polynomial_decay多项式学习率迭代策略详解

在深度学习中学习率的往往根据自己的数据集验证最好的超参数，然而更好的学习策略可以帮助你不通过交叉验证来获得一个较好的学习率超参数。

tf.train.polynomial_decay(
    learning_rate,
    global_step,
    decay_steps,
    end_learning_rate=0.0001,
    power=1.0,
    cycle=False,
    name=None
)

所有学习率策略文件的完整定义在 [tensorflow/python/training/learning_rate_decay.py]
Applies a polynomial decay to the learning rate.

It is commonly observed that a monotonically decreasing learning rate, whose degree of change is carefully chosen, results in a better performing model. This function applies a polynomial decay function to a provided initiallearning_rate to reach an end_learning_rate in the given decay_steps.

It requires a global_step value to compute the decayed learning rate. You can just pass a TensorFlow variable that you increment at each training step.

The function returns the decayed learning rate. It is computed as:

global_step = min(global_step, decay_steps)
decayed_learning_rate = (learning_rate - end_learning_rate) *
                        (1 - global_step / decay_steps) ^ (power) +
                        end_learning_rate

If cycle is True then a multiple of decay_steps is used, the first one that is bigger than global_steps.

decay_steps = decay_steps * ceil(global_step / decay_steps)
decayed_learning_rate = (learning_rate - end_learning_rate) *
                        (1 - global_step / decay_steps) ^ (power) +
                        end_learning_rate

实例: 学习率在10000次迭代内从0.1衰减到0.01，使用开平方指数

global_step = tf.Variable(0, trainable=False)
starter_learning_rate = 0.1
end_learning_rate = 0.01
decay_steps = 10000
learning_rate = tf.train.polynomial_decay(starter_learning_rate, global_step,
                                          decay_steps, end_learning_rate,
                                          power=0.5)
# Passing global_step to minimize() will increment it at each step.
learning_step = (
    tf.train.GradientDescentOptimizer(learning_rate)
    .minimize(...my loss..., global_step=global_step)
)