Regret-based budgeted decision rules under severe uncertainty

• Published in: Information sciences 2024-04, Vol.665, p.120361, Article 120361
• Main Authors: Nakharutai, Nawapon, Destercke, Sébastien, Troffaes, Matthias C.M.
• Format: Article
• Language: English
• Subjects: Decision; Imprecise probability; Maximin; Minimax; Numerical algorithm; Optimization; Regret
• ISSN: 0020-0255; 1872-6291
• DOI: 10.1016/j.ins.2024.120361

One way to make decisions under uncertainty is to select an optimal option from a possible range of options, by maximizing the expected utilities derived from a probability model. However, under severe uncertainty, identifying precise probabilities is hard. For this reason, imprecise probability models uncertainty through convex sets of probabilities, and considers decision rules that can return multiple options to reflect insufficient information. Many well-founded decision rules have been studied in the past, but none of those standard rules are able to control the number of returned alternatives. This can be a problem for large decision problems, due to the cognitive burden decision makers have to face when presented with a large number of alternatives. Our contribution proposes regret-based ideas to construct new decision rules which return a bounded number of options, where the limit on the number of options is set in advance by the decision maker as an expression of their cognitive limitation. We also study their consistency and numerical behaviour. •Propose regret-based decision rules which return a limited number of options.•Study their consistency with respect to standard imprecise probability decision rules.•Provide algorithms for regret-based decision rules and investigate their numerical behaviour.