AdamW optimization and implementation in PyTorch

The AdamW method was proposed in the paper “Decoupled Weight Decay Regularization” by Ilya Loshchilov and Frank Hutter. While the paper was officially published at the prestigious International Conference on Learning Representations (ICLR) in 2019, the influential preprint first appeared on the academic server arXiv in late 2017. This is when the method began to gain significant attention and adoption within the research community.

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AdamW is a modification of the popular Adam optimizer that addresses a fundamental flaw in how Adam handles weight decay, a crucial regularization technique for preventing overfitting. The “W” in AdamW stands for “Weight Decay.”

The key innovation of AdamW is the decoupling of weight decay from the gradient update. This seemingly small change has a significant impact on the training dynamics and the final performance of the model, often leading to better generalization and more stable training, especially for large and complex models.

The Problem with Adam’s Weight Decay

To understand AdamW, it’s essential to first grasp the issue with the original Adam optimizer’s implementation of weight decay. In deep learning, weight decay is a form of L2 regularization that penalizes large weights in the model. This is typically achieved by adding a term to the loss function that is proportional to the squared magnitude of the weights.

In the standard Adam optimizer, this L2 regularization term is incorporated directly into the gradient. This means that the adaptive learning rates, a core feature of Adam that adjusts the learning rate for each parameter, are also applied to the weight decay term. This coupling can lead to suboptimal performance.

Specifically, for weights with large gradients, the effective weight decay is reduced because the adaptive learning rate for that weight will be smaller. Conversely, for weights with small gradients, the effective weight decay is larger. This interaction can hinder the optimizer’s ability to find the most optimal set of weights and can make the training process more sensitive to the choice of hyperparameters.

AdamW to the Rescue: Decoupled Weight Decay

AdamW solves this problem by separating the weight decay from the gradient update. Instead of modifying the gradient, AdamW applies the weight decay directly to the weights after the gradient-based update.

Here’s a simplified breakdown of the process:

1. Calculate the gradients of the loss function with respect to the model’s weights.
2. Update the moving averages of the gradients and their squared values, just like in the standard Adam algorithm.
3. Perform the Adam update on the weights using these moving averages.
4. Apply weight decay by directly multiplying the updated weights by a factor slightly less than one.

This decoupling ensures that the weight decay is applied uniformly to all weights, regardless of the magnitude of their gradients. This leads to a more predictable and effective regularization, allowing the optimizer to converge to a better solution.

Advantages of Using AdamW

The primary benefits of using AdamW over the standard Adam optimizer include:

• Improved Generalization: By providing more effective regularization, AdamW helps models to generalize better to unseen data, reducing the risk of overfitting.
• More Stable Training: The decoupled weight decay leads to a more stable training process, making it less sensitive to the choice of learning rate and weight decay hyperparameters.
• Better Performance on Large Models: AdamW has been shown to be particularly effective for training large, complex models, such as transformers, which are prone to overfitting.

In essence, AdamW offers a more robust and reliable way to train deep neural networks by correcting a subtle but significant flaw in the original Adam optimizer. Its superior performance and stability have made it the optimizer of choice for many deep learning practitioners^.

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Implementation of AdamW in PyTorch 👨‍💻

Using AdamW in PyTorch is incredibly straightforward because it’s a built-in optimizer. You don’t need to implement the logic yourself; you simply import it and instantiate it like any other optimizer.

The class you need is torch.optim.AdamW. The key difference from using the standard torch.optim.Adam is that the weight_decay parameter in AdamW correctly applies the decoupled weight decay as proposed in the paper.

Here is a typical implementation snippet:

Python

import torch
import torch.nn as nn
import torch.optim as optim

# 1. Define your model (e.g., a simple linear layer)
model = nn.Linear(in_features=50, out_features=10)

# 2. Instantiate the AdamW optimizer
# Pass the model's parameters to the optimizer.
# Set the learning rate (lr) and the weight_decay value.
optimizer = optim.AdamW(
    model.parameters(), 
    lr=1e-3,           # Learning rate
    weight_decay=1e-2  # Weight decay coefficient
)

# 3. A standard training loop
# Assume 'data' and 'targets' are your input tensors
for data, targets in your_dataloader:
    # Zero out previous gradients
    optimizer.zero_grad()
    
    # Forward pass
    predictions = model(data)
    
    # Calculate loss
    loss = your_loss_function(predictions, targets)
    
    # Backward pass to compute gradients
    loss.backward()
    
    # Update the model's weights
    # This step applies the AdamW update rule, including the decoupled weight decay.
    optimizer.step()

In this code, the line optimizer = optim.AdamW(...) is where the magic happens. By choosing AdamW and setting a non-zero weight_decay, you are leveraging this improved optimization strategy to train your model more effectively.