Added find_optimal_parameters()

dlib/optimization/find_optimal_parameters.h

+// Copyright (C) 2016  Davis E. King (davis@dlib.net)
+// License: Boost Software License   See LICENSE.txt for the full license.
+#ifndef DLIB_fIND_OPTIMAL_PARAMETERS_Hh_
+#define DLIB_fIND_OPTIMAL_PARAMETERS_Hh_
+
+#include "../matrix.h"
+#include "find_optimal_parameters_abstract.h"
+#include "optimization_bobyqa.h"
+#include "optimization_line_search.h"
+
+namespace dlib
+{
+
+// ----------------------------------------------------------------------------------------
+
+    template <
+        typename funct
+        >
+    double find_optimal_parameters (
+        double initial_search_radius,
+        double eps,
+        const unsigned int max_f_evals,
+        matrix<double,0,1>& x,
+        const matrix<double,0,1>& x_lower,
+        const matrix<double,0,1>& x_upper,
+        const funct& f
+    ) 
+    /*!
+        requires
+            - f(x) must be a valid expression that evaluates to a double
+            - x.size() == x_lower.size() == x_upper.size()
+            - x.size() > 0
+            - 0 < eps < initial_search_radius 
+            - max_f_evals > 1
+            - min(x_upper - x_lower) > 0 
+            - min(x - x_lower) >= 0 && min(x_upper - x) >= 0
+              (i.e. the given x should be within the bounds defined by x_lower and x_upper)
+        ensures
+            - Performs a constrained minimization of the function f() starting from 
+              the initial point x.  
+            - This function does not require derivatives of f().  Instead, it uses
+              derivative free methods to find the best setting of x.  In particular, it
+              will begin by searching within a sphere of radius initial_search_radius
+              around x and will continue searching until either f() has been called
+              max_f_evals times or the search area has been shrunk to less than eps radius.
+            - #x == the value of x (within the bounds defined by x_lower and x_upper) that 
+              was found to minimize f().  More precisely, it will always be true that:
+                - min(#x - x_lower) >= 0 && min(x_upper - #x) >= 0
+            - returns f(#x). 
+        throws
+            - No exception is thrown for executing max_f_evals iterations.  This function
+              will simply output the best x it has seen if it runs out of iterations.
+    !*/
+    {
+        DLIB_CASSERT(x.size() == x_lower.size() && x_lower.size() == x_upper.size() && x.size() > 0,
+            "\t double find_optimal_parameters()"
+            << "\n\t x.size():       " << x.size()
+            << "\n\t x_lower.size(): " << x_lower.size()
+            << "\n\t x_upper.size(): " << x_upper.size()
+            );
+
+        // check the requirements.  Also split the assert up so that the error message isn't huge.
+        DLIB_CASSERT(max_f_evals > 1 && eps > 0 && initial_search_radius > eps,
+            "\t double find_optimal_parameters()"
+            << "\n\t Invalid arguments have been given to this function"
+            << "\n\t initial_search_radius: " << initial_search_radius
+            << "\n\t eps:                   " << eps
+            << "\n\t max_f_evals:           " << max_f_evals
+        );
+
+        DLIB_CASSERT( min(x_upper - x_lower) > 0 &&
+                     min(x - x_lower) >= 0 && min(x_upper - x) >= 0,
+            "\t double find_optimal_parameters()"
+            << "\n\t The bounds constraints have to make sense and also contain the starting point."
+            << "\n\t min(x_upper - x_lower):                         " << min(x_upper - x_lower) 
+            << "\n\t min(x - x_lower) >= 0 && min(x_upper - x) >= 0: " << (min(x - x_lower) >= 0 && min(x_upper - x) >= 0)
+        );
+
+        // if the search radius is too big then shrink it so it fits inside the bounds.
+        if (initial_search_radius*2 >= min(x_upper-x_lower))
+            initial_search_radius = 0.5*min(x_upper-x_lower)*0.99;
+
+
+        double objective_val = std::numeric_limits<double>::infinity();
+        size_t num_iter_used = 0;
+        if (x.size() == 1)
+        {
+            // BOBYQA requires x to have at least 2 variables in it.  So we can't call it in
+            // this case.  Instead we call find_min_single_variable().
+            matrix<double,0,1> temp(1);
+            auto ff = [&](const double& xx)
+            {
+                temp = xx;
+                double obj = f(temp);  
+                ++num_iter_used;
+                // keep track of the best x.
+                if (obj < objective_val)
+                {
+                    objective_val = obj;
+                    x = temp;
+                }
+                return obj;
+            };
+            try
+            {
+                double dx = x(0);
+                find_min_single_variable(ff, dx, x_lower(0), x_upper(0), eps, max_f_evals, initial_search_radius);
+            } catch (optimize_single_variable_failure& )
+            {
+            }
+        }
+        else
+        {
+            auto ff = [&](const matrix<double,0,1>& xx)
+            {
+                double obj = f(xx); 
+                ++num_iter_used;
+                // keep track of the best x.
+                if (obj < objective_val)
+                {
+                    objective_val = obj;
+                    x = xx;
+                }
+                return obj;
+            };
+            try
+            {
+                matrix<double,0,1> start_x = x;
+                find_min_bobyqa(ff, start_x, 2*x.size()+1, x_lower, x_upper, initial_search_radius, eps, max_f_evals);
+            } catch (bobyqa_failure& )
+            {
+            }
+        }
+
+        return objective_val;
+    }
+
+// ----------------------------------------------------------------------------------------
+
+}
+
+#endif // DLIB_fIND_OPTIMAL_PARAMETERS_Hh_
+

