Random partition techniques for lasso and elastic net

I have implemented lasso, elastic net and a different estimator on a real data set. I used 10-fold cross-validation (CV) one time without replication for each method. Then I report the coefficient estimates and the test set mse values. But someone said one time is not enough to compare the estimators and suggested me to use random partitions technique.

I'm confused about this situation. I searched on internet, but could not find random partitions technique in the notion of penalized regression.

What should I do?

• Repeat CV 5 or 10 times. Report the average of test mse values.

But in this case, I can not report the coefficient estimates because it changes for all splitting. Also, the selected variables are not the same for all CV replicates.

OR

• Perform CV one time. Report coefficient estimates with bootstrap standard errors of these estimates.

Is this the point of random partitions technique?

Thanks in advance.