Optimizers

Introduction to TensorFlow in Python

Isaiah Hull

Visiting Associate Professor of Finance, BI Norwegian Business School

How to find a minimum

The image shows the Grand Canyon.

¹ Source: U.S. National Park Service

How to find a minimum

The image shows the Grand Canyon.

¹ Source: U.S. National Park Service

How to find a minimum

The image shows the Grand Canyon.

¹ Source: U.S. National Park Service

The figure shows the learning path of the SGD, RMS prop, and Adam optimizers for a simple problem.

The gradient descent optimizer

Stochastic gradient descent (SGD) optimizer
- tf.keras.optimizers.SGD()
- learning_rate
Simple and easy to interpret

The RMS prop optimizer

Root mean squared (RMS) propagation optimizer
- Applies different learning rates to each feature
- tf.keras.optimizers.RMSprop()
- learning_rate
- momentum
- decay
Allows for momentum to both build and decay

The adam optimizer

Adaptive moment (adam) optimizer
- tf.keras.optimizers.Adam()
- learning_rate
- beta1
Performs well with default parameter values

A complete example

import tensorflow as tf

# Define the model function
def model(bias, weights, features = borrower_features):
    product = tf.matmul(features, weights)
    return tf.keras.activations.sigmoid(product+bias)

# Compute the predicted values and loss
def loss_function(bias, weights, targets = default, features = borrower_features):
    predictions = model(bias, weights)
    return tf.keras.losses.binary_crossentropy(targets, predictions)

# Minimize the loss function with RMS propagation
opt = tf.keras.optimizers.RMSprop(learning_rate=0.01, momentum=0.9)
opt.minimize(lambda: loss_function(bias, weights), var_list=[bias, weights])

Let's practice!

Introduction to TensorFlow in Python