A Span Seminorm Approach to Controlled Markov Set-Chains

摘要

In a controlled Markov set-chain with finite state and action spaces, we find a policy, called average-optimal, which maximizes Cesaro sums of each timeu27s reward over all stationaly policies under some partial order. Under uniformly scrambling conditions, the dynamic programming operator for our model is proved to be a contraction in a span seminorm. And, analysing the behavior of expected total rewards over the T-horizon as T approaches ∞ by a fixed point of a span-contraction operator we give a constructive proof for the existence of an average-optimal policy.