRisk( const Teuchos::RCP<Distribution<Real> > &dist,
                const int nQuad,
                const Teuchos::RCP<PlusFunction<Real> > &pf)
    : RiskMeasure<Real>() {
    // Build generalized trapezoidal rule
    std::vector<Real> wts(nQuad), pts(nQuad);
    buildQuadFromDist(pts,wts,nQuad,dist);
    // Build mixed quantile quadrangle risk measure
    buildMixedQuantile(pts,wts,pf);
    // Check inputs
    checkInputs(dist);
  }

  SpectralRisk(Teuchos::ParameterList &parlist)
    : RiskMeasure<Real>() {
    // Parse parameter list
    Teuchos::ParameterList &list
      = parlist.sublist("SOL").sublist("Risk Measure").sublist("Spectral Risk");
    int nQuad  = list.get("Number of Quadrature Points",5);
    bool print = list.get("Print Quadrature to Screen",false);
    // Build distribution
    Teuchos::RCP<Distribution<Real> > dist = DistributionFactory<Real>(list);
    // Build plus function approximation
    Teuchos::RCP<PlusFunction<Real> > pf = Teuchos::rcp(new PlusFunction<Real>(list));
    // Build generalized trapezoidal rule
    std::vector<Real> wts(nQuad), pts(nQuad);
    buildQuadFromDist(pts,wts,nQuad,dist);
    printQuad(pts,wts,print);
    // Build mixed quantile quadrangle risk measure
    buildMixedQuantile(pts,wts,pf);
    // Check inputs
    checkInputs(dist);
  }

  SpectralRisk( const std::vector<Real> &pts, const std::vector<Real> &wts,
                const Teuchos::RCP<PlusFunction<Real> > &pf)
    : RiskMeasure<Real>() {
    buildMixedQuantile(pts,wts,pf);
    // Check inputs
    checkInputs();
  }

  Real computeStatistic(const Vector<Real> &x) const {
    std::vector<Real> xstat;
    Teuchos::dyn_cast<const RiskVector<Real> >(x).getStatistic(xstat);
    Real stat(0);
    int nQuad = static_cast<int>(wts_.size());
    for (int i = 0; i < nQuad; ++i) {
      stat += wts_[i] * xstat[i];
    }
    return stat;
  }

  void reset(Teuchos::RCP<Vector<Real> > &x0, const Vector<Real> &x) {
    mqq_->reset(x0,x);
  }

  void reset(Teuchos::RCP<Vector<Real> > &x0, const Vector<Real> &x,
             Teuchos::RCP<Vector<Real> > &v0, const Vector<Real> &v) {
    mqq_->reset(x0,x,v0,v);
  }

  void update(const Real val, const Real weight) {
    mqq_->update(val,weight);
  }

  void update(const Real val, const Vector<Real> &g, const Real weight) {
    mqq_->update(val,g,weight);
  }

  void update(const Real val, const Vector<Real> &g, const Real gv, const Vector<Real> &hv,
              const Real weight) {
    mqq_->update(val,g,gv,hv,weight);
  }

  Real getValue(SampleGenerator<Real> &sampler) {
    return mqq_->getValue(sampler);
  }

  void getGradient(Vector<Real> &g, SampleGenerator<Real> &sampler) {
    mqq_->getGradient(g,sampler);
  }

  void getHessVec(Vector<Real> &hv, SampleGenerator<Real> &sampler) {
    mqq_->getHessVec(hv,sampler);
  }
};

}

#endif