TensorFlow使用记录 (三）： Learning rate

Posted 2022-12-22 xuanyuyt

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file: tensorflow/python/training/learning_rate_decay.py

参考：tensorflow中常用学习率更新策略

神经网络中通过超参数 learning rate，来控制每次参数更新的幅度。学习率太小会降低网络优化的速度，增加训练时间；学习率太大则可能导致可能导致参数在局部最优解两侧来回振荡，网络不能收敛。

tensorflow 定义了很多的学习率衰减方式：

指数衰减 tf.train.exponential_decay()

指数衰减是比较常用的衰减方法，学习率是跟当前的训练轮次指数相关的。

tf.train.exponential_decay(
    learning_rate,     # 初始学习率
    global_step,       # 当前训练轮次
    decay_steps,       # 衰减周期
    decay_rate,        # 衰减率系数
    staircase=False,   # 定义是否是阶梯型衰减，还是连续衰减，默认是 False
    name=None
)
‘‘‘
decayed_learning_rate = learning_rate *
                      decay_rate ^ (global_step / decay_steps)
‘‘‘

示例代码：

import tensorflow as tf
import matplotlib.pyplot as plt
style1 = []
style2 = []
N = 200

with tf.Session() as sess:
  sess.run(tf.global_variables_initializer())
  for step in range(N):
    # 标准指数型衰减
    learing_rate1 = tf.train.exponential_decay(
      learning_rate=0.5, global_step=step, decay_steps=10, decay_rate=0.9, staircase=False)
    # 阶梯型衰减
    learing_rate2 = tf.train.exponential_decay(
      learning_rate=0.5, global_step=step, decay_steps=10, decay_rate=0.9, staircase=True)
    lr1 = sess.run([learing_rate1])
    lr2 = sess.run([learing_rate2])
    style1.append(lr1)
    style2.append(lr2)

step = range(N)

plt.plot(step, style1, ‘g-‘, linewidth=2, label=‘exponential_decay‘)
plt.plot(step, style2, ‘r--‘, linewidth=1, label=‘exponential_decay_staircase‘)
plt.title(‘exponential_decay‘)
plt.xlabel(‘step‘)
plt.ylabel(‘learing rate‘)
plt.legend(loc=‘upper right‘)
plt.tight_layout()
plt.show()

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分段常数衰减 tf.train.piecewise_constant()

tf.train.piecewise_constant_decay(
    x,                # 当前训练轮次
    boundaries,       # 学习率应用区间
    values,           # 学习率常数列表
    name=None
)
‘‘‘
learning_rate value is `values[0]` when `x <= boundaries[0]`,
    `values[1]` when `x > boundaries[0]` and `x <= boundaries[1]`, ...,
    and values[-1] when `x > boundaries[-1]`.
‘‘‘

示例代码：

import tensorflow as tf
import matplotlib.pyplot as plt
boundaries = [10, 20, 30]
learing_rates = [0.1, 0.07, 0.025, 0.0125]

style = []
N = 40

with tf.Session() as sess:
  sess.run(tf.global_variables_initializer())
  for step in range(N):
    learing_rate = tf.train.piecewise_constant(step, boundaries=boundaries, values=learing_rates)
    lr = sess.run([learing_rate])
    style.append(lr)


step = range(N)

plt.plot(step, style, ‘r-‘, linewidth=2)
plt.title(‘piecewise_constant‘)
plt.xlabel(‘step‘)
plt.ylabel(‘learing rate‘)
plt.tight_layout()
plt.show()

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多项式衰减 tf.train.polynomial_decay()

tf.train.polynomial_decay(
    learning_rate,               # 初始学习率
    global_step,                 # 当前训练轮次
    decay_steps,                 # 大衰减周期
    end_learning_rate=0.0001,    # 最小的学习率
    power=1.0,                   # 多项式的幂
    cycle=False,                 # 学习率是否循环
    name=None)
‘‘‘
global_step = min(global_step, decay_steps)
decayed_learning_rate = (learning_rate - end_learning_rate) *
                        (1 - global_step / decay_steps) ^ (power) +
                         end_learning_rate
‘‘‘

