学习率：余弦退火衰减策略（附代码+在cifar10上采用余弦退火衰减）

学习率会在刚开始的时候上升，加快模型的收敛速度，寻找最优点位置，到达一定step后，学习率下降，此时我们可以认为这是一个模型在微调的过程。上升采用线性上升，下降采用cos函数下降。

step = （训练样本数 * 训练epoch ）/batch_size
0.001是自己设置的learning_base点。

下面为cifar-10数据集，学习采用余弦退火衰减

实现方式如下，利用Callback实现，与普通的ReduceLROnPlateau调用方式类似：

import numpy as np
import matplotlib.pyplot as plt
import keras
from keras import backend as K
from keras.layers import Flatten,Conv2D,Dropout,Input,Dense,MaxPooling2D
from keras.models import Model

def exponent(global_epoch,
            learning_rate_base,
            decay_rate,
            min_learn_rate=0,
            ):

    learning_rate = learning_rate_base * pow(decay_rate, global_epoch)
    learning_rate = max(learning_rate,min_learn_rate)
    return learning_rate


class ExponentDecayScheduler(keras.callbacks.Callback):
    """
    继承Callback，实现对学习率的调度
    """
    def __init__(self,
                 learning_rate_base,
                 decay_rate,
                 global_epoch_init=0,
                 min_learn_rate=0,
                 verbose=0):
        super(ExponentDecayScheduler, self).__init__()
        # 基础的学习率
        self.learning_rate_base = learning_rate_base
        # 全局初始化epoch
        self.global_epoch = global_epoch_init

        self.decay_rate = decay_rate
        # 参数显示  
        self.verbose = verbose
        # learning_rates用于记录每次更新后的学习率，方便图形化观察
        self.min_learn_rate = min_learn_rate
        self.learning_rates = []

    def on_epoch_end(self, epochs ,logs=None):
        self.global_epoch = self.global_epoch + 1
        lr = K.get_value(self.model.optimizer.lr)
        self.learning_rates.append(lr)
	#更新学习率
    def on_epoch_begin(self, batch, logs=None):
        lr = exponent(global_epoch=self.global_epoch,
                    learning_rate_base=self.learning_rate_base,
                    decay_rate = self.decay_rate,
                    min_learn_rate = self.min_learn_rate)
        K.set_value(self.model.optimizer.lr, lr)
        if self.verbose > 0:
            print('\nBatch %05d: setting learning '
                  'rate to %s.' % (self.global_epoch + 1, lr))

# 载入Mnist手写数据集
cifar10= keras.datasets.cifar10
(x_train, y_train), (x_test, y_test) = cifar10.load_data()
x_train, x_test = x_train / 255.0, x_test / 255.0

#-----------------------------#
#   创建模型
#-----------------------------#
inputs = Input([28,28,1])
x = Conv2D(32, kernel_size= 5,padding = 'same',activation="relu")(inputs)
x = MaxPooling2D(pool_size = 2, strides = 2, padding = 'same',)(x)
x = Conv2D(64, kernel_size= 5,padding = 'same',activation="relu")(x)
x = MaxPooling2D(pool_size = 2, strides = 2, padding = 'same',)(x)
x = Flatten()(x)
x = Dense(1024)(x)
x = Dense(256)(x)
out = Dense(10, activation='softmax')(x)
model = Model(inputs,out)

# 设定优化器，loss，计算准确率
model.compile(optimizer='adam',
              loss='sparse_categorical_crossentropy',
              metrics=['accuracy'])

# 设置训练参数
epochs = 10

init_epoch = 0
# 每一次训练使用多少个Batch
batch_size = 256
# 最大学习率
learning_rate_base = 1e-3

sample_count = len(x_train)

# 学习率
exponent_lr = ExponentDecayScheduler(learning_rate_base = learning_rate_base,
                                    global_epoch_init = init_epoch,
                                    decay_rate = 0.9,
                                    min_learn_rate = 1e-6
                                    )

# 利用fit进行训练
model.fit(x_train, y_train, epochs=epochs, batch_size=batch_size,
            verbose=1, callbacks=[exponent_lr])
            
plt.plot(exponent_lr.learning_rates)
plt.xlabel('Step', fontsize=20)
plt.ylabel('lr', fontsize=20)
plt.axis([0, epochs, 0, learning_rate_base*1.1])
plt.xticks(np.arange(0, epochs, 1))
plt.grid()
plt.title('lr decay with exponent', fontsize=20)
plt.show()