标题： 波兰空间中折扣连续时间约束马尔可夫决策过程 显示英文标题

标题： Discounted continuous-time constrained Markov decision processes in Polish spaces

摘要： 本文致力于研究受限的连续时间马尔可夫决策过程（MDP），所考虑的策略类依赖于状态的历史信息。 转移速率可能是无界的，奖励和代价函数允许上下无界，并且状态空间和行动空间均为波莱尔空间。 优化目标是最小化预期折扣奖励，而约束条件可以是对预期折扣代价的限制。 首先，我们给出保证基础过程非爆炸以及预期折扣奖励/代价有限性的条件。 其次，利用占用测度技术，我们证明了连续时间MDP的受限最优性可以通过一个等价问题（最优性问题）来转化，该等价问题是在一类概率测度上定义的。 基于这个等价问题以及本文发展的所谓$\bar{w}$-弱收敛性，我们证明了存在一个受限的最优策略。 第三，通过提供等价问题的线性规划公式，我们展示了受限最优策略的可解性。 最后，我们用两个可计算的例子来说明我们的主要结果。 显示英文摘要

摘要： This paper is devoted to studying constrained continuous-time Markov decision processes (MDPs) in the class of randomized policies depending on state histories. The transition rates may be unbounded, the reward and costs are admitted to be unbounded from above and from below, and the state and action spaces are Polish spaces. The optimality criterion to be maximized is the expected discounted rewards, and the constraints can be imposed on the expected discounted costs. First, we give conditions for the nonexplosion of underlying processes and the finiteness of the expected discounted rewards/costs. Second, using a technique of occupation measures, we prove that the constrained optimality of continuous-time MDPs can be transformed to an equivalent (optimality) problem over a class of probability measures. Based on the equivalent problem and a so-called $\bar{w}$-weak convergence of probability measures developed in this paper, we show the existence of a constrained optimal policy. Third, by providing a linear programming formulation of the equivalent problem, we show the solvability of constrained optimal policies. Finally, we use two computable examples to illustrate our main results.