newton_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 "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_twice_differentiable_objective_function.h"
#include "num_collect/opt/descent_method_base.h"
 
namespace num_collect::opt {
 
constexpr auto newton_optimizer_tag =
    logging::log_tag_view("num_collect::opt::newton_optimizer");
 
template <concepts::multi_variate_twice_differentiable_objective_function
              ObjectiveFunction,
    concepts::line_searcher LineSearcher =
        backtracking_line_searcher<ObjectiveFunction>,
    typename HessianSolver =
        Eigen::LLT<typename ObjectiveFunction::hessian_type>>
class newton_optimizer
    : public descent_method_base<
          newton_optimizer<ObjectiveFunction, LineSearcher, HessianSolver>,
          LineSearcher> {
public:
    using this_type =
        newton_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 hessian_type = typename objective_function_type::hessian_type;
 
    using hessian_solver_type = HessianSolver;
 
    explicit newton_optimizer(
        const objective_function_type& obj_fun = objective_function_type())
        : base_type(newton_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 typename base_type::value_type;
 
    [[nodiscard]] auto hessian() const -> const hessian_type& {
        return line_searcher().obj_fun().hessian();
    }
 
    [[nodiscard]] auto calc_direction() -> variable_type {
        return calc_direction_impl(hessian());
    }
 
    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:
    [[nodiscard]] auto calc_direction_impl(const hessian_type& hessian)
        -> variable_type {
        solver_.compute(hessian);
        return -solver_.solve(gradient());
    }
 
    hessian_solver_type solver_;
};
 
}  // namespace num_collect::opt