Percentile objective criteria in limiting average Markov control problems

The point of view is adopted that there are many natural situations in which the controller is interested in finding a policy that will achieve a sufficiently high long-run average reward, that is, a target level with a sufficiently high probability, that is, a percentile. The key conceptual difference between this approach and the classical problem is that the present controller is not searching for an optimal policy but rather for a policy that is `good enough´, knowing that such a policy will typically fail to exist if the target level and the percentile are set too high. Conceptually, the approach is somewhat analogous to that often adopted by statisticians in testing of hypotheses where it is desirable (but usually not possible) to minimize simultaneously the so-called `type 1´ and the `type 2´ errors