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_CORE_KERNELS_SQUARED_LOSS_H_ |
17 | #define TENSORFLOW_CORE_KERNELS_SQUARED_LOSS_H_ |
18 | |
19 | #include "tensorflow/core/kernels/loss.h" |
20 | |
21 | namespace tensorflow { |
22 | |
23 | class SquaredLossUpdater : public DualLossUpdater { |
24 | public: |
25 | // Closed form solution that decreases the dual squared loss. |
26 | // See page 23 of http://arxiv.org/pdf/1309.2375v2.pdf for the derivation of |
27 | // the update rule when the example weights are equal to 1.0. |
28 | // Note: There is a typo in the formula in the paper: the denominator should |
29 | // be 1 + ||x_i||^2/(\lambda n) (without the 2 multiplier). |
30 | // |
31 | // The CoCoA+ modification is detailed in readme.md. |
32 | double ComputeUpdatedDual(const int num_loss_partitions, const double label, |
33 | const double example_weight, |
34 | const double current_dual, const double wx, |
35 | const double weighted_example_norm) const final { |
36 | const double delta_numerator = label - current_dual - wx; |
37 | const double delta_denominator = |
38 | 1 + num_loss_partitions * weighted_example_norm * example_weight; |
39 | return current_dual + delta_numerator / delta_denominator; |
40 | } |
41 | |
42 | // Dual of squared loss function. |
43 | // https://en.wikipedia.org/wiki/Convex_conjugate |
44 | double ComputeDualLoss(const double current_dual, const double example_label, |
45 | const double example_weight) const final { |
46 | // Dual of the squared loss function = b * (y + b/2), where b is the |
47 | // dual variable and y is the label. This is Dual(-b). |
48 | return current_dual * (0.5 * current_dual - example_label) * example_weight; |
49 | } |
50 | |
51 | // Squared loss for linear regression. |
52 | double ComputePrimalLoss(const double wx, const double example_label, |
53 | const double example_weight) const final { |
54 | const double error = wx - example_label; |
55 | return error * error * example_weight * 0.5; |
56 | } |
57 | |
58 | inline double PrimalLossDerivative(const double wx, const double label, |
59 | const double example_weight) const final { |
60 | return (wx - label) * example_weight; |
61 | } |
62 | |
63 | inline double SmoothnessConstant() const final { return 1.0; } |
64 | |
65 | // Labels don't require conversion for linear regression. |
66 | Status ConvertLabel(float* const example_label) const final { |
67 | return OkStatus(); |
68 | } |
69 | }; |
70 | |
71 | } // namespace tensorflow |
72 | |
73 | #endif // TENSORFLOW_CORE_KERNELS_SQUARED_LOSS_H_ |
74 | |