ROL_HMCRObjective.hpp

Go to the documentation of this file.

// @HEADER
// ************************************************************************
//
//               Rapid Optimization Library (ROL) Package
//                 Copyright (2014) Sandia Corporation
//
// Under terms of Contract DE-AC04-94AL85000, there is a non-exclusive
// license for use of this work by or on behalf of the U.S. Government.
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are
// met:
//
// 1. Redistributions of source code must retain the above copyright
// notice, this list of conditions and the following disclaimer.
//
// 2. Redistributions in binary form must reproduce the above copyright
// notice, this list of conditions and the following disclaimer in the
// documentation and/or other materials provided with the distribution.
//
// 3. Neither the name of the Corporation nor the names of the
// contributors may be used to endorse or promote products derived from
// this software without specific prior written permission.
//
// THIS SOFTWARE IS PROVIDED BY SANDIA CORPORATION "AS IS" AND ANY
// EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
// PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL SANDIA CORPORATION OR THE
// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
// LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
//
// Questions? Contact lead developers:
//              Drew Kouri   (dpkouri@sandia.gov) and
//              Denis Ridzal (dridzal@sandia.gov)
//
// ************************************************************************
// @HEADER

#ifndef ROL_HMCROBJECTIVE_HPP
#define ROL_HMCROBJECTIVE_HPP

#include "Teuchos_RCP.hpp"
#include "ROL_RiskVector.hpp"
#include "ROL_Objective.hpp"
#include "ROL_SampleGenerator.hpp"

namespace ROL {

template<class Real>
class HMCRObjective : public Objective<Real> {
private:
  Teuchos::RCP<Objective<Real> > ParametrizedObjective_;

  Real order_;
  Real prob_;

  Teuchos::RCP<SampleGenerator<Real> > ValueSampler_;
  Teuchos::RCP<SampleGenerator<Real> > GradientSampler_;
  Teuchos::RCP<SampleGenerator<Real> > HessianSampler_;

  Teuchos::RCP<Vector<Real> > pointGrad_;
  Teuchos::RCP<Vector<Real> > pointHess_;

  Teuchos::RCP<Vector<Real> > gradient0_;
  Teuchos::RCP<Vector<Real> > sumGrad0_;
  Teuchos::RCP<Vector<Real> > gradient1_;
  Teuchos::RCP<Vector<Real> > sumGrad1_;
  Teuchos::RCP<Vector<Real> > gradient2_;
  Teuchos::RCP<Vector<Real> > sumGrad2_;
  Teuchos::RCP<Vector<Real> > hessvec_;
  Teuchos::RCP<Vector<Real> > sumHess_;
 
  bool initialized_;
  bool storage_;

  std::map<std::vector<Real>,Real> value_storage_;
  std::map<std::vector<Real>,Teuchos::RCP<Vector<Real> > > gradient_storage_;

  void initialize(const Vector<Real> &x) {
    pointGrad_ = x.dual().clone();
    pointHess_ = x.dual().clone();
    gradient0_ = x.dual().clone();
    sumGrad0_  = x.dual().clone();
    gradient1_ = x.dual().clone();
    sumGrad1_  = x.dual().clone();
    gradient2_ = x.dual().clone();
    sumGrad2_  = x.dual().clone();
    hessvec_   = x.dual().clone();
    sumHess_   = x.dual().clone();
    initialized_ = true;
  }

  void unwrap_const_CVaR_vector(Teuchos::RCP<Vector<Real> > &xvec, Real &xvar,
                          const Vector<Real> &x) {
    xvec = Teuchos::rcp_const_cast<Vector<Real> >(Teuchos::dyn_cast<const RiskVector<Real> >(x).getVector());
    xvar = Teuchos::dyn_cast<const RiskVector<Real> >(x).getStatistic(0);
    if ( !initialized_ ) {
      initialize(*xvec);
    }
  }

  void getValue(Real &val, const Vector<Real> &x,
          const std::vector<Real> &param, Real &tol) {
    if ( storage_ && value_storage_.count(param) ) {
      val = value_storage_[param];
    }
    else {
      ParametrizedObjective_->setParameter(param);
      val = ParametrizedObjective_->value(x,tol);
      if ( storage_ ) {
        value_storage_.insert(std::pair<std::vector<Real>,Real>(param,val));
      }
    }
  }