dlib/optimization/find_optimal_parameters_abstract.h

+// Copyright (C) 2016  Davis E. King (davis@dlib.net)
+// License: Boost Software License   See LICENSE.txt for the full license.
+#undef DLIB_fIND_OPTIMAL_PARAMETERS_ABSTRACT_Hh_
+#ifdef DLIB_fIND_OPTIMAL_PARAMETERS_ABSTRACT_Hh_
+
+#include "../matrix.h"
+
+namespace dlib
+{
+
+// ----------------------------------------------------------------------------------------
+
+    template <
+        typename funct
+        >
+    double find_optimal_parameters (
+        double initial_search_radius,
+        double eps,
+        const unsigned int max_f_evals,
+        matrix<double,0,1>& x,
+        const matrix<double,0,1>& x_lower,
+        const matrix<double,0,1>& x_upper,
+        const funct& f
+    );
+    /*!
+        requires
+            - f(x) must be a valid expression that evaluates to a double
+            - x.size() == x_lower.size() == x_upper.size()
+            - x.size() > 0
+            - 0 < eps < initial_search_radius 
+            - max_f_evals > 1
+            - min(x_upper - x_lower) > 0 
+            - min(x - x_lower) >= 0 && min(x_upper - x) >= 0
+              (i.e. the given x should be within the bounds defined by x_lower and x_upper)
+        ensures
+            - Performs a constrained minimization of the function f() starting from 
+              the initial point x.  
+            - This function does not require derivatives of f().  Instead, it uses
+              derivative free methods to find the best setting of x.  In particular, it
+              will begin by searching within a sphere of radius initial_search_radius
+              around x and will continue searching until either f() has been called
+              max_f_evals times or the search area has been shrunk to less than eps radius.
+            - #x == the value of x (within the bounds defined by x_lower and x_upper) that 
+              was found to minimize f().  More precisely, it will always be true that:
+                - min(#x - x_lower) >= 0 && min(x_upper - #x) >= 0
+            - returns f(#x). 
+        throws
+            - No exception is thrown for executing max_f_evals iterations.  This function
+              will simply output the best x it has seen if it runs out of iterations.
+    !*/
+
+// ----------------------------------------------------------------------------------------
+
+}
+
+#endif // DLIB_fIND_OPTIMAL_PARAMETERS_ABSTRACT_Hh_
+
+

dlib/test/CMakeLists.txt

@@ -155,6 +155,7 @@ if (COMPILER_CAN_DO_CPP_11)
    set(tests ${tests}
       dnn.cpp
       cublas.cpp
+      find_optimal_parameters.cpp
       )
 endif()
 

dlib/test/find_optimal_parameters.cpp

+// Copyright (C) 2008  Davis E. King (davis@dlib.net)
+// License: Boost Software License   See LICENSE.txt for the full license.
+
+
+#include <dlib/optimization/find_optimal_parameters.h>
+#include "tester.h"
+
+
+namespace  
+{
+
+    using namespace test;
+    using namespace dlib;
+    using namespace std;
+
+    logger dlog("test.find_optimal_parameters");
+
+// ----------------------------------------------------------------------------------------
+
+
+    class find_optimal_parameters : public tester
+    {
+    public:
+        find_optimal_parameters (
+        ) :
+            tester ("test_find_optimal_parameters",
+                    "Runs tests on find_optimal_parameters().")
+        {}
+
+        void perform_test (
+        )
+        {
+            print_spinner();
+            matrix<double,0,1> params = {0.5, 0.5};
+            dlib::find_optimal_parameters(4, 0.001, 100, params, {-0.1, -0.01}, {5, 5}, [](const matrix<double,0,1>& params) {
+                cout << ".";
+                return sum(squared(params));
+            });
+
+            matrix<double,0,1> true_params = {0,0};
+
+            DLIB_TEST(max(abs(true_params - params)) < 1e-10);
+
+            params = {0.1};
+            dlib::find_optimal_parameters(4, 0.001, 100, params, {-0.01}, {5}, [](const matrix<double,0,1>& params) {
+                cout << ".";
+                return sum(squared(params));
+            });
+
+            true_params = {0};
+            DLIB_TEST(max(abs(true_params - params)) < 1e-10);
+        }
+    } a;
+
+}
+
+
+