EVOLUTION-MANAGER

Edit File: logistic-loss.h

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==============================================================================*/

#ifndef TENSORFLOW_CORE_KERNELS_LOGISTIC_LOSS_H_
#define TENSORFLOW_CORE_KERNELS_LOGISTIC_LOSS_H_

#include <cmath>

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

namespace tensorflow {

class LogisticLossUpdater : public DualLossUpdater {
 public:
  // Adding vs. Averaging in Distributed Primal-Dual Optimization.
  // Chenxin Ma, Virginia Smith, Martin Jaggi, Michael I. Jordan, Peter
  // Richtarik, Martin Takac http://arxiv.org/abs/1502.03508
  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 {
    // Newton algorithm converges quadratically so 10 steps will be largely
    // enough to achieve a very good precision
    static const int newton_total_steps = 10;
    double x = 0;
    for (int i = 0; i < newton_total_steps; ++i) {
      x = NewtonStep(x, num_loss_partitions, label, wx, example_weight,
                     weighted_example_norm, current_dual);
    }
    return 0.5 * (1 + tanh(x)) / label;
  }

// Dual of logistic loss function.
  // https://en.wikipedia.org/wiki/Convex_conjugate
  double ComputeDualLoss(const double current_dual, const double example_label,
                         const double example_weight) const final {
    // Dual of the logistic loss function is
    // ay * log(ay) + (1-ay) * log (1-ay), where a is the dual variable.
    const double ay = current_dual * example_label;
    const double log_ay = (ay > 0) ? log(ay) : 0;
    const double one_minus_ay = 1 - ay;
    const double log_one_minus_ay = (one_minus_ay > 0) ? log(one_minus_ay) : 0;
    return ((ay * log_ay) + (one_minus_ay * log_one_minus_ay)) * example_weight;
  }

// Logistic loss for binary classification.
  // https://en.wikipedia.org/wiki/Loss_functions_for_classification
  double ComputePrimalLoss(const double wx, const double example_label,
                           const double example_weight) const final {
    // Logistic loss:
    //   log(1 + e^(-ywx))
    //   log(e^0 + e^(-ywx))
    //   a + log(e^(0-a) + e^(-ywx - a)),  where a is max(0, -ywx)
    // https://hips.seas.harvard.edu/blog/2013/01/09/computing-log-sum-exp/
    const double y_wx = example_label * wx;
    if (y_wx > 0) {
      // 0 + log(e^(0) + e^(-ywx - 0))
      // log(1 + e^(-ywx))
      return log1p(exp(-y_wx)) * example_weight;
    }
    // -ywx + log(e^(ywx) + e^(-ywx + ywx))
    // log(e^(ywx) + e^(0)) - ywx
    // log(1 + e^(ywx)) - ywx
    return (log1p(exp(y_wx)) - y_wx) * example_weight;
  }

// Derivative of logistic loss
  double PrimalLossDerivative(const double wx, const double label,
                              const double example_weight) const final {
    double inverse_exp_term = 0;
    if (label * wx > 0) {
      inverse_exp_term = exp(-label * wx) / (1 + exp(-label * wx));
    } else {
      inverse_exp_term = 1 / (1 + exp(label * wx));
    }
    return -inverse_exp_term * label * example_weight;
  }

// The smoothness constant is 4 since the derivative of logistic loss, which
  // is exp(-x) / (1 + exp(-x)) can be shown to 0.25-Lipschitz (its derivative
  // is bounded by 0.25)
  double SmoothnessConstant() const final { return 4; }

// Converts binary example labels from 0.0 or 1.0 to -1.0 or 1.0 respectively
  // as expected by logistic regression.
  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);
  }

private:
  // We use Newton algorithm on a modified function (see readme.md).
  double NewtonStep(const double x, const int num_loss_partitions,
                    const double label, const double wx,
                    const double example_weight,
                    const double weighted_example_norm,
                    const double current_dual) const {
    const double tanhx = tanh(x);
    const double numerator = -2 * label * x - wx -
                             num_loss_partitions * weighted_example_norm *
                                 example_weight *
                                 (0.5 * (1 + tanhx) / label - current_dual);
    const double denominator =
        -2 * label - num_loss_partitions * weighted_example_norm *
                         example_weight * (1 - tanhx * tanhx) * 0.5 / label;
    return x - numerator / denominator;
  }
};

}  // namespace tensorflow

#endif  // TENSORFLOW_CORE_KERNELS_LOGISTIC_LOSS_H_