  void getGradient(Vector<Real> &g, const Vector<Real> &x,
             const std::vector<Real> &param, Real &tol) {
    if ( storage_ && gradient_storage_.count(param) ) {
      g.set(*(gradient_storage_[param]));
    }
    else {
      ParametrizedObjective_->setParameter(param);
      ParametrizedObjective_->gradient(g,x,tol);
      if ( storage_ ) {
        Teuchos::RCP<Vector<Real> > tmp = g.clone();
        gradient_storage_.insert(std::pair<std::vector<Real>,Teuchos::RCP<Vector<Real> > >(param,tmp));
        gradient_storage_[param]->set(g);
      }
    }
  }

  void getHessVec(Vector<Real> &hv, const Vector<Real> &v, const Vector<Real> &x,
            const std::vector<Real> &param, Real &tol) {
    ParametrizedObjective_->setParameter(param);
    ParametrizedObjective_->hessVec(hv,v,x,tol);
  }
 

public:
  virtual ~HMCRObjective() {}

  HMCRObjective( Teuchos::RCP<Objective<Real> > &pObj,
                 Real order, Real prob,
                 Teuchos::RCP<SampleGenerator<Real> > &vsampler, 
                 Teuchos::RCP<SampleGenerator<Real> > &gsampler,
                 Teuchos::RCP<SampleGenerator<Real> > &hsampler,
                 bool storage = true )
    : ParametrizedObjective_(pObj),
      ValueSampler_(vsampler), GradientSampler_(gsampler), HessianSampler_(hsampler),
      initialized_(false), storage_(storage) {
    order_ = ((order < 1.0) ? 1.0 : order);
    prob_  = ((prob > 1.0) ? 1.0 : ((prob < 0.0) ? 0.0 : prob));
    value_storage_.clear();
    gradient_storage_.clear();
  }

  HMCRObjective( Teuchos::RCP<Objective<Real> > &pObj,
                 Real order, Real prob,
                 Teuchos::RCP<SampleGenerator<Real> > &vsampler, 
                 Teuchos::RCP<SampleGenerator<Real> > &gsampler,
                 bool storage = true )
    : ParametrizedObjective_(pObj),
      ValueSampler_(vsampler), GradientSampler_(gsampler), HessianSampler_(gsampler),
      initialized_(false), storage_(storage) {
    order_ = ((order < 1.0) ? 1.0 : order);
    prob_  = ((prob > 1.0) ? 1.0 : ((prob < 0.0) ? 0.0 : prob));
    value_storage_.clear();
    gradient_storage_.clear();
  }

  HMCRObjective( Teuchos::RCP<Objective<Real> > &pObj,
                 Real order, Real prob,
                 Teuchos::RCP<SampleGenerator<Real> > &sampler,
                 bool storage = true )
    : ParametrizedObjective_(pObj), order_(order), prob_(prob),
      ValueSampler_(sampler), GradientSampler_(sampler), HessianSampler_(sampler),
      initialized_(false), storage_(storage) {
    order_ = ((order < 1.0) ? 1.0 : order);
    prob_  = ((prob > 1.0) ? 1.0 : ((prob < 0.0) ? 0.0 : prob));
    value_storage_.clear();
    gradient_storage_.clear();
  }

  void update( const Vector<Real> &x, bool flag = true, int iter = -1 ) {
    Teuchos::RCP<Vector<Real> > xvec; Real xvar = 0.0;
    unwrap_const_CVaR_vector(xvec,xvar,x);
    ParametrizedObjective_->update(*xvec,flag,iter);
    ValueSampler_->update(*xvec);
    if ( storage_ ) {
      value_storage_.clear();
    }
    if ( flag ) {
      GradientSampler_->update(*xvec);
      HessianSampler_->update(*xvec);
      if ( storage_ ) {
        gradient_storage_.clear();
      }
    }
  }

