dlib C++ Library - optimization_oca.h

// 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"
#include <chrono>
// ----------------------------------------------------------------------------------------
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;
 max_runtime = std::chrono::hours(24*356*290); // 290 years
 }
 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_max_runtime (
 const std::chrono::nanoseconds& max_runtime_
 ) 
 {
 max_runtime = max_runtime_;
 }
 std::chrono::nanoseconds get_max_runtime (
 ) const
 {
 return max_runtime;
 }
 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;
 const auto time_to_stop = std::chrono::steady_clock::now() + max_runtime;
 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;
 }
 if (std::chrono::steady_clock::now() >= time_to_stop)
 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;
 std::chrono::nanoseconds max_runtime;
 };
}
// ----------------------------------------------------------------------------------------
#endif // DLIB_OPTIMIZATIoN_OCA_Hh_