/usr/include/trilinos/ROL_KLDivergence.hpp is in libtrilinos-rol-dev 12.10.1-3.
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// ************************************************************************
//
// Rapid Optimization Library (ROL) Package
// Copyright (2014) Sandia Corporation
//
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// @HEADER
#ifndef ROL_KLDIVERGENCE_HPP
#define ROL_KLDIVERGENCE_HPP
#include "ROL_RiskMeasure.hpp"
/** @ingroup risk_group
\class ROL::KLDivergence
\brief Provides an interface for the Kullback-Leibler distributionally robust
expectation.
This class defines a risk measure \f$\mathcal{R}\f$ which arises in distributionally
robust stochastic programming. \f$\mathcal{R}\f$ is given by
\f[
\mathcal{R}(X) = \sup_{\vartheta\in\mathfrak{A}}
\mathbb{E}[\vartheta X]
\f]
where \f$\mathfrak{A}\f$ is called the ambiguity (or uncertainty) set and
is defined by a constraint on the Kullback-Leibler divergence, i.e.,
\f[
\mathfrak{A} = \{\vartheta\in\mathcal{X}^*\,:\,
\mathbb{E}[\vartheta] = 1,\; \vartheta \ge 0,\;\text{and}\;
\mathbb{E}[\vartheta\log(\vartheta)] \le \epsilon\}.
\f]
\f$\mathcal{R}\f$ is a law-invariant, coherent risk measure. Moreover, by a
duality argument, \f$\mathcal{R}\f$ can be reformulated as
\f[
\mathcal{R}(X) = \inf_{\lambda > 0}\left\{
\lambda \epsilon + \lambda\mathbb{E}\left[\exp\left(
\frac{X}{\lambda}\right)\right]\right\}.
\f]
ROL implements this by augmenting the optimization vector \f$x_0\f$ with
the parameter \f$\lambda\f$, then minimizes jointly for \f$(x_0,\lambda)\f$.
*/
namespace ROL {
template<class Real>
class KLDivergence : public RiskMeasure<Real> {
private:
Real eps_;
Real gval_;
Real gvval_;
Real hval_;
Teuchos::RCP<Vector<Real> > scaledGradient_;
Teuchos::RCP<Vector<Real> > scaledHessVec_;
Teuchos::RCP<Vector<Real> > dualVector1_;
Teuchos::RCP<Vector<Real> > dualVector2_;
Real xstat_;
Real vstat_;
bool firstReset_;
void checkInputs(void) const {
Real zero(0);
TEUCHOS_TEST_FOR_EXCEPTION((eps_ <= zero), std::invalid_argument,
">>> ERROR (ROL::KLDivergence): Threshold must be positive!");
}
public:
/** \brief Constructor.
@param[in] eps is the tolerance for the KL divergence constraint
*/
KLDivergence(const Real eps = 1.e-2)
: RiskMeasure<Real>(), eps_(eps), firstReset_(true) {
checkInputs();
}
/** \brief Constructor.
@param[in] parlist is a parameter list specifying inputs
parlist should contain sublists "SOL"->"Risk Measure"->"KL Divergence" and
within the "KL Divergence" sublist should have the following parameters
\li "Threshold" (greater than 0)
*/
KLDivergence(Teuchos::ParameterList &parlist)
: RiskMeasure<Real>(), firstReset_(true) {
Teuchos::ParameterList &list
= parlist.sublist("SOL").sublist("Risk Measure").sublist("KL Divergence");
eps_ = list.get<Real>("Threshold");
checkInputs();
}
void reset(Teuchos::RCP<Vector<Real> > &x0, const Vector<Real> &x) {
Real zero(0);
RiskMeasure<Real>::reset(x0,x);
xstat_ = Teuchos::dyn_cast<const RiskVector<Real> >(x).getStatistic(0);
if ( firstReset_ ) {
scaledGradient_ = (x0->dual()).clone();
scaledHessVec_ = (x0->dual()).clone();
dualVector1_ = (x0->dual()).clone();
dualVector2_ = (x0->dual()).clone();
firstReset_ = false;
}
gval_ = zero; gvval_ = zero; hval_ = zero;
scaledGradient_->zero(); scaledHessVec_->zero();
dualVector1_->zero(); dualVector2_->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> >(v).getVector());
vstat_ = Teuchos::dyn_cast<const RiskVector<Real> >(v).getStatistic(0);
}
void update(const Real val, const Real weight) {
Real ev = exponential(val,xstat_*eps_);
