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_