Combinations and Mixtures of Optimal Policies in Unichain Markov Decision Processes are Optimal
<|reference_start|>Combinations and Mixtures of Optimal Policies in Unichain Markov Decision Processes are Optimal: We show that combinations of optimal (stationary) policies in unichain Markov decision processes are optimal. That is, let M be a unichain Markov decision process with state space S, action space A and policies \pi_j^*: S -> A (1\leq j\leq n) with optimal average infinite horizon reward. Then any combination \pi of these policies, where for each state i in S there is a j such that \pi(i)=\pi_j^*(i), is optimal as well. Furthermore, we prove that any mixture of optimal policies, where at each visit in a state i an arbitrary action \pi_j^*(i) of an optimal policy is chosen, yields optimal average reward, too.<|reference_end|>
@article{ortner2005combinations,
    title={Combinations and Mixtures of Optimal Policies in Unichain Markov
  Decision Processes are Optimal},
    author={Ronald Ortner},
    journal={arXiv preprint arXiv:math/0508319},
    year={2005},
    archivePrefix={arXiv},
    eprint={math/0508319},
    primaryClass={math.CO cs.DM cs.LG math.OC math.PR}
}