How to pick the best learning rate and optimizer using LearningRateScheduler

Question

I have known the LearningRateScheduler from Coursera course but copying it the same way will result in poor model performance. Perhaps due to the range I set. The instructions from Keras website is limited.

def duo_LSTM_model(X_train, y_train, X_test,y_test,num_classes,batch_size=68,units=128, learning_rate=0.005, epochs=20, dropout=0.2, recurrent_dropout=0.2 ):

    model = tf.keras.models.Sequential()
    model.add(tf.keras.layers.Masking(mask_value=0.0, input_shape=(X_train.shape[1], X_train.shape[2])))
    model.add(tf.keras.layers.Bidirectional(LSTM(units, dropout=dropout, recurrent_dropout=recurrent_dropout,return_sequences=True)))
    model.add(tf.keras.layers.Bidirectional(LSTM(units, dropout=dropout, recurrent_dropout=recurrent_dropout)))
    model.add(Dense(num_classes, activation='softmax'))

    adamopt = tf.keras.optimizers.Adam(lr=learning_rate, beta_1=0.9, beta_2=0.999, epsilon=1e-8)
    RMSopt = tf.keras.optimizers.RMSprop(lr=learning_rate, rho=0.9, epsilon=1e-6)
    SGDopt = tf.keras.optimizers.SGD(lr=learning_rate, momentum=0.9, decay=0.1, nesterov=False)


    lr_schedule = tf.keras.callbacks.LearningRateScheduler(
    lambda epoch: 1e-8 * 10**(epoch / 20))

    model.compile(loss='binary_crossentropy',
                  optimizer=adamopt,
                  metrics=['accuracy'])

    history = model.fit(X_train, y_train,
                        batch_size=batch_size,
                        epochs=epochs,
                        validation_data=(X_test, y_test),
                        verbose=1,
                        callbacks=[lr_schedule])

    score, acc = model.evaluate(X_test, y_test,
                                batch_size=batch_size)

    yhat = model.predict(X_test)

    return history, that

I have two questions.

1. How 1e-8 * 10**(epoch / 20) does this work?

2. How should we choose the range for the 3 different optimizers?

Answer 1

Before answering the two questions in your post, let's first clarify LearningRateScheduler is not for picking the 'best' learning rate.

It is an alternative to using a fixed learning rate is to instead vary the learning rate over the training process.

I think what you really want to ask is "how to determine the best initial learning rate". If I am correct, then you need to learn about hyperparameter tuning.

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Answer to Q1:

In order to answer how 1e-8 * 10**(epoch / 20) works, let's create a simple regression task

import tensorflow as tf 
import tensorflow.keras.backend as K
from sklearn.model_selection import train_test_split
from tensorflow.keras.models import Model
from tensorflow.keras.layers import Input,Dense

x = np.linspace(0,100,1000)
y = np.sin(x) + x**2

x_train,x_val,y_train,y_val = train_test_split(x,y,test_size=0.3)

input_x = Input(shape=(1,))
y = Dense(10,activation='relu')(input_x)
y = Dense(1,activation='relu')(y)
model = Model(inputs=input_x,outputs=y)

adamopt = tf.keras.optimizers.Adam(lr=0.01, beta_1=0.9, beta_2=0.999, epsilon=1e-8)

def schedule_func(epoch):
    print()
    print('calling lr_scheduler on epoch %i' % epoch)
    print('current learning rate %.8f' % K.eval(model.optimizer.lr))
    print('returned value %.8f' % (1e-8 * 10**(epoch / 20)))
    return 1e-8 * 10**(epoch / 20)
    
lr_schedule = tf.keras.callbacks.LearningRateScheduler(schedule_func)

model.compile(loss='mse',optimizer=adamopt,metrics=['mae'])
history = model.fit(x_train,y_train,
                    batch_size=8,
                    epochs=10,
                    validation_data=(x_val, y_val),
                    verbose=1,
                    callbacks=[lr_schedule])

In the script above, instead of using a lambda function, I wrote a function schedule_func . Running the script, you will see that 1e-8 * 10**(epoch / 20) just set the learning rate for each epoch , and the learning rate is increasing.

Answer to Q2:

There are a bunch of nice posts, for example

1. Setting the learning rate of your neural network.
2. Choosing a learning rate