I$\text{'}$m learning about survival analysis and I$\text{'}$m interested in implementing L$1$ and L$2$ regularization in a survival model using PyTorch. Could someone provide a detailed explanation and code example on how to achieve this? Specifically, I would like to understand:

How to incorporate L$1$ regularization into the loss function for a survival model.

How to apply L$2$ regularization $($weight decay$)$ using an optimizer in PyTorch.

An example of a survival model, such as a Cox Proportional Hazards model, with these regularization techniques applied.

Thank you for your assistance!