The premiere journal in Machine Learning, the Journal of Machine Learning Research (JMLR), has existed in this format since 2001. It is explicitly mentioned in the petition for the boycott: https://openaccess.engineering.oregonstate.edu/
Thanks for sharing! I founded the group since I was fed up with the Computer Science Facebook group for Cornell -- while there was occasionally interesting CS content, it was flooded by a lot of stuff that's either no longer interesting to me (a lot of it is Cornell undergraduate centric, while I'm now a graduate student at MIT), or just meme/jokish in nature. My goal was to make a group with interesting, thought-provoking content and better quality discussion. If this appeals to you, feel free to join and contribute.
There's a large body of work on variations of the secretary problem. The one I know of which is most relevant to your question is section 4 of the following:
http://www.cs.cornell.edu/~rdk/papers/secArt4.pdf
Section 6 is particularly interesting, where you're further restricted - you want to choose multiple secretaries, but there's certain constraints on the sets you can choose. For example, the secretaries might be edges in a graph, and you can't pick a subset of edges which would result in a cycle (this is a "graphic matroid," which is an example of a mathematical object known as a matroid). The reason why this formulation of the problem is interesting is because the best known algorithm is O(sqrt(log k))-competitive (where k is the rank of the matroid), whereas it is conjectured that an O(1)-competitive algorithm exists.