Improving and benchmarking of algorithms for Γ-maximin, Γ-maximax and interval dominance

Nakharutai, Nawapon; Troffaes, Matthias C.M.; Caiado, Camila C.S.

Abstract

Γ-maximin, Γ-maximax and interval dominance are familiar decision criteria for making decisions under severe uncertainty, when probability distributions can only be partially identified. One can apply these three criteria by solving sequences of linear programs. In this study, we present new algorithms for these criteria and compare their performance to existing standard algorithms. Specifically, we use efficient ways, based on previous work, to find common initial feasible points for these algorithms. Exploiting these initial feasible points, we develop early stopping criteria to determine whether gambles are either Γ-maximin, Γ-maximax and interval dominant. We observe that the primal-dual interior point method benefits considerably from these improvements. In our simulation, we find that our proposed algorithms outperform the standard algorithms when the size of the domain of lower previsions is less or equal to the sizes of decisions and outcomes. However, our proposed algorithms do not outperform the standard algorithms in the case that the size of the domain of lower previsions is much larger than the sizes of decisions and outcomes.

Citation

Nakharutai, N., Troffaes, M. C., & Caiado, C. C. (2021). Improving and benchmarking of algorithms for Γ-maximin, Γ-maximax and interval dominance. International Journal of Approximate Reasoning: Uncertainty in Intelligent Systems, 133, 95-115. https://doi.org/10.1016/j.ijar.2021.03.005

• Journal Article Type: Article
• Acceptance Date: Mar 19, 2021
• Online Publication Date: Mar 24, 2021
• Publication Date: 2021-06
• Deposit Date: Mar 30, 2021
• Publicly Available Date: Mar 24, 2023
• Journal: International Journal of Approximate Reasoning
• Print ISSN: 0888-613X
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 133
• Pages: 95-115
• DOI: https://doi.org/10.1016/j.ijar.2021.03.005
• Public URL: https://durham-repository.worktribe.com/output/1250353
• Related Public URLs: https://arxiv.org/abs/2103.12423