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math/test/test_gradient_descent_optimizer.cpp
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#include "test_autodiff_reverse.hpp" // reuse for some basic options
#include "test_functions_for_optimization.hpp"
#include <boost/math/differentiation/autodiff_reverse.hpp>
#include <boost/math/optimization/gradient_descent.hpp>
#include <boost/math/optimization/minimizer.hpp>
namespace rdiff = boost::math::differentiation::reverse_mode;
namespace bopt = boost::math::optimization;
BOOST_AUTO_TEST_SUITE(basic_gradient_descent)
BOOST_AUTO_TEST_CASE_TEMPLATE(default_gd_test, T, all_float_types)
{
size_t NITER = 2000;
size_t N = 15;
T lr = T{1e-2};
RandomSample<T> rng{T(-100), (100)};
std::vector<rdiff::rvar<T, 1>> x_ad;
T eps = T{1e-3};
for (size_t i = 0; i < N; ++i) {
x_ad.push_back(rng.next());
}
auto gdopt = bopt::make_gradient_descent(&quadratic<rdiff::rvar<T, 1>>, x_ad, lr);
for (size_t i = 0; i < NITER; ++i) {
gdopt.step();
}
for (auto& x : x_ad) {
BOOST_REQUIRE_SMALL(x.item(), eps);
}
}
BOOST_AUTO_TEST_CASE_TEMPLATE(test_minimize, T, all_float_types)
{
size_t NITER = 2000;
size_t N = 15;
T lr = T{1e-2};
RandomSample<T> rng{T(-100), (100)};
std::vector<rdiff::rvar<T, 1>> x_ad;
T eps = T{1e-3};
for (size_t i = 0; i < N; ++i) {
x_ad.push_back(rng.next());
}
auto gdopt = bopt::make_gradient_descent(&quadratic<rdiff::rvar<T, 1>>, x_ad, lr);
auto z = minimize(gdopt);
for (auto& x : x_ad) {
BOOST_REQUIRE_SMALL(x.item(), eps);
}
}
BOOST_AUTO_TEST_CASE_TEMPLATE(random_initializer_test, T, all_float_types)
{
size_t N = 10;
T lr = T{1e-2};
std::vector<rdiff::rvar<T, 1>> x(N);
auto gdopt = bopt::make_gradient_descent(
&quadratic<rdiff::rvar<T, 1>>,
x,
lr,
bopt::random_uniform_initializer_rvar<T>(-2.0, 2.0, 1234)); // all initialized to 5
for (auto& xi : x) {
T v = xi.item();
BOOST_TEST(v >= -2);
BOOST_TEST(v <= 2);
}
gdopt.step();
}
BOOST_AUTO_TEST_CASE_TEMPLATE(const_initializer_test, T, all_float_types)
{
size_t N = 10;
T lr = T{1e-2};
std::vector<rdiff::rvar<T, 1>> x(N);
auto gdopt = bopt::make_gradient_descent(&quadratic<rdiff::rvar<T, 1>>,
x,
lr,
bopt::costant_initializer_rvar<T>(
T{5.0})); // all initialized to 5
for (auto& xi : x) {
T v = xi.item();
BOOST_REQUIRE_CLOSE(v, T{5.0}, T{1e-3});
}
gdopt.step();
}
BOOST_AUTO_TEST_CASE_TEMPLATE(box_constraint_test, T, all_float_types)
{
size_t N = 5;
T lr = T{1e-2};
std::vector<rdiff::rvar<T, 1>> x(N, T{10});
auto gdopt = bopt::make_gradient_descent(&quadratic<rdiff::rvar<T, 1>>, x, lr);
auto res = bopt::minimize(gdopt,
bopt::box_constraints<std::vector<rdiff::rvar<T, 1>>, T>(-1.0, 1.0));
for (auto& xi : x) {
BOOST_TEST(xi.item() >= -1.0);
BOOST_TEST(xi.item() <= 1.0);
}
}
BOOST_AUTO_TEST_CASE_TEMPLATE(max_iter_test, T, all_float_types)
{
size_t N = 2;
T lr = T{1e-6}; // very slow learning
std::vector<rdiff::rvar<T, 1>> x = {T{5}, T{5}};
auto gdopt = bopt::make_gradient_descent(&quadratic<rdiff::rvar<T, 1>>, x, lr);
size_t max_iter = 50;
auto res = bopt::minimize(gdopt,
