EVOLUTION-MANAGER

Edit File: hinge-loss.h

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#ifndef TENSORFLOW_CORE_KERNELS_HINGE_LOSS_H_
#define TENSORFLOW_CORE_KERNELS_HINGE_LOSS_H_

#include <algorithm>
#include <limits>

#include "tensorflow/core/kernels/loss.h"
#include "tensorflow/core/lib/core/errors.h"
#include "tensorflow/core/lib/core/status.h"

namespace tensorflow {

class HingeLossUpdater : public DualLossUpdater {
 public:
  // Computes the updated dual variable (corresponding) to a single example. The
  // updated dual value maximizes the objective function of the dual
  // optimization problem associated with hinge loss (conditioned on keeping the
  // rest of the dual variables intact). The method below finds an optimal delta
  // (difference between updated and previous dual value) using the update rule
  // within SDCA procedure (see http://arxiv.org/pdf/1209.1873v2.pdf, page 5)
  // and the particular form of conjugate function for hinge loss.
  //
  // The CoCoA+ modification is detailed in readme.md.
  //
  // TODO(sibyl-vie3Poto): Write up a doc with concrete derivation and point to it from
  // here.
  double ComputeUpdatedDual(const int num_loss_partitions, const double label,
                            const double example_weight,
                            const double current_dual, const double wx,
                            const double weighted_example_norm) const final {
    // Intuitively there are 3 cases:
    // a. new optimal value of the dual variable falls within the admissible
    // range [0, 1]. In this case we set new dual to this value.
    // b. new optimal value is < 0. Then, because of convexity, the optimal
    // valid value for new dual = 0
    // c. new optimal value > 1.0. Then new optimal value should be set to 1.0.
    const double candidate_optimal_dual =
        current_dual + (label - wx) / (num_loss_partitions * example_weight *
                                       weighted_example_norm);
    if (label * candidate_optimal_dual < 0) {
      return 0.0;
    }
    if (label * candidate_optimal_dual > 1.0) {
      return label;
    }
    return candidate_optimal_dual;
  }

// Conjugate of hinge loss. This is computed as:
  // \phi*(z) = z if z \in [-1, 0] and +infinity everywhere else. See for
  // instance http://www.eecs.berkeley.edu/~wainwrig/stat241b/lec10.pdf
  // Here we want the weighted version of the conjugate loss. It turns out, that
  // if w is the weight of an example, the conjugate of the weighted hinge loss
  // is given by:
  // \phi*(z) = z if z \in [-w, 0] and +infinity everywhere else. Here the
  // conjugate function depends not only on the weight of the example but also
  // on its label. In particular:
  // \phi_y*(z) = y*z if y*z \in [-w, 0] and +infinity everywhere else where
  // y \in {-1,1}. The following method implements \phi_y*(-\alpha/w).
  double ComputeDualLoss(const double current_dual, const double example_label,
                         const double example_weight) const final {
    // For binary classification, there are 2 conjugate functions, one per
    // label value (-1 and 1).
    const double y_alpha = current_dual * example_label;  // y \alpha
    if (y_alpha < 0 || y_alpha > 1.0) {
      return std::numeric_limits<double>::max();
    }
    return -y_alpha * example_weight;
  }

// Hinge loss for binary classification for a single example. Hinge loss
  // equals max(0, 1 - y * wx) (see https://en.wikipedia.org/wiki/Hinge_loss).
  // For weighted instances loss should be multiplied by the instance weight.
  double ComputePrimalLoss(const double wx, const double example_label,
                           const double example_weight) const final {
    const double y_wx = example_label * wx;
    return std::max(0.0, 1 - y_wx) * example_weight;
  }

double PrimalLossDerivative(const double wx, const double label,
                              const double example_weight) const final {
    if (label * wx < 1) {
      return -label * example_weight;
    }
    return 0;
  }

// The smoothness constant is 0 since the derivative of the loss is not
  // Lipschitz
  double SmoothnessConstant() const final { return 0; }

// Converts binary example labels from 0.0 or 1.0 to -1.0 or 1.0 respectively
  // as expected by hinge loss.
  Status ConvertLabel(float* const example_label) const final {
    if (*example_label == 0.0) {
      *example_label = -1;
      return Status::OK();
    }
    if (*example_label == 1.0) {
      return Status::OK();
    }
    return errors::InvalidArgument(
        "Only labels of 0.0 or 1.0 are supported right now. "
        "Found example with label: ",
        *example_label);
  }
};

}  // namespace tensorflow

#endif  // TENSORFLOW_CORE_KERNELS_HINGE_LOSS_H_