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### claude:

Here's how to implement L2 regularization (also known as weight decay or Ridge regularization) in the R torch package:

# Method 1: Using weight_decay in optimizer (recommended approach)
# Weight decay parameter is the L2 regularization strength
optimizer <- optim_sgd(net$parameters, lr = 0.01, weight_decay = 0.01)

The key difference compared to L1 regularization is:

    1. For L2 regularization, most optimizers (like SGD, Adam, etc.) have a built-in weight_decay parameter that implements L2 regularization efficiently.
    2. If implementing manually, L2 uses the sum of squared weights (torch_pow) instead of absolute values.


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### help for optim_rmsprop

optim_rmsprop              package:torch               R Documentation

RMSprop optimizer

Description:

     Proposed by G. Hinton in his course.

Usage:

     optim_rmsprop(
       params,
       lr = 0.01,
       alpha = 0.99,
       eps = 1e-08,
       weight_decay = 0,
       momentum = 0,
       centered = FALSE
     )
     
Arguments:

  params: (iterable): iterable of parameters to optimize or list
          defining parameter groups

      lr: (float, optional): learning rate (default: 1e-2)

   alpha: (float, optional): smoothing constant (default: 0.99)

     eps: (float, optional): term added to the denominator to improve
          numerical stability (default: 1e-8)

weight_decay: optional weight decay penalty. (default: 0)

momentum: (float, optional): momentum factor (default: 0)

centered: (bool, optional) : if ‘TRUE’, compute the centered RMSProp,
          the gradient is normalized by an estimation of its variance
          weight_decay (float, optional): weight decay (L2 penalty)
          (default: 0)