├── README.md
└── main.py


/README.md:
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1 | # PE-LTR
2 | 
3 | The demo codes for the paper "A Pareto-Eficient Algorithm for Multiple Objective Optimization in E-Commerce Recommendation".
4 | 


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/main.py:
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 1 | #!/usr/bin/env python2
 2 | # -*- coding: utf-8 -*-
 3 | """
 4 | This is the example code for PE-LTR.
 5 | The losses and inputs can be modified.
 6 | The core part is the pareto step.
 7 | The example is an illustration for the zero constraints on the priorities.
 8 | Created on Wed Oct  9 11:27:53 2019
 9 | 
10 | @author: jackielinxiao
11 | """
12 | 
13 | import tensorflow as tf
14 | import numpy as np
15 | 
16 | x_data = np.float32(np.random.rand(2, 100)) 
17 | y_data = np.dot([0.100, 0.200], x_data) + 0.300
18 | 
19 | weight_a = tf.placeholder(tf.float32)
20 | weight_b = tf.placeholder(tf.float32)
21 | 
22 | b = tf.Variable(tf.zeros([1]))
23 | W = tf.Variable(tf.random_uniform([1, 2], -1.0, 1.0))
24 | y = tf.matmul(W, x_data) + b
25 | 
26 | loss_a = tf.reduce_mean(tf.square(y - y_data))
27 | loss_b = tf.reduce_mean(tf.square(W))
28 | loss = weight_a * loss_a + weight_b * loss_b    
29 | 
30 | optimizer = tf.train.GradientDescentOptimizer(0.5)
31 | 
32 | a_gradients = tf.gradients(loss_a, W)
33 | b_gradients = tf.gradients(loss_b, W)
34 | 
35 | train = optimizer.minimize(loss)
36 | 
37 | 
38 | init = tf.initialize_all_variables()
39 | 
40 | sess = tf.Session()
41 | sess.run(init)
42 | 
43 | def pareto_step(weights_list, out_gradients_list):
44 |     model_gradients = out_gradients_list
45 |     M1 = np.matmul(model_gradients,np.transpose(model_gradients))
46 |     e = np.mat(np.ones(np.shape(weights_list)))
47 |     M = np.hstack((M1,np.transpose(e)))
48 |     mid = np.hstack((e,np.mat(np.zeros((1,1)))))
49 |     M = np.vstack((M,mid))
50 |     z = np.mat(np.zeros(np.shape(weights_list)))
51 |     nid = np.hstack((z,np.mat(np.ones((1,1)))))
52 |     w = np.matmul(np.matmul(M,np.linalg.inv(np.matmul(M,np.transpose(M)))),np.transpose(nid))
53 |     if len(w)>1:
54 |         w = np.transpose(w)
55 |         w = w[0,0:np.shape(w)[1]]
56 |         mid = np.where(w > 0, 1.0, 0)
57 |         nid = np.multiply(mid, w)
58 |         uid = sorted(nid[0].tolist()[0], reverse=True)
59 |         sv = np.cumsum(uid)
60 |         rho = np.where(uid > (sv - 1.0) / range(1,len(uid)+1), 1.0, 0.0)
61 |         r = max(np.argwhere(rho))
62 |         theta = max(0, (sv[r] - 1.0) / (r+1))
63 |         w = np.where(nid - theta>0.0, nid - theta, 0)
64 |     return w
65 | 
66 | 
67 | w_a = 0.5
68 | w_b = 0.5
69 | for step in xrange(0, 50):
70 |     res = sess.run([a_gradients,b_gradients,train],feed_dict={weight_a:w_a,weight_b:w_b})
71 |     #res[0]
72 |     weights = np.mat([w_a, w_b])
73 |     paras = np.vstack((res[0][0],res[1][0]))
74 |     mid = pareto_step(weights,paras)
75 |     w_a, w_b = mid[0,0], mid[0,1]
76 |     print w_a, w_b, step, sess.run(W), sess.run(b)
77 |     #print alpha, 1.0-alpha


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