If we multiply one of predictors by a constant $c$ in the regression set-up for all data points. What happens to the weights (or specifically weight corresponding to that predictor) if we are doing Lasso/Ridge regression?
In the case of OLS it is clear the effect would be the corresponding weight will be multiplied by $1/c$. Now if we assume $c=2$ and let's assume we are doing Lasso. If we multiply that corresponding weight by $1/2$ the mean squared part of loss function doesn't change and the $L^1$ part decreases. So you can say the minima of the new loss function will be less than the older one. But I'm not sure whether this implies anything about the individual coefficients or not. This might also depend whether $c>1$ or $c<1$.