RiskMeasure<Real>::val_ += weight * ev;
}
Real getValue(SampleGenerator<Real> &sampler) {
if ( xstat_ == static_cast<Real>(0) ) {
return ROL_INF<Real>();
}
Real val = RiskMeasure<Real>::val_, ev(0);
sampler.sumAll(&val,&ev,1);
return (static_cast<Real>(1) + std::log(ev)/eps_)/xstat_;
}
void update(const Real val, const Vector<Real> &g, const Real weight) {
Real ev = exponential(val,xstat_*eps_);
RiskMeasure<Real>::val_ += weight * ev;
gval_ += weight * ev * val;
RiskMeasure<Real>::g_->axpy(weight*ev,g);
}
void getGradient(Vector<Real> &g, SampleGenerator<Real> &sampler) {
std::vector<Real> local(2), global(2);
local[0] = RiskMeasure<Real>::val_;
local[1] = gval_;
sampler.sumAll(&local[0],&global[0],2);
Real ev = global[0], egval = global[1];
sampler.sumAll(*(RiskMeasure<Real>::g_),*dualVector1_);
dualVector1_->scale(static_cast<Real>(1)/ev);
Teuchos::dyn_cast<RiskVector<Real> >(g).setVector(*dualVector1_);
Real gstat(0);
if ( xstat_ == static_cast<Real>(0) ) {
gstat = ROL_INF<Real>();
}
else {
gstat = -((static_cast<Real>(1) + std::log(ev)/eps_)/xstat_
- egval/ev)/xstat_;
}
Teuchos::dyn_cast<RiskVector<Real> >(g).setStatistic(gstat);
}
void update(const Real val, const Vector<Real> &g, const Real gv, const Vector<Real> &hv,
const Real weight) {
Real ev = exponential(val,xstat_*eps_);
RiskMeasure<Real>::val_ += weight * ev;
RiskMeasure<Real>::gv_ += weight * ev * gv;
gval_ += weight * ev * val;
gvval_ += weight * ev * val * gv;
hval_ += weight * ev * val * val;
RiskMeasure<Real>::g_->axpy(weight*ev,g);
RiskMeasure<Real>::hv_->axpy(weight*ev,hv);
scaledGradient_->axpy(weight*ev*gv,g);
scaledHessVec_->axpy(weight*ev*val,g);
}
void getHessVec(Vector<Real> &hv, SampleGenerator<Real> &sampler) {
std::vector<Real> local(5), global(5);
local[0] = RiskMeasure<Real>::val_;
local[1] = RiskMeasure<Real>::gv_;
local[2] = gval_;
local[3] = gvval_;
local[4] = hval_;
sampler.sumAll(&local[0],&global[0],5);
Real ev = global[0], egv = global[1], egval = global[2];
Real egvval = global[3], ehval = global[4];
Real c0 = static_cast<Real>(1)/ev, c1 = c0*egval, c2 = c0*egv, c3 = eps_*c0;
sampler.sumAll(*(RiskMeasure<Real>::hv_),*dualVector1_);
sampler.sumAll(*scaledGradient_,*dualVector2_);
dualVector1_->axpy(xstat_*eps_,*dualVector2_);
dualVector1_->scale(c0);
dualVector2_->zero();
sampler.sumAll(*(RiskMeasure<Real>::g_),*dualVector2_);
dualVector1_->axpy(-c3*(vstat_*c1 + xstat_*c2),*dualVector2_);
dualVector2_->zero();
sampler.sumAll(*scaledHessVec_,*dualVector2_);
dualVector1_->axpy(vstat_*c3,*dualVector2_);
Teuchos::dyn_cast<RiskVector<Real> >(hv).setVector(*dualVector1_);
Real hstat(0);
if ( xstat_ == static_cast<Real>(0) ) {
hstat = ROL_INF<Real>();
}
else {
Real xstat2 = static_cast<Real>(2)/(xstat_*xstat_);
Real h11 = xstat2*((static_cast<Real>(1) + std::log(ev)/eps_)/xstat_ - c1)
+ (c3*ehval - eps_*c1*c1)/xstat_;
hstat = vstat_ * h11 + (c3*egvval - eps_*c1*c2);
}
Teuchos::dyn_cast<RiskVector<Real> >(hv).setStatistic(hstat);
}
private:
Real exponential(const Real arg1, const Real arg2) const {
if ( arg1 < arg2 ) {
return power(exponential(arg1),arg2);
}
else {
return power(exponential(arg2),arg1);
}
}
Real exponential(const Real arg) const {
if ( arg >= std::log(ROL_INF<Real>()) ) {
return ROL_INF<Real>();
}
else {
return std::exp(arg);
}
}
Real power(const Real arg, const Real pow) const {
if ( arg >= std::pow(ROL_INF<Real>(),static_cast<Real>(1)/pow) ) {
return ROL_INF<Real>();
}
else {
return std::pow(arg,pow);
}
}
};
}
#endif
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