Improving and benchmarking of algorithms for decision making with lower previsions

Abstract

Maximality, interval dominance, and E-admissibility are three well-known criteria for decision making under severe uncertainty using lower previsions. We present a new fast algorithm for nding maximal gambles. We compare its performance to existing algorithms, one proposed by Troaes and Hable (2014), and one by Jansen, Augustin, and Schollmeyer (2017). To do so, we develop a new method for generating random decision problems with pre-specied ratios of maximal and interval dominant gambles. Based on earlier work, we present ecient ways to nd common feasible starting points in these algorithms. We then exploit these feasible starting points to develop early stopping criteria for the primal-dual interior point method, further improving eciency. We nd that the primal-dual interior point method works best. We also investigate the use of interval dominance to eliminate non-maximal gambles. This can make the problem smaller, and we observe that this ben- ets Jansen et al.'s algorithm, but perhaps surprisingly, not the other two algorithms. We nd that our algorithm, without using interval dominance, outperforms all other algorithms in all scenarios in our benchmarking.