// Copyright (C) 2010 Davis E. King (davis@dlib.net) // License: Boost Software License See LICENSE.txt for the full license. #undef DLIB_OPTIMIZATION_OCA_ABsTRACT_Hh_ #ifdef DLIB_OPTIMIZATION_OCA_ABsTRACT_Hh_ // ---------------------------------------------------------------------------------------- namespace dlib{template <typename matrix_type> classoca_problem{/*! REQUIREMENTS ON matrix_type - matrix_type == a dlib::matrix capable of storing column vectors WHAT THIS OBJECT REPRESENTS This object is the interface used to define the optimization problems solved by the oca optimizer defined later in this file. OCA solves optimization problems with the following form: Minimize: f(w) == 0.5*length_squared(w) + C*R(w) Where R(w) is a user-supplied convex function and C > 0. Optionally, there can also be non-negativity constraints on some or all of the elements of w. Or it can alternatively solve: Minimize: f(w) == 0.5*length_squared(w-prior) + C*R(w) Where prior is a user supplied vector and R(w) has the same interpretation as above. Or it can use the elastic net regularizer: Minimize: f(w) == 0.5*(1-lasso_lambda)*length_squared(w) + lasso_lambda*sum(abs(w)) + C*R(w) Where lasso_lambda is a number in the range [0, 1) and controls trade-off between doing L1 and L2 regularization. R(w) has the same interpretation as above. Note that the stopping condition must be provided by the user in the form of the optimization_status() function. !*/ public: typedef typename matrix_type::type scalar_type; virtual ~oca_problem(){}virtualboolrisk_has_lower_bound( scalar_type& lower_bound ) const{return false;}/*! ensures - if (R(w) >= a constant for all values of w) then - returns true - #lower_bound == the constant that lower bounds R(w) - else - returns false !*/ virtualbooloptimization_status( scalar_type current_objective_value, scalar_type current_error_gap, scalar_type current_risk_value, scalar_type current_risk_gap,unsignedlongnum_cutting_planes,unsignedlongnum_iterations ) const = 0; /*! requires - This function is called by the OCA optimizer each iteration. - current_objective_value == the current value of the objective function f(w) - current_error_gap == The bound on how much lower the objective function can drop before we reach the optimal point. At the optimal solution the error gap is equal to 0. - current_risk_value == the current value of the R(w) term of the objective function. - current_risk_gap == the bound on how much lower the risk term can go. At the optimal solution the risk gap is zero. - num_cutting_planes == the number of cutting planes the algorithm is currently using. - num_iterations == A count of the total number of iterations that have executed since we started running the optimization. ensures - If it is appropriate to terminate the optimization then this function returns true and false otherwise. !*/ virtual scalar_typeget_c( ) const = 0; /*! ensures - returns the C parameter !*/ virtuallongget_num_dimensions( ) const = 0; /*! ensures - returns the number of free variables in this optimization problem !*/ virtualvoidget_risk( matrix_type& current_solution, scalar_type& risk_value, matrix_type& risk_subgradient ) const = 0; /*! requires - is_col_vector(current_solution) == true - current_solution.size() == get_num_dimensions() ensures - #current_solution will be set to one of the following: - current_solution (i.e. it won't be modified at all) - The result of a line search passing through current_solution. - #risk_value == R(#current_solution) - #risk_subgradient == an element of the subgradient of R() at the point #current_solution - Note that #risk_value and #risk_subgradient are NOT multiplied by get_c() !*/}; // ---------------------------------------------------------------------------------------- classoca{/*! INITIAL VALUE - get_subproblem_epsilon() == 1e-2 - get_subproblem_max_iterations() == 50000 - get_inactive_plane_threshold() == 20 WHAT THIS OBJECT REPRESENTS This object is a tool for solving the optimization problem defined above by the oca_problem abstract class. For reference, OCA solves optimization problems with the following form: Minimize: f(w) == 0.5*length_squared(w) + C*R(w) Where R(w) is a user-supplied convex function and C > 0. Optionally, this object can also add non-negativity constraints to some or all of the elements of w. Or it can alternatively solve: Minimize: f(w) == 0.5*length_squared(w-prior) + C*R(w) Where prior is a user supplied vector and R(w) has the same interpretation as above. Or it can use the elastic net regularizer: Minimize: f(w) == 0.5*(1-lasso_lambda)*length_squared(w) + lasso_lambda*sum(abs(w)) + C*R(w) Where lasso_lambda is a number in the range [0, 1) and controls trade-off between doing L1 and L2 regularization. R(w) has the same interpretation as above. For a detailed discussion you should consult the following papers from the Journal of Machine Learning Research: Optimized Cutting Plane Algorithm for Large-Scale Risk Minimization Vojtech Franc, Soren Sonnenburg; 10(Oct):2157--2192, 2009. Bundle Methods for Regularized Risk Minimization Choon Hui Teo, S.V.N. Vishwanthan, Alex J. Smola, Quoc V. Le; 11(Jan):311-365, 2010. !