Weighted Markov decision processes with perturbation

Considers the weighted reward MDPs with perturbation. The authors give the proof of existence of a δ-optimal simple ultimately deterministic policy under the assumption of “scalar value”. The authors also prove that there exists a δ-i-optimal simple ultimately deterministic policy in the perturbed weighted MDP, for all ε ∈[0,ε´] even without the assumption of “scalar value”