Aichallenge.org has started their third AI contest this year: Ants.
The AI Challenge is all about creating artificial intelligence, whether you are a beginning programmer or an expert. ... [Y]ou will create a computer program (in any language) that controls a colony of ants which fight against other colonies for domination. ... The current phase of the contest will end December 18th at 11:59pm EST. At that time submissions will be closed. Shortly thereafter the final tournament will be started. ... Upon completion the contest winner will be announced and all results will be publically available.
Ants is a multi-player strategy game set on a plot of dirt with water for obstacles and food that randomly drops. Each player has one or more hills where ants will spawn. The objective is for players to seek and destroy the most enemy ant hills while defending their own hills. Players must also gather food to spawn more ants, however, if all of a player's hills are destroyed they can't spawn any more ants.
I mentioned this in the open thread, and there was a discussion about possibly making one or more "official" LessWrong teams. D_Alex has offered a motivational prize. If this interests you, please discuss in the comments!
I would not expect to win without a method that I could see to approximate or to exceed linear-programming formulations of multi-agent path planning, for example here (2005/2008) or here (2001). Those methods don't fully cover the stochasticity of resource gathering or the adversariality of combat, but they partly cover resource-finding and patrolling (when up-to-date visual information about unknowns is an objective) and deployment, and they provide a framework into which to fit tradeoffs among options evaluated by more specialized models, such as for combat, exploration, or gathering.
One approximation would be a relaxation) of the ant indicator function to a basis) of wavelet-like vectors (for example diffusion kernels) on the graph of connected land squares. (The basis vectors should overlap smoothly, because under a rigorous relaxation, non-overlapping basis vectors would allow approximated ants to teleport across the support) of basis elements.)
Lots of food for thought there. Clearly I didn't have enough math in college.
For global ant allocation and food gathering, it's very possible that the approach you're describing is the best you could practically do. For more local combat situations, though, I don't think that's clear at all-- if I had infinite computing resources, I'd be using an appropriate adaptation of minimax.
Anyway, you gave me some words for concepts and some new concepts, so upvote for you.