The Hurwicz Criterion for Data-Driven Decision-Making under Uncertainty
DescriptionThe Hurwicz criterion is arguably one of the most widely used rules in decision-making under uncertainty. It allows the decision maker to simultaneously take into account the best and the worst possible outcomes, by articulating a "coefficient of optimism" that determines the emphasis on the best end. The Hurwicz criterion can be viewed as a weighted average of the best and the worst uncertainty realizations. Hence, it generalizes the most optimistic Maximax criterion and the most pessimistic Maximin criterion--- both are popular alternative rules for decision-making under uncertainty---in a unified manner. The classical Hurwicz criterion models uncertainty as a random variable governed by a known probability distribution. As such, the decision maker possesses perfect knowledge for precise evaluation of loss under the criterion. However, such a desirable perfection is rarely available in practice. For many real-world applications, the decision maker usually encounters a data-driven setting entailing distributional ambiguity: the distribution of the uncertainty is ambiguous and only partial knowledge, including the prior statistical information (such as support and moments) and historical observations of the uncertainty, is available. In addition, the classical Hurwicz criterion merely considers the best and the worst outcomes that may only happen with small probabilities, while neglecting all other aforementioned distributional information that is valuable for characterizing the uncertainty's ambiguous distribution. Hence, the classical Hurwicz criterion needs to be revised to address the challenge of incorporating distributional information under distributional ambiguity in emerging data-driven analytics. In this project, we plan to revisit and reformulate the Hurwicz criterion to articulate the tradeoff between optimism and pessimism under distributional ambiguity, by considering the best- and the worst-case expected losses that may arise from a family of distributions. We propose leveraging the distributionally robust optimization framework to incorporate distributional information of the uncertainty into this family based on available knowledge.
|Effective start/end date||1/09/20 → …|