*/ public:oca( ); /*! ensures - this object is properly initialized !*/ template < typename matrix_type > typename matrix_type::typeoperator() ( const oca_problem<matrix_type>& problem, matrix_type& w,unsignedlongnum_nonnegative = 0,unsignedlongforce_weight_to_1 = std::numeric_limits<unsignedlong>::max() ) const; /*! requires - problem.get_c() > 0 - problem.get_num_dimensions() > 0 ensures - solves the given oca problem and stores the solution in #w. In particular, this function solves: Minimize: f(w) == 0.5*length_squared(w) + C*R(w) - The optimization algorithm runs until problem.optimization_status() indicates it is time to stop. - returns the objective value at the solution #w - if (num_nonnegative != 0) then - Adds the constraint that #w(i) >= 0 for all i < num_nonnegative. That is, the first num_nonnegative elements of #w will always be non-negative. This includes the copies of w passed to get_risk() in the form of the current_solution vector as well as the final output of this function. - if (force_weight_to_1 < problem.get_num_dimensions()) then - The optimizer enforces the following constraints: - #w(force_weight_to_1) == 1 - for all i > force_weight_to_1: - #w(i) == 0 - That is, the element in the weight vector at the index indicated by force_weight_to_1 will have a value of 1 upon completion of this function, while all subsequent elements of w will have values of 0. !*/ template < typename matrix_type > typename matrix_type::typeoperator() ( const oca_problem<matrix_type>& problem, matrix_type& w, const matrix_type& prior ) const; /*! requires - problem.get_c() > 0 - problem.get_num_dimensions() > 0 - is_col_vector(prior) == true - prior.size() == problem.get_num_dimensions() ensures - solves the given oca problem and stores the solution in #w. - In this mode, we solve a version of the problem with a different regularizer. In particular, this function solves: Minimize: f(w) == 0.5*length_squared(w-prior) + C*R(w) - The optimization algorithm runs until problem.optimization_status() indicates it is time to stop. - returns the objective value at the solution #w !*/ template < typename matrix_type > typename matrix_type::typesolve_with_elastic_net( const oca_problem<matrix_type>& problem, matrix_type& w, scalar_type lasso_lambda,unsignedlongforce_weight_to_1 = std::numeric_limits<unsignedlong>::max() ) const; /*! requires - problem.get_c() > 0 - problem.get_num_dimensions() > 0 - 0 <= lasso_lambda < 1 ensures - Solves the given oca problem and stores the solution in #w, but uses an elastic net regularizer instead of the normal L2 regularizer. In particular, this function solves: Minimize: f(w) == 0.5*(1-lasso_lambda)*length_squared(w) + lasso_lambda*sum(abs(w)) + C*R(w) - The optimization algorithm runs until problem.optimization_status() indicates it is time to stop. - returns the objective value at the solution #w - if (force_weight_to_1 < problem.get_num_dimensions()) then - The optimizer enforces the following constraints: - #w(force_weight_to_1) == 1 - for all i > force_weight_to_1: - #w(i) == 0 - That is, the element in the weight vector at the index indicated by force_weight_to_1 will have a value of 1 upon completion of this function, while all subsequent elements of w will have values of 0. !*/voidset_subproblem_epsilon(doubleeps ); /*! requires - eps > 0 ensures - #get_subproblem_epsilon() == eps !*/doubleget_subproblem_epsilon( ) const; /*! ensures - returns the accuracy used in solving the quadratic programming subproblem that is part of the overall OCA algorithm. !*/voidset_subproblem_max_iterations(unsignedlongsub_max_iter ); /*! requires - sub_max_iter > 0 ensures - #get_subproblem_max_iterations() == sub_max_iter !*/unsignedlongget_subproblem_max_iterations( ) const; /*! ensures - returns the maximum number of iterations this object will perform while attempting to solve each quadratic programming subproblem. !*/voidset_inactive_plane_threshold(unsignedlonginactive_thresh ); /*! requires - inactive_thresh > 0 ensures - #get_inactive_plane_threshold() == inactive_thresh !*/unsignedlongget_inactive_plane_threshold( ) const; /*! ensures - As OCA runs it builds up a set of cutting planes. Typically cutting planes become inactive after a certain point and can then be removed. This function returns the number of iterations of inactivity required before a cutting plane is removed. !*/};}// ---------------------------------------------------------------------------------------- #endif // DLIB_OPTIMIZATION_OCA_ABsTRACT_Hh_