// Copyright (C) 2010 Davis E. King (davis@dlib.net)
// License: Boost Software License See LICENSE.txt for the full license.
#ifndef DLIB_OPTIMIZATIoN_OCA_Hh_
#define DLIB_OPTIMIZATIoN_OCA_Hh_
#include "optimization_oca_abstract.h"
#include "../matrix.h"
#include "optimization_solve_qp_using_smo.h"
#include <vector>
#include "../sequence.h"
// ----------------------------------------------------------------------------------------
namespace dlib
{
template <typename matrix_type>
class oca_problem
{
public:
typedef typename matrix_type::type scalar_type;
virtual ~oca_problem() {}
virtual bool risk_has_lower_bound (
scalar_type&
) const { return false; }
virtual bool optimization_status (
scalar_type ,
scalar_type ,
scalar_type ,
scalar_type ,
unsigned long,
unsigned long
) const = 0;
virtual scalar_type get_c (
) const = 0;
virtual long get_num_dimensions (
) const = 0;
virtual void get_risk (
matrix_type& current_solution,
scalar_type& risk_value,
matrix_type& risk_subgradient
) const = 0;
};
// ----------------------------------------------------------------------------------------
class oca
{
public:
oca ()
{
sub_eps = 1e-2;
sub_max_iter = 50000;
inactive_thresh = 20;
}
void set_subproblem_epsilon (
double eps_
) { sub_eps = eps_; }
double get_subproblem_epsilon (
) const { return sub_eps; }
void set_subproblem_max_iterations (
unsigned long sub_max_iter_
)
{
// make sure requires clause is not broken
DLIB_ASSERT(sub_max_iter_ > 0,
"\t void oca::set_subproblem_max_iterations"
<< "\n\t max iterations must be greater than 0"
<< "\n\t sub_max_iter_: " << sub_max_iter_
<< "\n\t this: " << this
);
sub_max_iter = sub_max_iter_;
}
unsigned long get_subproblem_max_iterations (
) const { return sub_max_iter; }
void set_inactive_plane_threshold (
unsigned long inactive_thresh_
)
{
// make sure requires clause is not broken
DLIB_ASSERT(inactive_thresh_ > 0,
"\t void oca::set_inactive_plane_threshold"
<< "\n\t inactive threshold must be greater than 0"
<< "\n\t inactive_thresh_: " << inactive_thresh_
<< "\n\t this: " << this
);
inactive_thresh = inactive_thresh_;
}
unsigned long get_inactive_plane_threshold (
) const { return inactive_thresh; }
template <
typename matrix_type
>
typename matrix_type::type operator() (
const oca_problem<matrix_type>& problem,
matrix_type& w,
unsigned long num_nonnegative = 0,
unsigned long force_weight_to_1 = std::numeric_limits<unsigned long>::max()
) const
{
matrix_type empty_prior;
return oca_impl(problem, w, empty_prior, false, num_nonnegative, force_weight_to_1, 0);
}
template <
typename matrix_type
>
typename matrix_type::type solve_with_elastic_net (
const oca_problem<matrix_type>& problem,
matrix_type& w,
double lasso_lambda,
unsigned long force_weight_to_1 = std::numeric_limits<unsigned long>::max()
) const
{
matrix_type empty_prior;
return oca_impl(problem, w, empty_prior, false, 0, force_weight_to_1, lasso_lambda);
}
template <
typename matrix_type
>
typename matrix_type::type operator() (
const oca_problem<matrix_type>& problem,
matrix_type& w,
const matrix_type& prior
) const
{
// make sure requires clause is not broken
DLIB_ASSERT(is_col_vector(prior) && prior.size() == problem.get_num_dimensions(),
"\t scalar_type oca::operator()"
<< "\n\t The prior vector does not have the correct dimensions."
