Optimization

Advanced Optimization: Adam Algorithm

Better Than Gradient Descent

Introduction to Optimization Challenges

• Gradient descent is a widely used optimization algorithm in machine learning
• Foundation for linear regression, logistic regression, and early neural networks
• However, newer optimization algorithms can train neural networks much faster

Note

Standard gradient descent updates parameters using: w_j = w_j - α * ∂J/∂w_j, where α is the learning rate.

Limitations of Standard Gradient Descent

Too Small Learning Rate

• When starting far from minimum
• Steps are small and in similar directions
• Convergence is unnecessarily slow
• Ideally would increase learning rate

Too Large Learning Rate

• When close to minimum or in narrow valleys
• Steps oscillate back and forth
• Never properly converges
• Ideally would decrease learning rate

Caution

The optimal learning rate often changes during training - too small in some regions, too large in others.

The Adam Algorithm

Adaptive Moment Estimation

• Adaptive Moment Estimation (Adam)
• Automatically adjusts learning rates during training
• Uses different learning rates for each parameter in your model
• For w₁ through w₁₀ and b, it maintains 11 different learning rates

Key Intuition:

• If parameter w_j consistently moves in same direction:

• Increase the learning rate for that specific parameter

• Accelerates progress toward minimum

• If parameter oscillates back and forth:

• Decrease the learning rate for that specific parameter

• Prevents bouncing and allows convergence

Note

The detailed mathematics of how Adam adjusts these rates is complex and beyond the scope of this course, but can be studied in advanced deep learning courses.

Implementation in TensorFlow

Adam Implementation

model = Sequential([
 Dense(25, activation='relu'),
 Dense(15, activation='relu'),
 Dense(1, activation='sigmoid')
])

model.compile(
 loss=tf.keras.losses.BinaryCrossentropy(),
 optimizer=tf.keras.optimizers.Adam(1e-3),  # Initial learning rate of 0.001
)

Tip

While Adam adapts learning rates automatically, it still requires an initial global learning rate. Try a few values (larger and smaller) to find what gives the fastest learning performance.

Advantages of Adam

• Typically works much faster than gradient descent
• More robust to the choice of initial learning rate
• Has become the de facto standard for training neural networks
• Safe choice for most deep learning applications

Practitioner's Choice

Note

“A safe choice would be to just use the Adam optimization algorithm, and most practitioners today will use Adam rather than the optional gradient descent algorithm.”

Looking Ahead

• Next videos will cover more advanced neural network concepts
• Will explore alternative layer types for neural networks

The Adam optimization algorithm provides significant training speedups by adaptively adjusting learning rates for each parameter. Instead of using a single global learning rate, it increases rates for parameters moving consistently in one direction and decreases rates for oscillating parameters. This adaptive approach has made Adam the preferred choice for most modern neural network training.