/usr/include/trilinos/ROL_SmoothedWorstCaseQuadrangle.hpp is in libtrilinos-rol-dev 12.10.1-3.
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// ************************************************************************
//
// Rapid Optimization Library (ROL) Package
// Copyright (2014) Sandia Corporation
//
// Under terms of Contract DE-AC04-94AL85000, there is a non-exclusive
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// met:
//
// 1. Redistributions of source code must retain the above copyright
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// 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
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// Drew Kouri (dpkouri@sandia.gov) and
// Denis Ridzal (dridzal@sandia.gov)
//
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// @HEADER
#ifndef ROL_SMOOTHEDWORSTCASEQUAD_HPP
#define ROL_SMOOTHEDWORSTCASEQUAD_HPP
#include "ROL_ExpectationQuad.hpp"
/** @ingroup risk_group
\class ROL::SmoothedWorstCaseQuadrangle
\brief Provides an interface for a smoothed version of the worst-case
scenario risk measure using the expectation risk quadrangle.
The worst-case scenario risk measure is
\f[
\mathcal{R}(X) = \sup_{\omega\in\Omega} X(\omega).
\f]
\f$\mathcal{R}\f$ is a law-invariant coherent risk measure.
Clearly, \f$\mathcal{R}\f$ is not differentiable. As such, this class
defines a smoothed version of \f$\mathcal{R}\f$ the expectation risk
quadrangle. In the nonsmooth case, the scalar regret function is
\f$v(x) = 0\f$ if \f$x \le 0\f$ and \f$v(x) = \infty\f$ if \f$x > 0\f$.
Similarly, the scalar error function is \f$e(x) = -x\f$ if \f$x \le 0 \f$
and \f$e(x) = \infty\f$ if \f$x > 0\f$. To smooth \f$\mathcal{R}\f$, we
perform Moreau-Yosida regularization on the scalar error function, i.e.,
\f[
e_\epsilon(x) = \inf_{y\in\mathbb{R}} \left\{ e(y) + \frac{1}{2\epsilon}
(x-y)^2\right\}
% = \left\{\begin{array}{l l}
% -\left(x+\frac{\epsilon}{2}\right) &
% \text{if \f$x \le -\epsilon\f$}\\
% \frac{1}{2\epsilon}x^2 & \text{if \f$x > -\epsilon\f$}.
% \end{array}\right.
\f]
for \f$\epsilon > 0\f$. The corresponding scalar regret function is
\f$v_\epsilon(x) = e_\epsilon(x) + x\f$. \f$\mathcal{R}\f$ is then
implemented as
\f[
\mathcal{R}(X) = \inf_{t\in\mathbb{R}}\left\{
t + \mathbb{E}[v_\epsilon(X-t)] \right\}.
\f]
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 SmoothedWorstCaseQuadrangle : public ExpectationQuad<Real> {
private:
Real eps_;
void checkInputs(void) const {
Real zero(0);
TEUCHOS_TEST_FOR_EXCEPTION((eps_ <= zero), std::invalid_argument,
">>> ERROR (ROL::SmoothedWorstCaseQuadrangle): Smoothing parameter must be positive!");
}
public:
/** \brief Constructor.
@param[in] eps is the regularization parameter
*/
SmoothedWorstCaseQuadrangle(const Real eps)
: ExpectationQuad<Real>(), eps_(eps) {
checkInputs();
}
/** \brief Constructor.
@param[in] parlist is a parameter list specifying inputs
parlist should contain sublists "SOL"->"Risk Measure"->"Smoothed Worst-Case Quadrangle" and
within the "Smoothed Worst-Case Quadrangle" sublist should have the following parameters
\li "Smoothing Parameter" (must be positive).
*/
SmoothedWorstCaseQuadrangle(Teuchos::ParameterList &parlist) : ExpectationQuad<Real>() {
Teuchos::ParameterList& list
= parlist.sublist("SOL").sublist("Risk Measure").sublist("Smoothed Worst-Case Quadrangle");
eps_ = list.get<Real>("Smoothing Parameter");
checkInputs();
}
Real error(Real x, int deriv = 0) {
Real err(0), zero(0), half(0.5), one(1);
if (deriv == 0) {
err = (x <= -eps_) ? -(x+half*eps_) : half*x*x/eps_;
}
else if (deriv == 1) {
err = (x <= -eps_) ? -one : x/eps_;
}
else {
err = (x <= -eps_) ? zero : one/eps_;
}
return err;
}
Real regret(Real x, int deriv = 0) {
Real zero(0), one(1);
Real X = ((deriv==0) ? x : ((deriv==1) ? one : zero));
Real reg = error(x,deriv) + X;
return reg;
}
void checkRegret(void) {
ExpectationQuad<Real>::checkRegret();
// Check v'(-eps)
Real x = -eps_, zero(0), one(1), two(2), p1(0.1);
Real vx = zero, vy = zero;
Real dv = regret(x,1);
Real t = one;
Real diff = zero;
Real err = zero;
std::cout << std::right << std::setw(20) << "CHECK REGRET: v'(-eps) 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))/2t"
<< std::setw(20) << "Error"
<< "\n";
for (int i = 0; i < 13; i++) {
vy = regret(x+t,0);
vx = regret(x-t,0);
diff = (vy-vx)/(two*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''(-eps)
vx = zero;
vy = zero;
dv = regret(x,2);
t = one;
diff = zero;
err = zero;
std::cout << std::right << std::setw(20) << "CHECK REGRET: v''(-eps) 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))/2t"
<< std::setw(20) << "Error"
<< "\n";
for (int i = 0; i < 13; i++) {
vy = regret(x+t,1);
vx = regret(x-t,1);
diff = (vy-vx)/(two*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'(0)
x = zero;
vx = zero;
vy = zero;
dv = regret(x,1);
t = one;
diff = zero;
err = zero;
std::cout << std::right << std::setw(20) << "CHECK REGRET: v'(0) 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))/2t"
<< std::setw(20) << "Error"
<< "\n";
for (int i = 0; i < 13; i++) {
vy = regret(x+t,0);
vx = regret(x-t,0);
diff = (vy-vx)/(two*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''(0)
vx = zero;
vy = zero;
dv = regret(x,2);
t = one;
diff = zero;
err = zero;
std::cout << std::right << std::setw(20) << "CHECK REGRET: v''(0) 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))/2t"
<< std::setw(20) << "Error"
<< "\n";
for (int i = 0; i < 13; i++) {
vy = regret(x+t,1);
vx = regret(x-t,1);
diff = (vy-vx)/(two*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'(-1-eps)
x = -eps_-one;
vx = zero;
vy = zero;
dv = regret(x,1);
t = one;
diff = zero;
err = zero;
std::cout << std::right << std::setw(20) << "CHECK REGRET: v'(-1-eps) 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))/2t"
<< std::setw(20) << "Error"
<< "\n";
for (int i = 0; i < 13; i++) {
vy = regret(x+t,0);
vx = regret(x-t,0);
diff = (vy-vx)/(two*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''(-1-eps)
vx = zero;
vy = zero;
dv = regret(x,2);
t = one;
diff = zero;
err = zero;
std::cout << std::right << std::setw(20) << "CHECK REGRET: v''(-1-eps) 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))/2t"
<< std::setw(20) << "Error"
<< "\n";
for (int i = 0; i < 13; i++) {
vy = regret(x+t,1);
vx = regret(x-t,1);
diff = (vy-vx)/(two*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";
}
};
}
#endif
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