Remembering to Be Fair: On Non-Markovian Fairness in Sequential DecisionMaking

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.