I am currently a Math PhD about to defend in January. I work in a field in functional analysis that uses a lot of measure theory (but no stats).

I have been considering transitioning careers since I don't enjoy my research area anymore. I have enjoyed taking a couple graduate courses in Machine learning/DS at my University and performed well in these. I have since had the itch to do research in these areas (I have been especially enjoying bandits and reinforcement learning in general due to their deep mathematical roots). All the research related jobs/internships I have looked at so far seem to require either a graduate degree in CS or publications in ML (which I do not have due to being new in this field)

My questions are as follows: Is it realistically possible transition into a job doing research in ML without a second PhD? What steps could I take to get some publications (are there research topics that are easier to transition into?)

Thanks very much for your help!