Learning Rate decay

Learning Rate Decay

Learning rate decay is a technique used to adjust the learning rate during training in order to improve the convergence of the optimization algorithm. The idea behind learning rate decay is to gradually decrease the learning rate over time as the training progresses, so that the optimization process can focus on the finer details of the loss function.

Learning Rate Decay methods:

Exponential decay:    lr = lr_0 * e^(- d * t)
  • The learning rate is decreased exponentially over time, where the decay rate d and initial learning rate lr_0 are hyperparameters.
  • The learning rate decreases quickly at the beginning and then slows down as time goes by.
Time-based decay:    lr = lr_0 / (1 + d * t)
  • The learning rate is decreased linearly over time, where the decay rate d and initial learning rate lr_0 are hyperparameters.
  • The learning rate decreases in a steady and gradual manner.

Step decay:    lr = lr_0 * d^(epoch // epoch_drops)
  • The learning rate is decreased by a factor of d after a fixed number of epochs, where the number of epochs before each drop and the drop factor d are hyperparameters.
  • The learning rate decreases suddenly at specific epochs.

Mechanism:

  • Gradually reduces the learning rate as training progresses.
  • Can be implemented in various ways such as step decay, exponential decay, and polynomial decay.

Pros:

  • Can help the optimizer converge faster and more reliably
  • Can help prevent the optimization process from overshooting the minimum
  • Can lead to better generalization and lower test error
  • Can be implemented easily and efficiently

Cons:

  • There are too many hyper-parameters that require tuning
  • Hard to know when the learning rate should drop ahead of training
  • Because the hyper-parameters are static, it’s not adaptive
  • Better to use adaptive learning rate optimization methods (RMSprop, Adam, etc.)

Code with numpy:

def learning_rate_decay(alpha, decay_rate, global_step, decay_step):
    """
    @alpha is the original learning rate
    @decay_rate is the weight used to
    determine the rate at which alpha will decay
    @global_step is the number of passes of gradient descent that have elapsed
    @decay_step is the number of passes of gradient descent
    that should occur before alpha is decayed further
    Returns: the updated value for alpha
    """
    alpha = alpha / (1 + decay_rate * np.floor(global_step / decay_step))
    return alpha

Code with tensorflow:

def learning_rate_decay(alpha, decay_rate, global_step, decay_step):
    """
    @alpha is the original learning rate
    @decay_rate is the weight used to determine
    the rate at which alpha will decay
    @global_step is the number of passes of gradient descent that have elapsed
    @decay_step is the number of passes of gradient descent that
    should occur before alpha is decayed further
    Returns: the learning rate decay operation
    """

    learning_rate = tf.train.inverse_time_decay(alpha,
                                                global_step,
                                                decay_step,
                                                decay_rate,
                                                staircase=True)

    return learning_rate

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