学术报告（刘源远 2026.5.16）

摘要：In this talk, we will present some advances on discrete-time singular perturbations in Markov chains and Markov decision processes (MDPs) with general state spaces. For a singularly perturbed MDP, we will consider the optimal policy and the asymptotically optimal policy for the expected long-run average cost. Furthermore, we derive the error bounds on the difference betwen the value function for the perturbed MDP and the value function of the limit MDP. Our work extends existing results of the literature in the following two directions: the perturbed MDP is defined on general state and action spaces and we do not impose strong conditions on the recurrence structure of the MDP such as Doeblin’s condition.