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

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#ifndef ROL_EXPECTATIONQUAD_HPP
#define ROL_EXPECTATIONQUAD_HPP

#include "ROL_RiskVector.hpp"
#include "ROL_RiskMeasure.hpp"
#include "ROL_Types.hpp"

/** @ingroup risk_group
    \class ROL::ExpectationQuad
    \brief Provides a general interface for risk measures generated through
           the expectation risk quadrangle.

    The expectation risk quadrangle is a specialization of the general
    risk quadrangle that provides a rigorous connection between risk-averse
    optimization and statistical estimation.  The risk quadrangle provides
    fundamental relationships between measures of risk, regret, error and
    deviation.  An expectation risk quadrangle is defined through scalar
    regret and error functions.  The scalar regret function,
    \f$v:\mathbb{R}\to(-\infty,\infty]\f$, must be proper, closed, convex
    and satisfy \f$v(0)=0\f$ and \f$v(x) > x\f$ for all \f$x\neq 0\f$.
    Similarly, the scalar error function,
    \f$e:\mathbb{R}\to[0,\infty]\f$, must be proper, closed, convex
    and satisfy \f$e(0)=0\f$ and \f$e(x) > 0\f$ for all \f$x\neq 0\f$.
    \f$v\f$ and \f$e\f$ are obtained from one another through the relations
    \f[
       v(x) = e(x) + x \quad\text{and}\quad e(x) = v(x) - x.
    \f]
    Given \f$v\f$ (or equivalently \f$e\f$), the associated risk measure
    is
    \f[
       \mathcal{R}(X) = \inf_{t\in\mathbb{R}} \left\{
         t + \mathbb{E}\left[v(X-t)\right]
         \right\}.
    \f]
    In general, \f$\mathcal{R}\f$ is convex and translation equivariant.
    Moreover, \f$\mathcal{R}\f$ is monotonic if \f$v\f$ is increasing
    and \f$\mathcal{R}\f$ is positive homogeneous if \f$v\f$ is.
    ROL implements this by augmenting the optimization vector \f$x_0\f$ with
    the parameter \f$t\f$, then minimizes jointly for \f$(x_0,t)\f$.
*/


namespace ROL {

template<class Real>
class ExpectationQuad : public RiskMeasure<Real> {
private:

  Teuchos::RCP<Vector<Real> > dualVector_;

  Real xstat_;
  Real vstat_;

  bool firstReset_;

public:
  ExpectationQuad(void) : RiskMeasure<Real>(), xstat_(0), vstat_(0), firstReset_(true) {}

  /** \brief Evaluate the scalar regret function at x.

      @param[in]   x      is the scalar input
      @param[in]   deriv  is the derivative order

      This function returns \f$v(x)\f$ or a derivative of \f$v(x)\f$.
  */
  virtual Real regret(Real x, int deriv = 0) = 0;

  /** \brief Run default derivative tests for the scalar regret function.
  */
  virtual void checkRegret(void) {
    Real zero(0), half(0.5), two(2), one(1), oem3(1.e-3), fem4(5.e-4), p1(0.1);
    // Check v(0) = 0
    Real x = zero;
    Real vx = regret(x,0);
    std::cout << std::right << std::setw(20) << "CHECK REGRET: v(0) = 0? \n";
    std::cout << std::right << std::setw(20) << "v(0)" << "\n";
    std::cout << std::scientific << std::setprecision(11) << std::right 
              << std::setw(20) << std::abs(vx) 
              << "\n";
    std::cout << "\n";
    // Check v(x) > x
    Real scale = two;
    std::cout << std::right << std::setw(20) << "CHECK REGRET: x < v(x) for |x| > 0? \n";
    std::cout << std::right << std::setw(20) << "x"
              << std::right << std::setw(20) << "v(x)"
              << "\n";
    for (int i = 0; i < 10; i++) {
      x = scale*(Real)rand()/(Real)RAND_MAX - scale*half;
      vx = regret(x,0);
      std::cout << std::scientific << std::setprecision(11) << std::right
                << std::setw(20) << x 
                << std::setw(20) << vx 
                << "\n";
      scale *= two;
    }
    std::cout << "\n";
    // Check v(x) is convex
    Real y = zero;
    Real vy = zero;
    Real z = zero;
    Real vz = zero;
    Real l = zero; 
    scale = two;
    std::cout << std::right << std::setw(20) << "CHECK REGRET: v(x) is convex? \n";
    std::cout << std::right << std::setw(20) << "v(l*x+(1-l)*y)" 
                            << std::setw(20) << "l*v(x)+(1-l)*v(y)" 
                            << "\n";
    for (int i = 0; i < 10; i++) {
      x = scale*(Real)rand()/(Real)RAND_MAX - scale*half;
      vx = regret(x,0);
      y = scale*(Real)rand()/(Real)RAND_MAX - scale*half;
      vy = regret(y,0);
      l = (Real)rand()/(Real)RAND_MAX;
      z = l*x + (one-l)*y;
      vz = regret(z,0);
      std::cout << std::scientific << std::setprecision(11) << std::right
                << std::setw(20) << vz 
                << std::setw(20) << l*vx + (one-l)*vy 
                << "\n";
      scale *= two;
    }
    std::cout << "\n";
    // Check v'(x)
    x = oem3*(Real)rand()/(Real)RAND_MAX - fem4;
    vx = regret(x,0);
    Real dv = regret(x,1);
    Real t = one;
    Real diff = zero;
    Real err = zero;
    std::cout << std::right << std::setw(20) << "CHECK REGRET: v'(x) is correct? \n";
    std::cout << std::right << std::setw(20) << "t"
                            << std::setw(20) << "v'(x)"
                            << std::setw(20) << "(v(x+t)-v(x))/t"
                            << std::setw(20) << "Error"
                            << "\n";
    for (int i = 0; i < 13; i++) {
      y = x + t;
      vy = regret(y,0);
      diff = (vy-vx)/t;
      err = std::abs(diff-dv);
      std::cout << std::scientific << std::setprecision(11) << std::right 
                << std::setw(20) << t
                << std::setw(20) << dv 
                << std::setw(20) << diff 
                << std::setw(20) << err 
                << "\n";
      t *= p1;
    }
    std::cout << "\n";
    // Check v''(x)
    x = oem3*(Real)rand()/(Real)RAND_MAX - fem4;
    vx = regret(x,1);
    dv = regret(x,2);
    t = one;
    diff = zero;
    err = zero;
    std::cout << std::right << std::setw(20) << "CHECK REGRET: v''(x) is correct? \n";
    std::cout << std::right << std::setw(20) << "t"
                            << std::setw(20) << "v''(x)"
                            << std::setw(20) << "(v'(x+t)-v'(x))/t"
                            << std::setw(20) << "Error"
                            << "\n";
    for (int i = 0; i < 13; i++) {
      y = x + t;
      vy = regret(y,1);
      diff = (vy-vx)/t;
      err = std::abs(diff-dv);
      std::cout << std::scientific << std::setprecision(11) << std::right 
                << std::setw(20) << t
                << std::setw(20) << dv 
                << std::setw(20) << diff 
                << std::setw(20) << err 
                << "\n";
      t *= p1;
    }
    std::cout << "\n";
  }

