To implement cosine annealing or warm restarts in the context of training neural networks, you need to adjust the learning rate during training. Cosine annealing gradually reduces the learning rate using a cosine function, while warm restarts involve periodically resetting the learning rate to a higher value during training. Both methods help in improving the training process by allowing for better convergence and potentially escaping local minima.
To implement cosine annealing, you typically define a few parameters, such as the initial learning rate, the minimum learning rate, and the total number of training epochs. The learning rate at each epoch ( t ) can then be calculated using the formula:
[ \text{lr}(t) = \text{lr}{\text{min}} + 0.5 \times (\text{lr}{\text{initial}} - \text{lr}{\text{min}}) \times (1 + \cos(\frac{t}{T{\text{max}}} \times \pi)), ]
where ( T_{\text{max}} ) is the total number of epochs for one cycle. This method allows the learning rate to start high, reduce it gradually, and smooth out the training process by reducing noise and stabilizing updates.
Warm restarts build on cosine annealing by introducing periodic high learning rate resets. You can define various cycles, each with its own ( T_{\text{max}} ). After completing a cycle, you reset the learning rate back to a higher initial value (often called ( \text{lr}{\text{restart}} )) and repeat the cosine schedule. For example, in the first cycle, you might set ( T{\text{max}} ) to 10 epochs and after the first cycle, restart the learning to, say, 0.01. This strategy can be implemented using existing deep learning frameworks like PyTorch, which offer built-in support for such learning rate schedulers, making it easier for developers to apply these techniques without starting from scratch.