示例代码：

import tensorflow as tf
import matplotlib.pyplot as plt
style1 = []
style2 = []
N = 200

with tf.Session() as sess:
  sess.run(tf.global_variables_initializer())
  for step in range(N):
    # cycle=False
    learing_rate1 = tf.train.polynomial_decay(
      learning_rate=0.1, global_step=step, decay_steps=50,
      end_learning_rate=0.01, power=0.5, cycle=False)
    # cycle=True
    learing_rate2 = tf.train.polynomial_decay(
      learning_rate=0.1, global_step=step, decay_steps=50,
      end_learning_rate=0.01, power=0.5, cycle=True)
    lr1 = sess.run([learing_rate1])
    lr2 = sess.run([learing_rate2])
    style1.append(lr1)
    style2.append(lr2)


steps = range(N)

plt.plot(steps, style1, ‘g-‘, linewidth=2, label=‘polynomial_decay‘)
plt.plot(steps, style2, ‘r--‘, linewidth=1, label=‘polynomial_decay_cycle‘)
plt.title(‘polynomial_decay‘)
plt.xlabel(‘step‘)
plt.ylabel(‘learing rate‘)
plt.legend(loc=‘upper right‘)
plt.tight_layout()
plt.show()

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自然指数衰减 tf.train.natural_exp_decay()

tf.train.natural_exp_decay(
    learning_rate,        # 初始学习率
    global_step,          # 当前训练轮次
    decay_steps,          # 衰减周期
    decay_rate,           # 衰减率系数
    staircase=False,      # 定义是否是阶梯型衰减，还是连续衰减，默认是 False
    name=None
)
‘‘‘
decayed_learning_rate = learning_rate * exp(-decay_rate * global_step)
‘‘‘

示例代码：

import tensorflow as tf
import matplotlib.pyplot as plt
style1 = []
style2 = []
N = 200

with tf.Session() as sess:
  sess.run(tf.global_variables_initializer())
  for step in range(N):
    # 标准指数型衰减
    learing_rate1 = tf.train.natural_exp_decay(
      learning_rate=0.5, global_step=step, decay_steps=10, decay_rate=0.9, staircase=False)
    # 阶梯型衰减
    learing_rate2 = tf.train.natural_exp_decay(
      learning_rate=0.5, global_step=step, decay_steps=10, decay_rate=0.9, staircase=True)
    lr1 = sess.run([learing_rate1])
    lr2 = sess.run([learing_rate2])
    style1.append(lr1)
    style2.append(lr2)

step = range(N)

plt.plot(step, style1, ‘g-‘, linewidth=2, label=‘natural_exp_decay‘)
plt.plot(step, style2, ‘r--‘, linewidth=1, label=‘natural_exp_decay_staircase‘)
plt.title(‘natural_exp_decay‘)
plt.xlabel(‘step‘)
plt.ylabel(‘learing rate‘)
plt.legend(loc=‘upper right‘)
plt.tight_layout()
plt.show()

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倒数衰减 tf.train.inverse_time_decay()

tf.train.inverse_time_decay(
    learning_rate,     # 初始学习率
    global_step,       # 当前训练轮次
    decay_steps,       # 衰减周期
    decay_rate,        # 衰减率系数
    staircase=False,   # 定义是否是阶梯型衰减，还是连续衰减，默认是 False
    name=None
)
‘‘‘
decayed_learning_rate = learning_rate / (1 + decay_rate * global_step / decay_step)
‘‘‘

示例代码：

import tensorflow as tf
import matplotlib.pyplot as plt
style1 = []
style2 = []
N = 200

with tf.Session() as sess:
  sess.run(tf.global_variables_initializer())
  for step in range(N):
    # 标准指数型衰减
    learing_rate1 = tf.train.inverse_time_decay(
      learning_rate=0.5, global_step=step, decay_steps=20, decay_rate=0.2, staircase=False)
    # 阶梯型衰减
    learing_rate2 = tf.train.inverse_time_decay(
      learning_rate=0.5, global_step=step, decay_steps=20, decay_rate=0.2, staircase=True)
    lr1 = sess.run([learing_rate1])
    lr2 = sess.run([learing_rate2])
    style1.append(lr1)
    style2.append(lr2)

step = range(N)

plt.plot(step, style1, ‘g-‘, linewidth=2, label=‘inverse_time_decay‘)
plt.plot(step, style2, ‘r--‘, linewidth=1, label=‘inverse_time_decay_staircase‘)
plt.title(‘inverse_time_decay‘)
plt.xlabel(‘step‘)
plt.ylabel(‘learing rate‘)
plt.legend(loc=‘upper right‘)
plt.tight_layout()
plt.show()

