Is it reasonable to average LASSO coefficients from repeated reshuffling of training/test sets?
Suppose I randomly divide my data into testing & training sets, then within the training set use 10-fold cross-validation to choose an optimal $\lambda$, then refit on full training data and record the model coefficients. Now, suppose that I repeat this process $k$ number of times. Each iteration will choose slightly different coefficients. One might think to average these together. However, each iteration may not choose the same set of non-zero coefficients, therefore the average of all coefficients may contain many more non-zero coefficients than any single solution.
I found this similar brief discussion here, but I do not want to be confused by the additional discussion of multiple imputation: Combining LASSO coefficients across imputed datasets Please note that no answer was ever accepted for this question.