# Improving and benchmarking of algorithms for decision making with lower previsions

## TL;DR

This paper introduces a new fast algorithm for finding maximal gambles under severe uncertainty with lower previsions, outperforming existing algorithms through efficient methods and early stopping criteria.

## Contribution

A novel, efficient algorithm for identifying maximal gambles, with improved benchmarking and methods for generating decision problems under uncertainty.

## Key findings

- The new algorithm outperforms existing methods in all tested scenarios.
- Primal-dual interior point method is most effective among tested algorithms.
- Interval dominance can reduce problem size but does not always improve algorithm performance.

## 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 Troffaes 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-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.