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// ************************************************************************
//
// Rapid Optimization Library (ROL) Package
// Copyright (2014) Sandia Corporation
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// @HEADER
#ifndef ROL_MEANDEVIATIONFROMTARGET_HPP
#define ROL_MEANDEVIATIONFROMTARGET_HPP
#include "ROL_RiskMeasure.hpp"
#include "ROL_PositiveFunction.hpp"
#include "ROL_PlusFunction.hpp"
#include "ROL_AbsoluteValue.hpp"
#include "Teuchos_ParameterList.hpp"
#include "Teuchos_Array.hpp"
/** @ingroup risk_group
\class ROL::MeanDeviationFromTarget
\brief Provides an interface for the mean plus a sum of arbitrary order
deviations from targets.
The mean plus deviations from targets risk measure is
\f[
\mathcal{R}(X) = \mathbb{E}[X]
+ \sum_{k=1}^n c_k \mathbb{E}[\wp(X-t_k)^{p_k}]^{1/p_k}
\f]
where \f$\wp:\mathbb{R}\to[0,\infty)\f$ is either the absolute value
or \f$(x)_+ = \max\{0,x\}\f$, \f$c_k > 0\f$ and \f$p_k\in\mathbb{N}\f$.
In general, \f$\mathcal{R}\f$ is law-invariant, but not coherent since
it violates translation equivariance.
When using derivative-based optimization, the user can
provide a smooth approximation of \f$(\cdot)_+\f$ using the
ROL::PositiveFunction class.
*/
namespace ROL {
template<class Real>
class MeanDeviationFromTarget : public RiskMeasure<Real> {
typedef typename std::vector<Real>::size_type uint;
private:
Teuchos::RCP<PositiveFunction<Real> > positiveFunction_;
Teuchos::RCP<Vector<Real> > dualVector1_;
Teuchos::RCP<Vector<Real> > dualVector2_;
Teuchos::RCP<Vector<Real> > dualVector3_;
Teuchos::RCP<Vector<Real> > dualVector4_;
std::vector<Real> target_;
std::vector<Real> order_;
std::vector<Real> coeff_;
uint NumMoments_;
std::vector<Real> pval_;
std::vector<Real> pgv_;
std::vector<Teuchos::RCP<Vector<Real> > > pg0_;
std::vector<Teuchos::RCP<Vector<Real> > > pg_;
std::vector<Teuchos::RCP<Vector<Real> > > phv_;
bool firstReset_;
void initialize(void) {
// Initialize additional storage
pg_.clear(); pg0_.clear(); phv_.clear(); pval_.clear(); pgv_.clear();
pg_.resize(NumMoments_);
pg0_.resize(NumMoments_);
phv_.resize(NumMoments_);
pval_.resize(NumMoments_);
pgv_.resize(NumMoments_);
}
void checkInputs(void) const {
int oSize = order_.size(), cSize = coeff_.size(), tSize = target_.size();
TEUCHOS_TEST_FOR_EXCEPTION((oSize!=cSize),std::invalid_argument,
">>> ERROR (ROL::MeanDeviationFromTarget): Order and coefficient arrays have different sizes!");
TEUCHOS_TEST_FOR_EXCEPTION((oSize!=tSize),std::invalid_argument,
">>> ERROR (ROL::MeanDeviationFromTarget): Order and target arrays have different sizes!");
Real zero(0), two(2);
for (int i = 0; i < oSize; i++) {
TEUCHOS_TEST_FOR_EXCEPTION((order_[i] < two), std::invalid_argument,
">>> ERROR (ROL::MeanDeviationFromTarget): Element of order array out of range!");
TEUCHOS_TEST_FOR_EXCEPTION((coeff_[i] < zero), std::invalid_argument,
">>> ERROR (ROL::MeanDeviationFromTarget): Element of coefficient array out of range!");
}
TEUCHOS_TEST_FOR_EXCEPTION(positiveFunction_ == Teuchos::null, std::invalid_argument,
">>> ERROR (ROL::MeanDeviationFromTarget): PositiveFunction pointer is null!");
}
public:
/** \brief Constructor.
@param[in] target is the target scalar value
@param[in] order is the deviation order
@param[in] coeff is the weight for deviation term
@param[in] pf is the plus function or an approximation
This constructor produces a mean plus deviation from target risk measure
with a single deviation.
