For Logistic Regression, it is not necessary to break symmetry by using random initialization. It can learn from initial values of all zeros or any other symmetric initialization. Here is a thread which discusses that and shows the math behind this point. What you will see on that thread is that symmetry breaking is required once we graduate to real neural networks, but LR is a special case.
Now it may be possible that using random values could allow for faster learning, but I did a few quick experiments a couple of years ago and it didn’t really seem to make any significant difference in the performance of the training (the cpu time and wall clock time to achieve a given level of convergence). But perhaps I didn’t use a sophisticated enough initialization algorithm. I have not taken MLS, so I don’t know what is discussed there, but initialization algorithms are covered in DLS Course 1 and Course 2 in some detail. So as Luis says, “stay tuned” for more information on that.