Improving and benchmarking of algorithms for $\Gamma$-maximin, $\Gamma$-maximax and interval dominance

TL;DR

This paper introduces new algorithms for $\Gamma$-maximin, $\Gamma$-maximax, and interval dominance decision criteria under severe uncertainty, improving efficiency especially for smaller problem sizes.

Contribution

The authors develop and compare new algorithms that leverage common initial feasible points and early stopping, enhancing performance over standard methods in certain problem sizes.

Findings

Proposed algorithms outperform standard algorithms for smaller domain sizes.

Early stopping criteria significantly reduce computation time.

Performance gains diminish when domain size greatly exceeds decision and outcome sizes.

Abstract

$\Gamma$-maximin, $\Gamma$-maximax and inteval 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 $\Gamma$-maximin, $\Gamma$-maximax or 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.