Fair decision making has largely been studied with respect to a single decision. In this paper we investigate the notion of fairness in the context of sequential decision making where multiple stakeholders can be affected by the outcomes of decisions, and where decision making may be informed by additional constraints and criteria beyond the requirement of fairness. In this setting, we observe that fairness often depends on the history of the sequential decision-making process and not just on the current state. To advance our understanding of this class of fairness problems, we define the notion of non-Markovian fairness in the context of sequential decision making. We identify properties of non-Markovian fairness, including notions of long-term, anytime, periodic, and bounded fairness. We further explore the interplay between non-Markovian fairness and memory, and how this can support construction of fair policies in sequential decision-making settings.

翻译：公平决策的研究主要围绕单次决策展开。本文考察序贯决策情境下的公平概念——在此情境中，多个利益相关者可能受到决策结果的影响，且决策过程除了公平性要求外，还需考虑额外的约束和标准。我们观察到，在此设置下，公平性往往取决于序贯决策过程的历史记录，而非仅当前状态。为深化对此类公平问题的理解，我们在序贯决策背景下定义了非马尔可夫公平性概念。我们明确了非马尔可夫公平性的性质，包括长期公平、随时公平、周期公平和有界公平等概念。进一步探讨了非马尔可夫公平性与记忆之间的相互作用，以及这种交互如何支持序贯决策场景中公平策略的构建。