I have a use case where I want to train a linear regression model (could be any of ridge, lasso, elastic net) but instead of regularizing the weights such that the coefficients tend to zero, I would like to penalize coefficients for deviating from prior weights that I've passed when initializing the model.
From theoretical knowledge and similar datasets, I already know roughly what the weights should be (e.g., which variables should be positively and which negatively correlated), so I would like the model to use these weights unless the given dataset strongly suggests that a coefficient should be adapted.

Basically, instead of doing
$$\min_w |w|^2 = |w-0|^2$$

for the regularization, I would like to do
$$\min_w |w-w_{prior}|^2$$

To encourage the weights to stay close to the$w_{prior}$ that I have given.