G&R Blog Release Regulation

Pairwise 损失函数的计算

CTR/CVR/LTV 预估中, 反馈通常是非常稀疏的行为, 我们期望引入 pairwise 的 ranking 损失去精细化建模, 针对激活后付费预估任务增加 ranking 损失: 具体做法对一个 batch 里面的 label, 构造正负样本 logit 对, 损失计算的是 log(sigmoid(s_i-s_j))/pair_nums

核心思想是

$$\text{pairwise-loss}=-\sum_{i\in\{y_i=1\}}\sum_{j\in\{y_j\ne 1\}}\log(\text{sigmoid}(s_i,s_j))$$

实际操作是

$$\text{pairwise-loss}=-\frac{\sum_{i\in\{y_i=1\}}\sum_{j\in\{y_j\ne 1\}}\log(\text{sigmoid}(logit_i-logit_j))}{\sum_{i\in\{y_i=1\}}\sum_{j\in\{y_j\ne 1\}}1}$$ $$\text{loss}=\text{pairwise-loss}\cdot \exp(-w_1)+\text{pairwise-loss}\cdot \exp(-w_2)+0.5w_1+0.5w_2$$

实现 & 测试代码

import tensorflow as tf
import numpy as np

tensor = [0, 1, 2, 3]
t_mask = np.array([True, False, True, False])
b = tf.boolean_mask(tensor, t_mask)
tf.print(b)

def pairwise_ranking_loss_with_logits(self, labels, logits, name=None):
  labels = tf.reshape(tf.cast(labels, tf.float32), [-1, 1])
  logits = tf.reshape(tf.cast(logits, tf.float32), [-1, 1])

  pos_mask = tf.clip_by_value(labels, 0.0, 1.0)
  neg_mask = 1.0 - pos_mask

  pos_nums = tf.reduce_sum(pos_mask)
  neg_nums = tf.reduce_sum(neg_mask)
  pairs = pos_nums * neg_nums

  pos_logits = tf.reshape(tf.boolean_mask(logits, pos_mask), [-1, 1])
  neg_logits = tf.reshape(tf.boolean_mask(logits, neg_mask), [1, -1])
  pos_logits_matrix = tf.tile(pos_logits, [1, neg_nums])
  neg_logits_matrix = tf.tile(neg_logits, [pos_nums, 1])
  delta_logits_matrix = pos_logits_matrix - neg_logits_matrix
  rank_logits_mean = tf.where(tf.equal(pairs, 0.), 0.0, tf.reduce_sum(delta_logits_matrix) / pairs)

  ranknet_loss = tf.reduce_sum(-tf.math.log_sigmoid(delta_logits_matrix))
  ranknet_loss = tf.where(tf.equal(pairs, 0.), 0.0, ranknet_loss / pairs)
  return ranknet_loss

labels = [  1,  0,  0,   0,   0,  1]
logits = [0.8,0.3,0.2,0.15,0.01,0.7]

labels = tf.reshape(tf.cast(labels, tf.float32), [-1, 1])
logits = tf.reshape(tf.cast(logits, tf.float32), [-1, 1])

print(f"labels.shape()={labels.get_shape().as_list()}")
print(f"logits.shape()={logits.get_shape().as_list()}")

pos_mask = tf.clip_by_value(labels, 0.0, 1.0)
neg_mask = 1.0 - pos_mask

print("pos_mask:")
tf.print(pos_mask)

pos_nums = tf.reduce_sum(pos_mask)
neg_nums = tf.reduce_sum(neg_mask)

tf.print(pos_nums)
tf.print(neg_nums)

pairs = pos_nums * neg_nums
print("num_pairs:")
tf.print(pairs)

pos_logits = tf.reshape(tf.boolean_mask(logits, pos_mask), [-1, 1])
neg_logits = tf.reshape(tf.boolean_mask(logits, neg_mask), [1, -1])

tf.print(pos_logits)
tf.print(neg_logits)

pos_logits_matrix = tf.tile(pos_logits, [1, neg_nums])
neg_logits_matrix = tf.tile(neg_logits, [pos_nums, 1])
delta_logits_matrix = pos_logits_matrix - neg_logits_matrix

tf.print(pos_logits_matrix)
tf.print(neg_logits_matrix)
tf.print(delta_logits_matrix)

print(f"pos_logits_matrix.shape()={pos_logits_matrix.get_shape().as_list()}")

t = -tf.math.log_sigmoid(delta_logits_matrix)
tf.print(t)
ranknet_loss = tf.reduce_sum(-tf.math.log_sigmoid(delta_logits_matrix))
tf.print(ranknet_loss)

ranknet_loss_final = tf.where(tf.equal(pairs, 0.), 0.0, ranknet_loss / pairs)
tf.print(ranknet_loss_final)

Reference

[1]. On the Factory Floor: ML Engineering for Industrial-Scale Ads Recommendation Models.
[2]. Learning to Rank using Gradient Descent.

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