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 finding maximal gambles. We compare its performance to existing algorithms, one proposed by , and one by Jansen, Augustin, and Schollmeyer (2017). To do so, we develop a new method for generating random decision problems with pre-specified ratios of maximal and interval dominant gambles.Based on earlier work, we present efficient ways to find 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 efficiency. We find 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 benefits Jansen et al.'s algorithm, but perhaps surprisingly, not the other two algorithms. We find that our algorithm, without using interval dominance, outperforms all other algorithms in all scenarios in our benchmarking.

K-Partitioning with Imprecise Probabilistic Edges

“…To initialize , we take the value returned by Algorithm 1 with = 1. The idea behind the "init" version is that initializing with a set of possibly non-dominated solutions can reduce computational time (similar ideas can be found in Nakharutai et al (2019)). For every configuration, the results correspond to the average of the twenty instances.…”

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

“…Algorithms for decision criteria associated with lower previsions have been studied in the literature for quite some time. For example, see [20] for E-admissibility and [6] [8], [14] and [19, p. 336] for maximality. From these, only [14] provides in-depth benchmarking of their algorithms.…”

“…For example, see [20] for E-admissibility and [6] [8], [14] and [19, p. 336] for maximality. From these, only [14] provides in-depth benchmarking of their algorithms.…”

“…The contributions of this paper are as follows. Based on our earlier work [12,13,14], we propose new algorithms for Γ-maximin, Γ-maximax and interval dominance. Specifically, we implement a quick way to obtain feasible starting points for the linear programs and early stopping criteria to determine whether a gamble is Γ-maximin (or Γ-maximax).…”

“…For this to work best, ideally, we start the primal-dual method with feasible points. To obtain such feasible points, we can reuse the fast techniques proposed in [12,13,14]. Specifically, to find a starting feasible solution p(ω) for (P1) and (D2), we could employ the first phase of the two-phase method, similar to earlier work [13, §4.2].…”