<< "\n\t is_col_vector(prior): " << is_col_vector(prior)
<< "\n\t prior.size(): " << prior.size()
<< "\n\t problem.get_num_dimensions(): " << problem.get_num_dimensions()
<< "\n\t this: " << this
);
// disable the force weight to 1 option for this mode. We also disable the
// non-negative constraints.
unsigned long force_weight_to_1 = std::numeric_limits<unsigned long>::max();
return oca_impl(problem, w, prior, true, 0, force_weight_to_1, 0);
}
private:
template <
typename matrix_type
>
typename matrix_type::type oca_impl (
const oca_problem<matrix_type>& problem,
matrix_type& w,
const matrix_type& prior,
bool have_prior,
unsigned long num_nonnegative,
unsigned long force_weight_to_1,
const double lasso_lambda
) const
{
const unsigned long num_dims = problem.get_num_dimensions();
// make sure requires clause is not broken
DLIB_ASSERT(problem.get_c() > 0 &&
problem.get_num_dimensions() > 0 &&
0 <= lasso_lambda && lasso_lambda < 1,
"\t scalar_type oca::operator()"
<< "\n\t The oca_problem is invalid"
<< "\n\t problem.get_c(): " << problem.get_c()
<< "\n\t problem.get_num_dimensions(): " << num_dims
<< "\n\t lasso_lambda: " << lasso_lambda
<< "\n\t this: " << this
);
if (have_prior)
{
DLIB_ASSERT(lasso_lambda == 0, "Solver doesn't support using a prior with lasso.");
DLIB_ASSERT(num_nonnegative == 0, "Solver doesn't support using a prior with non-negative constraints.");
}
else if (lasso_lambda != 0)
{
DLIB_ASSERT(num_nonnegative == 0, "Solver doesn't support using lasso with non-negative constraints.");
}
const double ridge_lambda = 1-lasso_lambda;
if (num_nonnegative > num_dims)
num_nonnegative = num_dims;
typedef typename matrix_type::type scalar_type;
typedef typename matrix_type::layout_type layout_type;
typedef typename matrix_type::mem_manager_type mem_manager_type;
typedef matrix_type vect_type;
const scalar_type C = problem.get_c();
typename sequence<vect_type>::kernel_2a planes;
std::vector<scalar_type> bs, miss_count;
vect_type new_plane, alpha, btemp;
w.set_size(num_dims, 1);
w = 0;
// The current objective value. Note also that w always contains
// the current solution.
scalar_type cur_obj = std::numeric_limits<scalar_type>::max();
// This will hold the cutting plane objective value. This value is
// a lower bound on the true optimal objective value.
scalar_type cp_obj = 0;
matrix<scalar_type,0,0,mem_manager_type, layout_type> K, Ktmp;
matrix<scalar_type,0,1,mem_manager_type, layout_type> lambda, d;
if (lasso_lambda != 0)
d.set_size(num_dims);
else
d.set_size(num_nonnegative);
d = lasso_lambda*ones_matrix(d);
scalar_type R_lower_bound;
if (problem.risk_has_lower_bound(R_lower_bound))
{
// The flat lower bounding plane is always good to have if we know
// what it is.
bs.push_back(R_lower_bound);
new_plane = zeros_matrix(w);
planes.add(0, new_plane);
alpha = uniform_matrix<scalar_type>(1,1, C);
miss_count.push_back(0);
K.set_size(1,1);
K(0,0) = 0;
}
const double prior_norm = have_prior ? 0.5*dot(prior,prior) : 0;
unsigned long counter = 0;
while (true)
{
// add the next cutting plane
scalar_type cur_risk;
if (force_weight_to_1 < (unsigned long)w.size())
w(force_weight_to_1) = 1;
problem.get_risk(w, cur_risk, new_plane);
if (force_weight_to_1 < (unsigned long)w.size())
{
// We basically arrange for the w(force_weight_to_1) element and all
// subsequent elements of w to not be involved in the optimization at
// all. An easy way to do this is to just make sure the elements of w
// corresponding elements in the subgradient are always set to zero
// while we run the cutting plane algorithm. The only time
// w(force_weight_to_1) is 1 is when we pass it to the oca_problem.
set_rowm(w, range(force_weight_to_1, w.size()-1)) = 0;
set_rowm(new_plane, range(force_weight_to_1, new_plane.size()-1)) = 0;
}
if (have_prior)
bs.push_back(cur_risk - dot(w,new_plane) + dot(prior,new_plane));
else
bs.push_back(cur_risk - dot(w,new_plane));
planes.add(planes.size(), new_plane);
miss_count.push_back(0);
// If alpha is empty then initialize it (we must always have sum(alpha) == C).