bopt::unconstrained_policy<std::vector<rdiff::rvar<T, 1>>>{},
bopt::gradient_norm_convergence_policy<T>(T{1e-20}),
bopt::max_iter_termination_policy(max_iter));
BOOST_TEST(!res.converged); // should not converge with tiny lr
BOOST_REQUIRE_EQUAL(res.num_iter, max_iter);
}
BOOST_AUTO_TEST_CASE_TEMPLATE(history_tracking_test, T, all_float_types)
{
size_t N = 3;
T lr = T{1e-2};
std::vector<rdiff::rvar<T, 1>> x = {T{3}, T{-4}, T{5}};
auto gdopt = bopt::make_gradient_descent(&quadratic<rdiff::rvar<T, 1>>, x, lr);
auto res = bopt::minimize(gdopt,
bopt::unconstrained_policy<std::vector<rdiff::rvar<T, 1>>>{},
bopt::gradient_norm_convergence_policy<T>(T{1e-6}),
bopt::max_iter_termination_policy(1000),
true); // enable history
BOOST_TEST(!res.objective_history.empty());
BOOST_TEST(res.objective_history.front() > res.objective_history.back());
}
BOOST_AUTO_TEST_CASE_TEMPLATE(rosenbrock_test, T, all_float_types)
{
std::array<rdiff::rvar<T, 1>, 2> x = {T{-1.2}, T{1.0}}; // bad start
T lr = T{1e-3};
auto gdopt = bopt::make_gradient_descent(&rosenbrock_saddle<rdiff::rvar<T, 1>>, x, lr);
auto res = bopt::minimize(gdopt,
bopt::unconstrained_policy<std::array<rdiff::rvar<T, 1>, 2>>{},
bopt::gradient_norm_convergence_policy<T>(T{1e-4}),
bopt::max_iter_termination_policy(50000));
BOOST_TEST(res.converged);
BOOST_REQUIRE_CLOSE(x[0].item(), T{1.0}, T{1e-1});
BOOST_REQUIRE_CLOSE(x[1].item(), T{1.0}, T{1e-1});
}
BOOST_AUTO_TEST_CASE(objective_tol_convergence_test)
{
using policy_t = bopt::objective_tol_convergence_policy<double>;
policy_t pol(1e-3);
std::vector<double> dummy_grad;
BOOST_TEST(!pol(dummy_grad, 100.0));
BOOST_TEST(!pol(dummy_grad, 99.0));
BOOST_TEST(pol(dummy_grad, 99.0005));
}
BOOST_AUTO_TEST_CASE(relative_objective_tol_test)
{
using policy_t = bopt::relative_objective_tol_policy<double>;
policy_t pol(1e-3);
std::vector<double> dummy_grad;
BOOST_TEST(!pol(dummy_grad, 1000.0));
BOOST_TEST(!pol(dummy_grad, 1010.0));
BOOST_TEST(pol(dummy_grad, 1010.5));
}
BOOST_AUTO_TEST_CASE(combined_policy_test)
{
using pol_abs = bopt::objective_tol_convergence_policy<double>;
using pol_rel = bopt::relative_objective_tol_policy<double>;
using pol_comb = bopt::combined_convergence_policy<pol_abs, pol_rel>;
pol_abs abs_pol(1e-6);
pol_rel rel_pol(1e-3);
pol_comb comb(abs_pol, rel_pol);
std::vector<double> dummy_grad;
BOOST_TEST(!comb(dummy_grad, 100.0));
BOOST_TEST(!comb(dummy_grad, 110.0));
BOOST_TEST(comb(dummy_grad, 110.1));
BOOST_TEST(comb(dummy_grad, 110.1000001));
}
BOOST_AUTO_TEST_CASE(nonnegativity_constraint_test)
{
std::vector<double> x = {1.0, -2.0, 3.0, -4.0};
bopt::nonnegativity_constraint<std::vector<double>, double> proj;
proj(x);
for (auto& xi : x)
BOOST_TEST(xi >= 0.0);
BOOST_TEST(x == std::vector<double>({1.0, 0.0, 3.0, 0.0}));
}
BOOST_AUTO_TEST_CASE(l2_ball_constraint_test)
{
std::vector<double> x = {3.0, 4.0}; // norm = 5
bopt::l2_ball_constraint<std::vector<double>, double> proj(1.0);
proj(x);
double norm = std::sqrt(x[0] * x[0] + x[1] * x[1]);
