AdamW Optimizer Introduction | Generated by AI
Question: What is a comprehensive introduction to the AdamW optimizer?
Answer:
Introduction to AdamW Optimizer
The AdamW optimizer is a widely used variant of the Adam (Adaptive Moment Estimation) optimizer in deep learning. It was introduced to address limitations in how standard Adam handles weight regularization, leading to improved generalization and performance, especially in large-scale models like transformers.
AdamW stands for “Adam with decoupled Weight decay” and is based on the paper “Decoupled Weight Decay Regularization” by Ilya Loshchilov and Frank Hutter (2019).
Background: The Adam Optimizer
To understand AdamW, it’s helpful to first recall Adam:
- Adam combines ideas from Momentum (using the first moment: exponentially decaying average of past gradients) and RMSProp (using the second moment: exponentially decaying average of past squared gradients).
- It computes adaptive learning rates for each parameter.
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The update rule (simplified) is:
- Compute gradient \( g_t \)
- Update biased first moment: \( m_t = \beta_1 m_{t-1} + (1 - \beta_1) g_t \)
- Update biased second moment: \( v_t = \beta_2 v_{t-1} + (1 - \beta_2) g_t^2 \)
- Bias-correct: \( \hat{m}_t = m_t / (1 - \beta_1^t) \), \( \hat{v}_t = v_t / (1 - \beta_2^t) \)
- Update parameters: \( \theta_{t+1} = \theta_t - \eta \cdot \hat{m}_t / (\sqrt{\hat{v}_t} + \epsilon) \)
Typical hyperparameters: \( \eta = 0.001 \), \( \beta_1 = 0.9 \), \( \beta_2 = 0.999 \), \( \epsilon = 10^{-8} \).
Adam is efficient and requires little hyperparameter tuning, but it sometimes generalizes worse than SGD with momentum, especially with strong regularization.
The Problem with Weight Decay in Adam
Weight decay is a common regularization technique to prevent overfitting by penalizing large weights (equivalent to L2 regularization in SGD).
- In standard SGD, adding L2 regularization to the loss is mathematically equivalent to “weight decay” (directly shrinking parameters: \( \theta \leftarrow \theta (1 - \eta \lambda) - \eta g \)).
- However, in adaptive optimizers like Adam, these are not equivalent.
- Most early implementations of Adam added weight decay via L2 regularization (modifying the gradient: \( g_t \leftarrow g_t + \lambda \theta_t \)), which interferes with Adam’s adaptive learning rates.
- This coupling makes the effective regularization depend on the learning rate, leading to suboptimal generalization.
Key Innovation in AdamW: Decoupled Weight Decay
AdamW fixes this by decoupling weight decay from the gradient update:
- Perform the Adam update as usual (on the loss gradient only).
- Then, apply weight decay directly to the parameters.
The parameter update becomes:
\[ \theta_{t+1} = \theta_t - \eta_t \cdot \frac{\hat{m}_t}{\sqrt{\hat{v}_t} + \epsilon} - \lambda \eta_t \cdot \theta_t \]
(or equivalently, first apply decay: \( \theta_t \leftarrow \theta_t (1 - \lambda \eta_t) \), then Adam step).
This makes weight decay behave like true SGD weight decay: independent of the adaptive mechanism, and the optimal \( \lambda \) is less dependent on the learning rate \( \eta \).
Benefits of AdamW
- Better generalization: Significantly reduces overfitting compared to standard Adam with L2.
- Improved performance: Matches or exceeds SGD with momentum on tasks like image classification (e.g., better results on CIFAR-10/100, ImageNet).
- Stable training: Works well with learning rate schedules (e.g., cosine annealing, warm restarts).
- Decoupled hyperparameters: Easier tuning of learning rate and weight decay separately.
- Widely adopted in modern models: BERT, ViT, GPT series, and most transformer-based architectures use AdamW.
Usage and Hyperparameters
In libraries like PyTorch and TensorFlow/Keras:
- Typical settings: learning rate \( 10^{-4} \) to \( 10^{-3} \), weight decay \( 0.01 \) to \( 0.05 \).
- Often combined with learning rate warm-up and decay schedules.
Example in PyTorch:
optimizer = torch.optim.AdamW(model.parameters(), lr=3e-4, weight_decay=0.01)
When to Use AdamW
- Preferred over plain Adam for most supervised deep learning tasks, especially with large models or when regularization is important.
- Still adaptive and robust like Adam, but with better regularization properties.
In summary, AdamW is a simple yet powerful improvement over Adam that has become the default optimizer in many state-of-the-art deep learning pipelines.
References:
- Decoupled Weight Decay Regularization (original paper)
- PyTorch AdamW Documentation
- Keras AdamW Documentation