Another approach is to use Bayesian, and state some meaningful priors. This is implicit regularization (constraining) since the priors are "pulling" back the parameter values based on the data (likelihood), and in the end you get some kind of compromise between the two (posterior). One example I have is when estimating traffic flow, and I put a Poisson (or Half-Normal - works ok as well) distribution as my prior, with some gut-feeling/logically-reasonable parameters.