// But otherwise, just append a zero.
if (alpha.size() == 0)
alpha = uniform_matrix<scalar_type>(1,1, C);
else
alpha = join_cols(alpha,zeros_matrix<scalar_type>(1,1));
const scalar_type wnorm = 0.5*ridge_lambda*trans(w)*w + lasso_lambda*sum(abs(w));
const double prior_part = have_prior? dot(w,prior) : 0;
cur_obj = wnorm + C*cur_risk + prior_norm-prior_part;
// report current status
const scalar_type risk_gap = cur_risk - (cp_obj-wnorm+prior_part-prior_norm)/C;
if (counter > 0 && problem.optimization_status(cur_obj, cur_obj - cp_obj,
cur_risk, risk_gap, planes.size(), counter))
{
break;
}
// compute kernel matrix for all the planes
K.swap(Ktmp);
K.set_size(planes.size(), planes.size());
// copy over the old K matrix
set_subm(K, 0,0, Ktmp.nr(), Ktmp.nc()) = Ktmp;
// now add the new row and column to K
for (unsigned long c = 0; c < planes.size(); ++c)
{
K(c, Ktmp.nc()) = dot(planes[c], planes[planes.size()-1]);
K(Ktmp.nc(), c) = K(c,Ktmp.nc());
}
// solve the cutting plane subproblem for the next w. We solve it to an
// accuracy that is related to how big the error gap is. Also, we multiply
// by ridge_lambda because the objective function for the QP we solve was
// implicitly scaled by ridge_lambda. That is, we want to ask the QP
// solver to solve the problem until the duality gap is 0.1 times smaller
// than what it is now. So the factor of ridge_lambda is necessary to make
// this happen.
scalar_type eps = std::min<scalar_type>(sub_eps, 0.1*ridge_lambda*(cur_obj-cp_obj));
// just a sanity check
if (eps < 1e-16)
eps = 1e-16;
// Note that we warm start this optimization by using the alpha from the last
// iteration as the starting point.
if (lasso_lambda != 0)
{
// copy planes into a matrix so we can call solve_qp4_using_smo()
matrix<scalar_type,0,0,mem_manager_type, layout_type> planes_mat(num_dims,planes.size());
for (unsigned long i = 0; i < planes.size(); ++i)
set_colm(planes_mat,i) = planes[i];
btemp = ridge_lambda*mat(bs) - trans(planes_mat)*d;
solve_qp4_using_smo(planes_mat, K, btemp, d, alpha, lambda, eps, sub_max_iter, (scalar_type)(2*lasso_lambda));
}
else if (num_nonnegative != 0)
{
// copy planes into a matrix so we can call solve_qp4_using_smo()
matrix<scalar_type,0,0,mem_manager_type, layout_type> planes_mat(num_nonnegative,planes.size());
for (unsigned long i = 0; i < planes.size(); ++i)
set_colm(planes_mat,i) = colm(planes[i],0,num_nonnegative);
solve_qp4_using_smo(planes_mat, K, mat(bs), d, alpha, lambda, eps, sub_max_iter);
}
else
{
solve_qp_using_smo(K, mat(bs), alpha, eps, sub_max_iter);
}
// construct the w that minimized the subproblem.
w = -alpha(0)*planes[0];
for (unsigned long i = 1; i < planes.size(); ++i)
w -= alpha(i)*planes[i];
if (lasso_lambda != 0)
w = (lambda-d+w)/ridge_lambda;
else if (num_nonnegative != 0) // threshold the first num_nonnegative w elements if necessary.
set_rowm(w,range(0,num_nonnegative-1)) = lowerbound(rowm(w,range(0,num_nonnegative-1)),0);
for (long i = 0; i < alpha.size(); ++i)
{
if (alpha(i) != 0)
miss_count[i] = 0;
else
miss_count[i] += 1;
}
// Compute the lower bound on the true objective given to us by the cutting
// plane subproblem.
cp_obj = -0.5*ridge_lambda*trans(w)*w + trans(alpha)*mat(bs);
if (have_prior)
w += prior;
// If it has been a while since a cutting plane was an active constraint then
// we should throw it away.
while (max(mat(miss_count)) >= inactive_thresh)
{
const long idx = index_of_max(mat(miss_count));
bs.erase(bs.begin()+idx);
miss_count.erase(miss_count.begin()+idx);
K = removerc(K, idx, idx);
alpha = remove_row(alpha,idx);
planes.remove(idx, new_plane);
}
++counter;
}
if (force_weight_to_1 < (unsigned long)w.size())
w(force_weight_to_1) = 1;
return cur_obj;
}
double sub_eps;
unsigned long sub_max_iter;
unsigned long inactive_thresh;
};
}
// ----------------------------------------------------------------------------------------
#endif // DLIB_OPTIMIZATIoN_OCA_Hh_