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      1 /* Copyright 2016 The TensorFlow Authors. All Rights Reserved.
      2 
      3 Licensed under the Apache License, Version 2.0 (the "License");
      4 you may not use this file except in compliance with the License.
      5 You may obtain a copy of the License at
      6 
      7     http://www.apache.org/licenses/LICENSE-2.0
      8 
      9 Unless required by applicable law or agreed to in writing, software
     10 distributed under the License is distributed on an "AS IS" BASIS,
     11 WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
     12 See the License for the specific language governing permissions and
     13 limitations under the License.
     14 ==============================================================================*/
     15 
     16 #ifndef TENSORFLOW_KERNELS_SMOOTH_HINGE_LOSS_H_
     17 #define TENSORFLOW_KERNELS_SMOOTH_HINGE_LOSS_H_
     18 
     19 #include <limits>
     20 
     21 #include "tensorflow/core/kernels/loss.h"
     22 #include "tensorflow/core/lib/core/errors.h"
     23 #include "tensorflow/core/lib/core/status.h"
     24 
     25 namespace tensorflow {
     26 
     27 class SmoothHingeLossUpdater : public DualLossUpdater {
     28  public:
     29   // Computes the updated dual variable (corresponding) to a single example. The
     30   // updated dual value maximizes the objective function of the dual
     31   // optimization problem associated with smooth hinge loss. The computations
     32   // are detailed in readme.md.
     33   double ComputeUpdatedDual(const int num_partitions, const double label,
     34                             const double example_weight,
     35                             const double current_dual, const double wx,
     36                             const double weighted_example_norm) const final {
     37     // Intutitvely there are 3 cases:
     38     // a. new optimal value of the dual variable falls within the admissible
     39     // range [0, 1]. In this case we set new dual to this value.
     40     // b. new optimal value is < 0. Then, because of convexity, the optimal
     41     // valid value for new dual = 0
     42     // c. new optimal value > 1.0. Then new optimal value should be set to 1.0.
     43     const double candidate_optimal_dual =
     44         current_dual +
     45         (label - wx - gamma * current_dual) /
     46             (num_partitions * example_weight * weighted_example_norm + gamma);
     47     if (label * candidate_optimal_dual < 0) {
     48       return 0.0;
     49     }
     50     if (label * candidate_optimal_dual > 1.0) {
     51       return label;
     52     }
     53     return candidate_optimal_dual;
     54   }
     55 
     56   double ComputeDualLoss(const double current_dual, const double example_label,
     57                          const double example_weight) const final {
     58     // For binary classification, there are 2 conjugate functions, one per
     59     // label value (-1 and 1).
     60     const double y_alpha = current_dual * example_label;  // y \alpha
     61     if (y_alpha < 0 || y_alpha > 1.0) {
     62       return std::numeric_limits<double>::max();
     63     }
     64     return (-y_alpha + 0.5 * gamma * current_dual * current_dual) *
     65            example_weight;
     66   }
     67 
     68   double ComputePrimalLoss(const double wx, const double example_label,
     69                            const double example_weight) const final {
     70     const double y_wx = example_label * wx;
     71     if (y_wx >= 1) return 0;
     72     if (y_wx <= 1 - gamma) return (1 - y_wx - gamma / 2) * example_weight;
     73     return (1 - y_wx) * (1 - y_wx) * example_weight * 0.5 / gamma;
     74   }
     75 
     76   // Converts binary example labels from 0.0 or 1.0 to -1.0 or 1.0 respectively
     77   // as expected by smooth hinge loss.
     78   Status ConvertLabel(float* const example_label) const final {
     79     if (*example_label == 0.0) {
     80       *example_label = -1;
     81       return Status::OK();
     82     }
     83     if (*example_label == 1.0) {
     84       return Status::OK();
     85     }
     86     return errors::InvalidArgument(
     87         "Only labels of 0.0 or 1.0 are supported right now. "
     88         "Found example with label: ",
     89         *example_label);
     90   }
     91 
     92   double PrimalLossDerivative(const double wx, const double label,
     93                               const double example_weight) const final {
     94     if (label * wx >= 1) {
     95       return 0;
     96     }
     97     if (label * wx <= 1 - gamma) {
     98       return -label;
     99     }
    100     return (wx - label) / gamma;
    101   }
    102 
    103   double SmoothnessConstant() const final { return gamma; }
    104 
    105  private:
    106   // Smoothness constant of smooth hinge loss
    107   // TODO(sibyl-Aix6ihai): expose this parameter
    108   const double gamma = 1;
    109 };
    110 
    111 }  // namespace tensorflow
    112 
    113 #endif
    114 // TENSORFLOW_KERNELS_SMOOTH_HINGE_LOSS_H_
    115