Python ---------- Tensorflow (二）学习率

假设最小化函数 y = x² ， 选择初始点 x₀= 5

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1. 学习率为1的时候，x在5和-5之间震荡。

 #学习率为1

 import tensorflow as tf
 training_steps = 10
 learning_rate = 1
 x = tf.Variable(tf.constant(5, dtype=tf.float32),name="x")
 y = tf.square(x)

 train_op = tf.train.GradientDescentOptimizer(learning_rate).minimize(y)

 with tf.Session() as sess:
     sess.run(tf.global_variables_initializer())
     for i in range(training_steps):
         sess.run(train_op)
         x_value = sess.run(x)
         print("After %s iteration(s): x%s is %f."%(i+1,i+1,x_value))

 #输出结果：
 After 1 iteration(s): x1 is -5.000000.
 After 2 iteration(s): x2 is 5.000000.
 After 3 iteration(s): x3 is -5.000000.
 After 4 iteration(s): x4 is 5.000000.
 After 5 iteration(s): x5 is -5.000000.
 After 6 iteration(s): x6 is 5.000000.
 After 7 iteration(s): x7 is -5.000000.
 After 8 iteration(s): x8 is 5.000000.
 After 9 iteration(s): x9 is -5.000000.
 After 10 iteration(s): x10 is 5.000000.

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2.学习率为0.001的时候，下降速度过慢，在901轮时才收敛到0.823355.

 #学习率为0.001
 training_steps = 1000
 learning_rate = 0.001
 x = tf.Variable(tf.constant(5,dtype=tf.float32),name="x")
 y = tf.square(x)

 train_op = tf.train.GradientDescentOptimizer(learning_rate).minimize(y)

 with tf.Session() as sess:
     sess.run(tf.global_variables_initializer())
     for i in range(training_steps):
         sess.run(train_op)
         if i % 100 ==0:
             x_value = sess.run(x)
             print("After %s iteration(s): x%s is %f."%(i+1,i+1,x_value))

 #结果为：

 After 1 iteration(s): x1 is 4.990000.
 After 101 iteration(s): x101 is 4.084646.
 After 201 iteration(s): x201 is 3.343555.
 After 301 iteration(s): x301 is 2.736923.
 After 401 iteration(s): x401 is 2.240355.
 After 501 iteration(s): x501 is 1.833880.
 After 601 iteration(s): x601 is 1.501153.
 After 701 iteration(s): x701 is 1.228794.
 After 801 iteration(s): x801 is 1.005850.
 After 901 iteration(s): x901 is 0.823355.

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3.使用指数衰减的学习率，在迭代初期得到较高的下降速度，可以在较小的训练轮数下取得不错的收敛程度。

 TRAINING_STEPS = 100
 global_step = tf.Variable(0)
 LEARNING_RATE = tf.train.exponential_decay(0.1, global_step, 1, 0.96, staircase=True)

 x = tf.Variable(tf.constant(5, dtype=tf.float32), name="x")
 y = tf.square(x)
 train_op = tf.train.GradientDescentOptimizer(LEARNING_RATE).minimize(y, global_step=global_step)

 with tf.Session() as sess:
     sess.run(tf.global_variables_initializer())
     for i in range(TRAINING_STEPS):
         sess.run(train_op)
         if i % 10 == 0:
             LEARNING_RATE_value = sess.run(LEARNING_RATE)
             x_value = sess.run(x)
             print ("After %s iteration(s): x%s is %f, learning rate is %f."% (i+1, i+1, x_value, LEARNING_RATE_value))

 #输出结果：

 After 1 iteration(s): x1 is 4.000000, learning rate is 0.096000.
 After 11 iteration(s): x11 is 0.690561, learning rate is 0.063824.
 After 21 iteration(s): x21 is 0.222583, learning rate is 0.042432.
 After 31 iteration(s): x31 is 0.106405, learning rate is 0.028210.
 After 41 iteration(s): x41 is 0.065548, learning rate is 0.018755.
 After 51 iteration(s): x51 is 0.047625, learning rate is 0.012469.
 After 61 iteration(s): x61 is 0.038558, learning rate is 0.008290.
 After 71 iteration(s): x71 is 0.033523, learning rate is 0.005511.
 After 81 iteration(s): x81 is 0.030553, learning rate is 0.003664.
 After 91 iteration(s): x91 is 0.028727, learning rate is 0.002436.