quadratic_cost_approximation.h

/*
 * Copyright (c) 2019, The Regents of the University of California (Regents).
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions are
 * met:
 *
 *    1. Redistributions of source code must retain the above copyright
 *       notice, this list of conditions and the following disclaimer.
 *
 *    2. Redistributions in binary form must reproduce the above
 *       copyright notice, this list of conditions and the following
 *       disclaimer in the documentation and/or other materials provided
 *       with the distribution.
 *
 *    3. Neither the name of the copyright holder nor the names of its
 *       contributors may be used to endorse or promote products derived
 *       from this software without specific prior written permission.
 *
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS AS IS
 * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 * ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
 * LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
 * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
 * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
 * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
 * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
 * POSSIBILITY OF SUCH DAMAGE.
 *
 * Please contact the author(s) of this library if you have any questions.
 * Authors: David Fridovich-Keil   ( dfk@eecs.berkeley.edu )
 */

///////////////////////////////////////////////////////////////////////////////
//
// Container to store a quadratic approximation of a single player's cost at a
// particular moment in time. That is, each player should have a time-indexed
// set of these QuadraticApproximations.
//
// Notation is taken from Basar and Olsder, Corollary 6.1.
// -- Q is the Hessian with respect to state
// -- l is the gradient with respect to state
// -- Rs[ii] is the Hessian with respect to the control input of player ii
// -- rs[ii] is the gradient with respect to the control input of player ii
//
///////////////////////////////////////////////////////////////////////////////

#ifndef ILQGAMES_UTILS_QUADRATIC_COST_APPROXIMATION_H
#define ILQGAMES_UTILS_QUADRATIC_COST_APPROXIMATION_H

#include <ilqgames/utils/types.h>

#include <glog/logging.h>
#include <unordered_map>

namespace ilqgames {

struct SingleCostApproximation {
  MatrixXf hess;
  VectorXf grad;

  // Construct from matrix/vector directly.
  SingleCostApproximation(const MatrixXf& hessian, const VectorXf& gradient)
      : hess(hessian), grad(gradient) {
    CHECK_EQ(hess.rows(), hess.cols());
    CHECK_EQ(hess.rows(), grad.size());
  }

  // Construct with zeros.
  SingleCostApproximation(Dimension dim, float regularization = 0.0)
      : hess(regularization * MatrixXf::Identity(dim, dim)),
        grad(VectorXf::Zero(dim)) {}
};  // struct SingleCostApproximation

struct QuadraticCostApproximation {
  SingleCostApproximation state;
  PlayerMap<SingleCostApproximation> control;

  // Construct from state dimension.
  explicit QuadraticCostApproximation(Dimension xdim,
                                      float regularization = 0.0)
      : state(xdim, regularization) {}
};  // struct QuadraticCostApproximation

}  // namespace ilqgames

#endif