论文标题
具有普遍可衡量的策略的离散时间随机控制中的战略措施和最佳性能
On Strategic Measures and Optimality Properties in Discrete-Time Stochastic Control with Universally Measurable Policies
论文作者
论文摘要
本文涉及具有Borel状态和动作空间以及普遍可衡量的策略的离散时间无限的随机控制系统。我们研究了这些系统中政策引起的战略措施的优化问题。然后将结果应用于风险中性和风险敏感的马尔可夫决策过程及其部分可观察到的对应物，以建立最佳价值函数的可衡量性，并存在普遍的$ε$ $ - $ $ - $ - $ - $ - $ - $ - $ - 优越的政策的普通成本成本标准和风险标准和风险标准和风险criteria的情况。我们还将分析扩展到一类Minimax控制问题，并在分析确定性的公理下建立相似的最佳结果。
This paper concerns discrete-time infinite-horizon stochastic control systems with Borel state and action spaces and universally measurable policies. We study optimization problems on strategic measures induced by the policies in these systems. The results are then applied to risk-neutral and risk-sensitive Markov decision processes, as well as their partially observable counterparts, to establish the measurability of the optimal value functions and the existence of universally measurable, randomized or nonrandomized, $ε$-optimal policies, for a variety of average cost criteria and risk criteria. We also extend our analysis to a class of minimax control problems and establish similar optimality results under the axiom of analytic determinacy.
