Let's say I run an Ordinary Least Square regression with a Ridge regression on 100.000 points randomly sampled from a huge dataset. The best regularization strength found is C=1.
What is approximately the optimal regularization strength I can expect if I run the same algorithm on 1.000.000 points from the same dataset ?
Are there general rules that link the optimal regularization strength and the problem size ? Do these rules rely on statistical assumptions ? / What is their robustness ?