  Real value( const Vector<Real> &x, Real &tol ) {
    Teuchos::RCP<Vector<Real> > xvec; Real xvar = 0.0;
    unwrap_const_CVaR_vector(xvec,xvar,x);
    // Initialize storage
    std::vector<Real> point;
    Real weight = 0.0, myval = 0.0, pval = 0.0, val = 0.0;
    int start = ValueSampler_->start(), end = ValueSampler_->numMySamples();
    for ( int i = start; i < end; i++ ) {
      weight = ValueSampler_->getMyWeight(i);
      point  = ValueSampler_->getMyPoint(i);
      // Compute f(xvec,xi)
      getValue(pval,*xvec,point,tol);
      if ( pval > xvar ) {
        // Build partial sum depending on value
        myval += weight*((order_ == 1.0) ? pval-xvar
                          : std::pow(pval-xvar,order_));
      }
    }
    // Update expected value
    ValueSampler_->sumAll(&myval,&val,1);
    // Return HMCR value
    if (std::abs(val) < ROL_EPSILON<Real>()) {
      return xvar;
    }
    return xvar + ((order_ == 1.0) ? val
                    : ((order_ == 2.0) ? std::sqrt(val)
                      : std::pow(val,1.0/order_)))/(1.0-prob_);
  }

  void gradient( Vector<Real> &g, const Vector<Real> &x, Real &tol ) {
    Teuchos::RCP<Vector<Real> > xvec; Real xvar = 0.0;
    unwrap_const_CVaR_vector(xvec,xvar,x);
    RiskVector<Real> &gc = Teuchos::dyn_cast<RiskVector<Real> >(g);
    // Initialize storage
    g.zero(); sumGrad0_->zero();
    std::vector<Real> point, val(2,0.0), myval(2,0.0);
    Real weight = 0.0, pval = 0.0, pvalp0 = 0.0, pvalp1 = 0.0;
    int start = GradientSampler_->start(), end = GradientSampler_->numMySamples();
    for ( int i = start; i < end; i++ ) {
      weight = GradientSampler_->getMyWeight(i);
      point  = GradientSampler_->getMyPoint(i);
      // Compute the value of f(xvec,xi)
      getValue(pval,*xvec,point,tol);
      if ( pval > xvar ) {
        // Compute max(0,f(xvec,xi)-xvar)^order
        pvalp0 = ((order_ == 1.0) ? pval-xvar
                   : std::pow(pval-xvar,order_));
        pvalp1 = ((order_ == 1.0) ? 1.0
                   : ((order_ == 2.0) ? pval-xvar
                     : std::pow(pval-xvar,order_-1.0)));
        // Build partial sums depending on value
        myval[0] += weight*pvalp0;
        myval[1] += weight*pvalp1;
        // Compute gradient of f(xvec,xi)
        getGradient(*pointGrad_,*xvec,point,tol);
        // Build partial sum depending on gradient
        sumGrad0_->axpy(weight*pvalp1,*pointGrad_);
      }
    }
    Real gvar = 1.0; gradient0_->zero();
    // Combine partial sums
    GradientSampler_->sumAll(&myval[0],&val[0],2);
    if (std::abs(val[0]) >= ROL_EPSILON<Real>()) {
      GradientSampler_->sumAll(*sumGrad0_,*gradient0_);
      // Compute VaR gradient and HMCR gradient
      Real norm = ((order_ == 1.0) ? 1.0
                    : ((order_ == 2.0) ? std::sqrt(val[0])
                      : std::pow(val[0],(order_-1.0)/order_)));
      gvar -= val[1]/((1.0-prob_)*norm);
      gradient0_->scale(1.0/((1.0-prob_)*norm));
    }
    // Set gradient components of CVaR vector
    gc.setStatistic(gvar);
    gc.setVector(*gradient0_);
  }