*/
MeanDeviationFromTarget( const Real target, const Real order, const Real coeff,
const Teuchos::RCP<PositiveFunction<Real> > &pf )
: RiskMeasure<Real>(), positiveFunction_(pf), firstReset_(true) {
order_.clear(); order_.push_back(order);
coeff_.clear(); coeff_.push_back(coeff);
target_.clear(); target_.push_back(target);
checkInputs();
NumMoments_ = order_.size();
initialize();
}
/** \brief Constructor.
@param[in] target is a vector of targets
@param[in] order is a vector of deviation orders
@param[in] coeff is a vector of weights for the deviation terms
@param[in] pf is the plus function or an approximation
This constructor produces a mean plus deviation from target risk measure
with an arbitrary number of deviations.
*/
MeanDeviationFromTarget( const std::vector<Real> &target,
const std::vector<Real> &order,
const std::vector<Real> &coeff,
const Teuchos::RCP<PositiveFunction<Real> > &pf )
: RiskMeasure<Real>(), positiveFunction_(pf), firstReset_(true) {
target_.clear(); order_.clear(); coeff_.clear();
for ( uint i = 0; i < target.size(); i++ ) {
target_.push_back(target[i]);
}
for ( uint i = 0; i < order.size(); i++ ) {
order_.push_back(order[i]);
}
for ( uint i = 0; i < coeff.size(); i++ ) {
coeff_.push_back(coeff[i]);
}
checkInputs();
NumMoments_ = order_.size();
initialize();
}
/** \brief Constructor.
@param[in] parlist is a parameter list specifying inputs
parlist should contain sublists "SOL"->"Risk Measure"->"Mean Plus Deviation From Target" and
within the "Mean Plus Deviation From Target" sublist should have the following parameters
\li "Targets" (array of scalars)
\li "Orders" (array of unsigned integers)
\li "Coefficients" (array of positive scalars)
\li "Deviation Type" (eighter "Upper" or "Absolute")
\li A sublist for positive function information.
*/
MeanDeviationFromTarget( Teuchos::ParameterList &parlist )
: RiskMeasure<Real>(), firstReset_(true) {
Teuchos::ParameterList &list
= parlist.sublist("SOL").sublist("Risk Measure").sublist("Mean Plus Deviation From Target");
// Get data from parameter list
Teuchos::Array<Real> target
= Teuchos::getArrayFromStringParameter<double>(list,"Targets");
target_ = target.toVector();
Teuchos::Array<Real> order
= Teuchos::getArrayFromStringParameter<double>(list,"Orders");
order_ = order.toVector();
Teuchos::Array<Real> coeff
= Teuchos::getArrayFromStringParameter<double>(list,"Coefficients");
coeff_ = coeff.toVector();
// Build (approximate) positive function
std::string type = list.get<std::string>("Deviation Type");
if ( type == "Upper" ) {
positiveFunction_ = Teuchos::rcp(new PlusFunction<Real>(list));
}
else if ( type == "Absolute" ) {
positiveFunction_ = Teuchos::rcp(new AbsoluteValue<Real>(list));
}
else {
TEUCHOS_TEST_FOR_EXCEPTION(true, std::invalid_argument,
">>> (ROL::MeanDeviation): Deviation type is not recoginized!");
}
// Check inputs
checkInputs();
NumMoments_ = order.size();
initialize();
}
void reset(Teuchos::RCP<Vector<Real> > &x0, const Vector<Real> &x) {
Real zero(0);
RiskMeasure<Real>::reset(x0,x);
if (firstReset_) {
for ( uint p = 0; p < NumMoments_; p++ ) {
pg0_[p] = (x0->dual()).clone();
pg_[p] = (x0->dual()).clone();
phv_[p] = (x0->dual()).clone();
}
dualVector1_ = (x0->dual()).clone();
dualVector2_ = (x0->dual()).clone();
dualVector3_ = (x0->dual()).clone();
dualVector4_ = (x0->dual()).clone();
firstReset_ = false;
}
for ( uint p = 0; p < NumMoments_; p++ ) {
pg0_[p]->zero(); pg_[p]->zero(); phv_[p]->zero();
