They work on hyper parameters. They will not have assumptions. They work with big data and when you have big data, they are rarely parametric.

In linear regression, the linear model parameter can be estimated by Ordinary Least Squares (OLS). The estimator can have a bias and a large variance. If the linear model contains many predictor variables or if these variables are correlated, the standard OLS parameter estimates have large variance, thus making the model unreliable.

Regularization is a technique to reduce many predictor variables by penalization of the coefficients, allowing to decrease this variance at the cost of introducing some bias. Ridge regression and LASSO regression are two different penalizations. There are some recommendation, which of them can be preferred in a situation. Elastic net is a convex combination of Ridge and Lasso. They do not imply different assumptions.

Thank you so much Anuraj Nayarisseri and Manfred Staat for your answer. It is a very great help for me