BOOST_TEST(std::abs(norm - 1.0) < 1e-12); // projected to unit circle
}
BOOST_AUTO_TEST_CASE(l1_ball_constraint_test)
{
std::vector<double> x = {3.0, 4.0}; // L1 norm = 7
bopt::l1_ball_constraint<std::vector<double>, double> proj(2.0);
proj(x);
double norm1 = std::abs(x[0]) + std::abs(x[1]);
BOOST_TEST(std::abs(norm1 - 2.0) < 1e-12);
}
BOOST_AUTO_TEST_CASE(simplex_constraint_test)
{
std::vector<double> x = {-1.0, 2.0, 3.0}; // has negative and sum != 1
bopt::simplex_constraint<std::vector<double>, double> proj;
proj(x);
double sum = 0.0;
for (auto& xi : x) {
BOOST_TEST(xi >= 0.0); // all nonnegative
sum += xi;
}
BOOST_TEST(std::abs(sum - 1.0) < 1e-12); // normalized to sum=1
}
BOOST_AUTO_TEST_CASE(unit_sphere_constraint_test)
{
std::vector<double> x = {0.3, 0.4}; // norm = 0.5
bopt::unit_sphere_constraint<std::vector<double>, double> proj;
proj(x);
double norm = std::sqrt(x[0] * x[0] + x[1] * x[1]);
BOOST_TEST(std::abs(norm - 1.0) < 1e-12); // always projected to sphere
}
BOOST_AUTO_TEST_CASE(function_constraint_test)
{
auto clip_to_half = [](std::vector<double>& v) {
for (auto& xi : v)
if (xi > 0.5)
xi = 0.5;
};
bopt::function_constraint<std::vector<double>> proj(clip_to_half);
std::vector<double> x = {0.2, 0.7, 1.5};
proj(x);
BOOST_TEST(x == std::vector<double>({0.2, 0.5, 0.5}));
}
template<typename RealType>
struct no_init_policy
{
void operator()(std::vector<RealType>& x) const noexcept {}
};
template<typename RealType>
struct analytic_objective_eval_pol
{
template<typename Objective, typename ArgumentContainer>
RealType operator()(Objective&& objective, ArgumentContainer& x)
{
return objective(x);
}
};
template<typename RealType>
struct analytic_gradient_eval_pol
{
std::vector<RealType> grad_container;
template<typename ArgumentContainer>
void bind(ArgumentContainer& x, std::vector<std::reference_wrapper<RealType>>& g)
{
grad_container.resize(x.size(), RealType{0.0});
g.clear();
g.reserve(x.size());
for (size_t i = 0; i < x.size(); ++i) {
g.push_back(std::ref(grad_container[i]));
}
}
template<class Objective, class ArgumentContainer, class FunctionEvaluationPolicy>
void operator()(Objective&& obj_f,
ArgumentContainer& x,
FunctionEvaluationPolicy&& f_eval_pol,
RealType& obj_v)
{
// compute objective via eval policy that takes care of tape
RealType v = f_eval_pol(obj_f, x);
obj_v = v;
for (size_t i = 0; i < x.size(); ++i) {
grad_container[i] = 2 * x[i];
}
}
};
BOOST_AUTO_TEST_CASE_TEMPLATE(analytic_derivative_policies, T, all_float_types)
{
std::vector<T> x;
size_t NITER = 2000;
size_t N = 15;
T lr = T{1e-2};
RandomSample<T> rng{T(-100), (100)};
T eps = T{1e-3};
for (size_t i = 0; i < N; ++i) {
x.push_back(rng.next());
}
auto gdopt = bopt::make_gradient_descent(&quadratic<T>,
x,
lr,
no_init_policy<T>{},
analytic_objective_eval_pol<T>{},
analytic_gradient_eval_pol<T>{});
for (size_t i = 0; i < NITER; ++i) {
gdopt.step();
}
for (auto& xi : x) {
BOOST_REQUIRE_SMALL(xi, eps);
}
}
BOOST_AUTO_TEST_SUITE_END()
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