On Average Optimality for Non-Stationary Markov Decision Processes in Borel Spaces

This paper studies Borel models of nonstationary Markov decision processes (MDPs) with average criteria. We establish a suitable fixed point theorem, which is used to show the existence of solutions to the average optimality equation (AOE), without using contractions. The existence of optimal policies follows from the obtained solutions to the AOE. Furthermore, we show that versions of the rolling horizon algorithm can be used to produce an optimal policy or an ϵ-optimal policy. Finally, we compare the optimality conditions imposed in this paper with the existing ones in the literature, and demonstrate that they can be satisfied while the previous ones are not. Funding: This research was supported by National Key Research and Development Program of China [2022YFA1004600], National Natural Science Foundation of China [No. 12301170], Guangdong Basic and Applied Research Foundation [2023A1515012644], and the Fundamental Research Funds for the Central Universities, Sun Yat-Sen University [No. 23qnpy39].