  void hessVec( Vector<Real> &hv, const Vector<Real> &v,
                        const Vector<Real> &x, Real &tol ) {
    Teuchos::RCP<Vector<Real> > xvec; Real xvar = 0.0;
    unwrap_const_CVaR_vector(xvec,xvar,x);
    Teuchos::RCP<Vector<Real> > vvec; Real vvar = 0.0;
    unwrap_const_CVaR_vector(vvec,vvar,v);
    RiskVector<Real> &hvc = Teuchos::dyn_cast<RiskVector<Real> >(hv);
    // Initialize storage
    hv.zero();
    sumGrad0_->zero(); sumGrad1_->zero(); sumGrad2_->zero(); sumHess_->zero();
    gradient0_->zero(); gradient1_->zero(); gradient2_->zero();
    Real weight = 0.0;
    std::vector<Real> point;
    Real pval = 0.0, pvalp0 = 0.0, pvalp1 = 0.0, pvalp2 = 0.0, gv = 0.0;
    std::vector<Real> val(5,0.0), myval(5,0.0);
    int start = HessianSampler_->start(), end = HessianSampler_->numMySamples();
    for ( int i = start; i < end; i++ ) {
      // Get sample and associated probability
      weight = HessianSampler_->getMyWeight(i);
      point  = HessianSampler_->getMyPoint(i);
      // Compute the value of f(xvec,xi)
      getValue(pval,*xvec,point,tol);
      if ( pval > xvar ) {
        // Compute max(0,f(xvec,xi)-xvar)^order
        pvalp0 = ((order_ == 1.0) ? pval-xvar
                   : std::pow(pval-xvar,order_));
        pvalp1 = ((order_ == 1.0) ? 1.0
                   : ((order_ == 2.0) ? pval-xvar
                     : std::pow(pval-xvar,order_-1.0)));
        pvalp2 = ((order_ == 1.0) ? 0.0
                   : ((order_ == 2.0) ? 1.0
                     : ((order_ == 3.0) ? pval-xvar
                       : std::pow(pval-xvar,order_-2.0))));
        // Build partial sums depending on value
        myval[0] += weight*pvalp0;
        myval[1] += weight*pvalp1;
        myval[2] += weight*pvalp2;
        // Compute the gradient and directional derivative of f(xvec,xi)
        getGradient(*pointGrad_,*xvec,point,tol);
        gv = pointGrad_->dot(vvec->dual());
        // Build partial sums depending on gradient
        myval[3] += weight*pvalp1*gv;
        myval[4] += weight*pvalp2*gv;
        sumGrad0_->axpy(weight*pvalp1,*pointGrad_);
        sumGrad1_->axpy(weight*pvalp2,*pointGrad_);
        sumGrad2_->axpy(weight*pvalp2*gv,*pointGrad_);
        // Compute the hessian of f(xvec,xi) in the direction vvec
        getHessVec(*pointHess_,*vvec,*xvec,point,tol);
        // Build partial sum depending on the hessian
        sumHess_->axpy(weight*pvalp1,*pointHess_);
      }
    }
    Real hvar = 0.0; hessvec_->zero();
    HessianSampler_->sumAll(&myval[0],&val[0],5);
    if (std::abs(val[0]) >= ROL_EPSILON<Real>()) {
    // Compile partial sums
      HessianSampler_->sumAll(*sumGrad0_,*gradient0_);
      HessianSampler_->sumAll(*sumGrad1_,*gradient1_);
      HessianSampler_->sumAll(*sumGrad2_,*gradient2_);
      HessianSampler_->sumAll(*sumHess_,*hessvec_);
      // Compute VaR Hessian-times-a-vector and HMCR Hessian-times-a-vector
      Real norm0 = (1.0-prob_)*((order_ == 1.0) ? 1.0
                                 : ((order_ == 2.0) ? std::sqrt(val[0])
                                   : std::pow(val[0],(order_-1.0)/order_)));
      Real norm1 = (1.0-prob_)*((order_ == 1.0) ? 1.0
                                 : std::pow(val[0],(2.0*order_-1.0)/order_));
      hvar = (order_-1.0)*((val[2]/norm0 - val[1]*val[1]/norm1)*vvar
                               -(val[4]/norm0 - val[3]*val[1]/norm1));
      hessvec_->scale(1.0/norm0); //(order_-1.0)/norm0);
      hessvec_->axpy(-(order_-1.0)*vvar/norm0,*gradient1_);
      hessvec_->axpy((order_-1.0)*(vvar*val[1]-val[3])/norm1,*gradient0_);
      hessvec_->axpy((order_-1.0)/norm0,*gradient2_);
    }
    // Set gradient components of CVaR vector
    hvc.setStatistic(hvar);
    hvc.setVector(*hessvec_);
  }

  virtual void precond( Vector<Real> &Pv, const Vector<Real> &v,
                        const Vector<Real> &x, Real &tol ) {
    Pv.set(v.dual());
  }
};

}

#endif