Overview of AdamW
AdamW is a stochastic optimization method used to optimize machine learning models. It is an improvement on the traditional Adam algorithm by decoupling the weight decay from the gradient update. Weight decay is a common regularization technique used to prevent overfitting during training.
Background
Before understanding AdamW, it is important to understand some fundamental concepts in machine learning optimization. In machine learning, optimization refers to the process of finding the best set of model parameters that minimizes the training loss. The optimization algorithm used to achieve this goal is also known as an optimizer.
One of the most popular optimization algorithms used in deep learning is the stochastic gradient descent (SGD) algorithm. SGD works by iteratively updating the model parameters using the gradient of the loss function with respect to the parameters. The gradient is multiplied by a learning rate, which determines the step size of the update.
While SGD is effective for many problems, it can become slow and inefficient for large-scale deep learning problems. Adam is an improvement on SGD that includes adaptive learning rates and momentum to speed up the optimization process. In addition, Adam includes L2 regularization (weight decay) to prevent overfitting during training.
The Problem with L2 Regularization in Adam
One issue with the traditional Adam algorithm is how it implements L2 regularization. L2 regularization involves adding a small penalty term to the loss function that encourages the model to have smaller parameter values. In Adam, L2 regularization is implemented by adding a weight decay term to the gradient update:
$$ g_{t} = \nabla f(\theta_{t}) + w_{t}\theta_{t} $$
This means that the weight decay term is added to the gradient before the learning rate is applied. The problem with this approach is that the weight decay term can dominate the update, especially when the learning rate is small. This can cause the model parameters to become too small, leading to poor performance.
AdamW to the Rescue
AdamW solves this problem by decoupling the weight decay from the gradient update. Instead of adding the weight decay term to the gradient, AdamW includes it in the update rule:
$$ \theta_{t+1, i} = \theta_{t, i} - \eta(\frac{1}{\sqrt{\hat{v}_{t} + \epsilon}}\cdot{\hat{m}_{t}} + w_{t, i}\theta_{t, i}), \forall{t} $$
Here, the weight decay term is included in the update directly, rather than being added to the gradient. This means that the weight decay can now be applied without affecting the learning rate as much.
AdamW has been shown to improve the performance of deep learning models compared to traditional Adam, especially for large-scale problems. It has become a popular optimization algorithm in the machine learning community and is supported by popular deep learning frameworks such as PyTorch and TensorFlow.
AdamW is a stochastic optimization method that improves upon the traditional Adam algorithm by decoupling the weight decay from the gradient update. This approach allows for more effective regularization during training without adversely affecting the learning rate. AdamW has become popular in the machine learning community and has been shown to improve the performance of deep learning models, especially for large-scale problems. Its implementation is supported by popular deep learning frameworks such as PyTorch and TensorFlow.
