Incremental self-improvement for life-time multi-agent reinforcement learning

Previous approaches to multi-agent reinforcement learning are either very limited or heuris-tic by nature. The main reason is: each agent's or \animat's" environment continually changes because the other learning animats keep changing. Traditional reinforcement learning algorithms cannot properly deal with this. Their convergence theorems require repeatable trials and strong (typically Markovian) assumptions about the environment. In this paper, however, we use a novel, general, sound method for multiple, reinforcement learning \animats", each living a single life with limited computational resources in an unrestricted, changing environment. The method is called \incremental self-improvement" (IS | Schmidhuber, 1994). IS properly takes into account that whatever some animat learns at some point may aaect learning conditions for other animats or for itself at any later point. The learning algorithm of an IS-based animat is embedded in its own policy | the animat cannot only improve its performance, but in principle also improve the way it improves etc. At certain times in the animat's life, IS uses reinforce-ment/time ratios to estimate from a single training example (namely the entire life so far) which previously learned things are still useful, and selectively keeps them but gets rid of those that start appearing harmful. IS is based on an ee-cient, stack-based backtracking procedure which is guaranteed to make each animat's learning history a history of long-term reinforcement accelerations. Experiments demonstrate IS' eeectiveness. In one experiment, IS learns a sequence of more and more complex function approximation problems. In another, a multi-agent system consisting of three co-evolving, IS-based animats chasing each other learns interesting, stochastic predator and prey strategies.