glmnet with binary logistic regression

I was also thinking of a bootstrapping approach where I would actually run
cv.glmnet say 100 times and then take the mean/median lambda across all the
cv.glmnet runs.  This way I generate a confidence interval for my optimal
lambda I woud use in the end.

A simpler approach is to increase the number of folds.  If you set the 
number of folds equal to n ("leave-one-out" cross validation), the 
outcome will no longer be random, as there is only one way of choosing 
the fold partitions.  The main reason people settle for 10-fold CV is 
computational convenience when n is large, which is not a large problem 
in your case.

Patrick Breheny
Assistant Professor
Department of Biostatistics
Department of Statistics
University of Kentucky