Probably start off by trying some off-the-shelf deep reinforcement learning algorithms, since some of these have been tested with similar environments.

At the very least it would be interesting to see what kind of stuff will happen when you put two of these against each other. I really like how this has been tried in the past with Toribash (found some threads from 2008 talking about NEATs).

Also: I just now realized what a simple, plug-and-play "AI solution" for Toribash could do to the game (more botting). I think this needs some good thinking before sharing anything.