  void reset(Teuchos::RCP<Vector<Real> > &x0, const Vector<Real> &x) {
    RiskMeasure<Real>::reset(x0,x);
    xstat_ = Teuchos::dyn_cast<const RiskVector<Real> >(
               Teuchos::dyn_cast<const Vector<Real> >(x)).getStatistic(0);
    if (firstReset_) {
      dualVector_            = (x0->dual()).clone();
      firstReset_ = false;
    }
    dualVector_->zero();
  }

  void reset(Teuchos::RCP<Vector<Real> > &x0, const Vector<Real> &x, 
             Teuchos::RCP<Vector<Real> > &v0, const Vector<Real> &v) {
    reset(x0,x);
    v0 = Teuchos::rcp_const_cast<Vector<Real> >(Teuchos::dyn_cast<const RiskVector<Real> >(
           Teuchos::dyn_cast<const Vector<Real> >(v)).getVector());
    vstat_ = Teuchos::dyn_cast<const RiskVector<Real> >(
               Teuchos::dyn_cast<const Vector<Real> >(v)).getStatistic(0);
  }

  void update(const Real val, const Real weight) {
    Real r = regret(val-xstat_,0);
    RiskMeasure<Real>::val_ += weight * r;
  }

  void update(const Real val, const Vector<Real> &g, const Real weight) {
    Real r = regret(val-xstat_,1);
    RiskMeasure<Real>::val_ -= weight * r;
    RiskMeasure<Real>::g_->axpy(weight*r,g);
  }

  void update(const Real val, const Vector<Real> &g, const Real gv, const Vector<Real> &hv, 
                      const Real weight) {
    Real r1 = regret(val-xstat_,1);
    Real r2 = regret(val-xstat_,2);
    RiskMeasure<Real>::val_ += weight * r2 * (vstat_ - gv);
    RiskMeasure<Real>::hv_->axpy(weight*r2*(gv-vstat_),g);
    RiskMeasure<Real>::hv_->axpy(weight*r1,hv);
  }

  Real getValue(SampleGenerator<Real> &sampler) {
    Real val  = RiskMeasure<Real>::val_, gval(0);
    sampler.sumAll(&val,&gval,1);
    gval += xstat_;
    return gval;
  }

  void getGradient(Vector<Real> &g, SampleGenerator<Real> &sampler) {
    RiskVector<Real> &gs = Teuchos::dyn_cast<RiskVector<Real> >(Teuchos::dyn_cast<Vector<Real> >(g));
    Real stat  = RiskMeasure<Real>::val_, gstat(0), one(1);
    sampler.sumAll(&stat,&gstat,1);
    gstat += one;
    gs.setStatistic(gstat);

    sampler.sumAll(*(RiskMeasure<Real>::g_),*dualVector_);
    gs.setVector(*dualVector_);
  }

  void getHessVec(Vector<Real> &hv, SampleGenerator<Real> &sampler) {
    RiskVector<Real> &hs = Teuchos::dyn_cast<RiskVector<Real> >(Teuchos::dyn_cast<Vector<Real> >(hv));
    Real stat  = RiskMeasure<Real>::val_, gstat(0);
    sampler.sumAll(&stat,&gstat,1);
    hs.setStatistic(gstat);

    sampler.sumAll(*(RiskMeasure<Real>::hv_),*dualVector_);
    hs.setVector(*dualVector_);
  }
};

}

#endif