pval_[p] = zero; pgv_[p] = zero;
}
dualVector1_->zero(); dualVector2_->zero();
dualVector3_->zero(); dualVector4_->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());
}
void update(const Real val, const Real weight) {
Real diff(0), pf0(0);
RiskMeasure<Real>::val_ += weight * val;
for ( uint p = 0; p < NumMoments_; p++ ) {
diff = val-target_[p];
pf0 = positiveFunction_->evaluate(diff,0);
pval_[p] += weight * std::pow(pf0,order_[p]);
}
}
void update(const Real val, const Vector<Real> &g, const Real weight) {
Real diff(0), pf0(0), pf1(0), c(0), one(1);
for ( uint p = 0; p < NumMoments_; p++ ) {
diff = val-target_[p];
pf0 = positiveFunction_->evaluate(diff,0);
pf1 = positiveFunction_->evaluate(diff,1);
c = std::pow(pf0,order_[p]-one) * pf1;
(pg_[p])->axpy(weight * c,g);
pval_[p] += weight * std::pow(pf0,order_[p]);
}
RiskMeasure<Real>::g_->axpy(weight,g);
}
void update(const Real val, const Vector<Real> &g, const Real gv, const Vector<Real> &hv,
const Real weight) {
Real diff(0), pf0(0), pf1(0), pf2(0), p0(0), p1(0), p2(0), c(0), one(1), two(2);
for ( uint p = 0; p < NumMoments_; p++ ) {
diff = val - target_[p];
pf0 = positiveFunction_->evaluate(diff,0);
pf1 = positiveFunction_->evaluate(diff,1);
pf2 = positiveFunction_->evaluate(diff,2);
p0 = std::pow(pf0,order_[p]);
p1 = std::pow(pf0,order_[p]-one);
p2 = std::pow(pf0,order_[p]-two);
c = -(order_[p]-one)*p1*pf1;
pg0_[p]->axpy(weight*c,g);
c = gv*((order_[p]-one)*p2*pf1*pf1 + p1*pf2);
pg_[p]->axpy(weight*c,g);
c = p1*pf1;
phv_[p]->axpy(weight*c,hv);
pval_[p] += weight*p0;
pgv_[p] += weight*p1*pf1*gv;
}
RiskMeasure<Real>::hv_->axpy(weight,hv);
}
Real getValue(SampleGenerator<Real> &sampler) {
Real val = RiskMeasure<Real>::val_, dev(0), one(1);
sampler.sumAll(&val,&dev,1);
std::vector<Real> pval_sum(NumMoments_);
sampler.sumAll(&(pval_)[0],&pval_sum[0],NumMoments_);
for ( uint p = 0; p < NumMoments_; p++ ) {
dev += coeff_[p] * std::pow(pval_sum[p],one/order_[p]);
}
return dev;
}
void getGradient(Vector<Real> &g, SampleGenerator<Real> &sampler) {
Real zero(0), one(1);
sampler.sumAll(*(RiskMeasure<Real>::g_),*dualVector1_);
std::vector<Real> pval_sum(NumMoments_);
sampler.sumAll(&(pval_)[0],&pval_sum[0],NumMoments_);
Teuchos::RCP<Vector<Real> > pg;
for ( uint p = 0; p < NumMoments_; p++ ) {
if ( pval_sum[p] > zero ) {
pg = (pg_[p])->clone();
sampler.sumAll(*(pg_[p]),*pg);
dualVector1_->axpy(coeff_[p]/std::pow(pval_sum[p],one-one/order_[p]),*pg);
}
}
// Set RiskVector
(Teuchos::dyn_cast<RiskVector<Real> >(g)).setVector(*dualVector1_);
}
void getHessVec(Vector<Real> &hv, SampleGenerator<Real> &sampler) {
Real zero(0), one(1), two(2);
sampler.sumAll(*(RiskMeasure<Real>::hv_),*dualVector1_);
std::vector<Real> pval_sum(NumMoments_);
sampler.sumAll(&(pval_)[0],&pval_sum[0],NumMoments_);
std::vector<Real> pgv_sum(NumMoments_);
sampler.sumAll(&(pgv_)[0],&pgv_sum[0],NumMoments_);
Real c(0);
for ( uint p = 0; p < NumMoments_; p++ ) {
if ( pval_sum[p] > zero ) {
sampler.sumAll(*(pg_[p]),*dualVector2_);
sampler.sumAll(*(pg0_[p]),*dualVector3_);
sampler.sumAll(*(phv_[p]),*dualVector4_);
c = coeff_[p]*(pgv_sum[p]/std::pow(pval_sum[p],two-one/order_[p]));
dualVector1_->axpy(c,*dualVector3_);
c = coeff_[p]/std::pow(pval_sum[p],one-one/order_[p]);
dualVector1_->axpy(c,*dualVector2_);
dualVector1_->axpy(c,*dualVector4_);
}
}
// Set RiskVector
(Teuchos::dyn_cast<RiskVector<Real> >(hv)).setVector(*dualVector1_);
}
};
}
#endif
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