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余弦衰减 tf.train.cosine_decay()

tf.train.cosine_decay(
    learning_rate,   # 初始学习率
    global_step,     # 当前训练轮次
    decay_steps,     # 衰减周期
    alpha=0.0,       # 最小的学习率
    name=None
)
‘‘‘
global_step = min(global_step, decay_steps)
cosine_decay = 0.5 * (1 + cos(pi * global_step / decay_steps))
decayed = (1 - alpha) * cosine_decay + alpha
decayed_learning_rate = learning_rate * decayed
‘‘‘

改进的余弦衰减方法还有：
线性余弦衰减，对应函数 tf.train.linear_cosine_decay()
噪声线性余弦衰减，对应函数 tf.train.noisy_linear_cosine_decay()

示例代码：

import tensorflow as tf
import matplotlib.pyplot as plt
style1 = []
style2 = []
style3 = []
N = 200

with tf.Session() as sess:
  sess.run(tf.global_variables_initializer())
  for step in range(N):
    # 余弦衰减
    learing_rate1 = tf.train.cosine_decay(
      learning_rate=0.1, global_step=step, decay_steps=50)
    # 线性余弦衰减
    learing_rate2 = tf.train.linear_cosine_decay(
      learning_rate=0.1, global_step=step, decay_steps=50)
    # 噪声线性余弦衰减
    learing_rate3 = tf.train.noisy_linear_cosine_decay(
      learning_rate=0.1, global_step=step, decay_steps=50,
      initial_variance=0.01, variance_decay=0.1, num_periods=0.2, alpha=0.5, beta=0.2)
    lr1 = sess.run([learing_rate1])
    lr2 = sess.run([learing_rate2])
    lr3 = sess.run([learing_rate3])
    style1.append(lr1)
    style2.append(lr2)
    style3.append(lr3)

step = range(N)

plt.plot(step, style1, ‘g-‘, linewidth=2, label=‘cosine_decay‘)
plt.plot(step, style2, ‘r--‘, linewidth=1, label=‘linear_cosine_decay‘)
plt.plot(step, style3, ‘b--‘, linewidth=1, label=‘linear_cosine_decay‘)
plt.title(‘cosine_decay‘)
plt.xlabel(‘step‘)
plt.ylabel(‘learing rate‘)
plt.legend(loc=‘upper right‘)
plt.tight_layout()
plt.show()

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余弦衰减 tf.train.cosine_decay_restarts()

这是在 fast.ai 中强推的衰减方式

tf.train.cosine_decay_restarts(
    learning_rate,      # 初始学习率
    global_step,        # 当前训练轮次
    first_decay_steps,  # 首次衰减周期
    t_mul=2.0,          # 随后每次衰减周期倍数
    m_mul=1.0,          # 随后每次初始学习率倍数
    alpha=0.0,          # 最小的学习率
    name=None
)
‘‘‘
See [Loshchilov & Hutter, ICLR2016], SGDR: Stochastic Gradient Descent
with Warm Restarts. https://arxiv.org/abs/1608.03983
The learning rate multiplier first decays
from 1 to `alpha` for `first_decay_steps` steps. Then, a warm
restart is performed. Each new warm restart runs for `t_mul` times more steps
and with `m_mul` times smaller initial learning rate.
‘‘‘

示例代码：

import tensorflow as tf
import matplotlib.pyplot as plt
style1 = []
style2 = []
N = 200

with tf.Session() as sess:
  sess.run(tf.global_variables_initializer())
  for step in range(N):
    # 余弦衰减
    learing_rate1 = tf.train.cosine_decay_restarts(
      learning_rate=0.1, global_step=step, first_decay_steps=50,
      )
    # 循环余弦衰减
    learing_rate2 = tf.train.cosine_decay(
      learning_rate=0.1, global_step=step, decay_steps=50)
    lr1 = sess.run([learing_rate1])
    lr2 = sess.run([learing_rate2])
    style1.append(lr1)
    style2.append(lr2)

step = range(N)

plt.plot(step, style1, ‘g-‘, linewidth=2, label=‘cosine_decay_restarts‘)
plt.plot(step, style2, ‘r--‘, linewidth=1, label=‘cosine_decay‘)
plt.title(‘cosine_decay_restarts‘)
plt.xlabel(‘step‘)
plt.ylabel(‘learing rate‘)
plt.legend(loc=‘upper right‘)
plt.tight_layout()
plt.show()

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技术图片

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