bfgs_optimizer.h

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/*
 * Copyright 2021 MusicScience37 (Kenta Kabashima)
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 *     http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */
#pragma once
 
#include <Eigen/Cholesky>
#include <Eigen/Core>
 
#include "num_collect/base/concepts/eigen_solver_of.h"
#include "num_collect/base/index_type.h"
#include "num_collect/logging/iterations/iteration_logger.h"
#include "num_collect/logging/log_tag_view.h"
#include "num_collect/opt/backtracking_line_searcher.h"
#include "num_collect/opt/concepts/line_searcher.h"
#include "num_collect/opt/concepts/multi_variate_differentiable_objective_function.h"
#include "num_collect/opt/descent_method_base.h"
 
namespace num_collect::opt {

constexpr auto bfgs_optimizer_tag =
    logging::log_tag_view("num_collect::opt::bfgs_optimizer");

template <
    concepts::multi_variate_differentiable_objective_function ObjectiveFunction,
    concepts::line_searcher LineSearcher =
        backtracking_line_searcher<ObjectiveFunction>,
    base::concepts::eigen_solver_of<
        Eigen::MatrixX<typename ObjectiveFunction::value_type>,
        typename ObjectiveFunction::variable_type>
        HessianSolver =
            Eigen::LLT<Eigen::MatrixX<typename ObjectiveFunction::value_type>>>
class bfgs_optimizer
    : public descent_method_base<
          bfgs_optimizer<ObjectiveFunction, LineSearcher, HessianSolver>,
          LineSearcher> {
public:
    using this_type =
        bfgs_optimizer<ObjectiveFunction, LineSearcher, HessianSolver>;

    using base_type = descent_method_base<this_type, LineSearcher>;
 
    using typename base_type::objective_function_type;
    using typename base_type::variable_type;

    using variable_scalar_type = typename variable_type::Scalar;

    using hessian_solver_type = HessianSolver;

    using hessian_type = typename hessian_solver_type::MatrixType;

    explicit bfgs_optimizer(
        const objective_function_type& obj_fun = objective_function_type())
        : base_type(bfgs_optimizer_tag, obj_fun) {}
 
    using base_type::evaluations;
    using base_type::gradient;
    using base_type::gradient_norm;
    using base_type::iterations;
    using base_type::line_searcher;
    using base_type::opt_value;
    using base_type::opt_variable;
    using typename base_type::value_type;

    void init(const variable_type& init_variable) {
        base_type::init(init_variable);
        const auto dimensions = init_variable.size();
        approx_hessian_ = hessian_type::Identity(dimensions, dimensions);
        has_first_iteration_done_ = false;
    }

    [[nodiscard]] auto calc_direction() -> variable_type {
        if (has_first_iteration_done_) {
            diff_var_ = opt_variable() - prev_var_;
            diff_grad_ = gradient() - prev_grad_;
            hessian_var_ = approx_hessian_ * diff_var_;
            approx_hessian_ = approx_hessian_ +
                (diff_grad_ * diff_grad_.transpose()) /
                    (diff_grad_.dot(diff_var_)) -
                (hessian_var_ * hessian_var_.transpose()) /
                    (diff_var_.dot(hessian_var_));
        }
        prev_var_ = opt_variable();
        prev_grad_ = gradient();
        has_first_iteration_done_ = true;
 
        solver_.compute(approx_hessian_);
        return -solver_.solve(prev_grad_);
    }

    void configure_iteration_logger(
        logging::iterations::iteration_logger<this_type>& iteration_logger)
        const {
        iteration_logger.template append<index_type>(
            "Iter.", &base_type::iterations);
        iteration_logger.template append<index_type>(
            "Eval.", &base_type::evaluations);
        iteration_logger.template append<value_type>(
            "Value", &base_type::opt_value);
        iteration_logger.template append<value_type>(
            "Grad.", &base_type::gradient_norm);
    }
 
private:
    hessian_type approx_hessian_{};

    variable_type prev_var_{};

    variable_type prev_grad_{};

    variable_type diff_var_{};

    variable_type diff_grad_{};

    variable_type hessian_var_{};

    bool has_first_iteration_done_{false};

    hessian_solver_type solver_{};
};
 
}  // namespace num_collect::opt