Decision Theory Meets Linear Optimization Beyond Computation

Jansen, Christoph; Augustin, Thomas; Schollmeyer, Georg

doi:10.1007/978-3-319-61581-3_30

Cited by 8 publications

(12 citation statements)

References 13 publications

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“…Note that Walley [1991, §3.8.1] uses a stronger ordering, which also includes pointwise dominance. Here, we follow Troffaes [2007], Troffaes and Hable [2014, §16.3.2] and Jansen et al [2017] and simply omit pointwise dominance from our definition.…”

Section: Lower Previsionsmentioning

confidence: 99%

“…Several authors proposed algorithms for finding maximal gambles, for example, Kikuti et al [2011], Troffaes and Hable [2014, p. 336] and Jansen et al [2017]. Troffaes and Hable [2014, Algorithm 16.4, p. 336] present an incremental algorithm where once some maximal gambles in the sets are known, we should compare the remaining gambles against those maximal gambles first.…”

Section: Introductionmentioning

confidence: 99%

“…We also use results from Nakharutai et al [2018] to quickly obtain feasible starting points, further improving the efficiency of these methods. Jansen et al [2017] proposed an algorithm that can verify whether a gamble is maximal by solving a single larger linear program. To improve this algorithm, we exploit the fact that if a gamble is not maximal in a given iteration, then it can be excluded from all future iterations.…”

Section: Introductionmentioning

confidence: 99%

“…The contributions of the paper are as follows. We propose a new algorithm for finding maximal gambles and compare its performance to the two algorithms proposed by Troffaes and Hable [2014, p. 336] and Jansen et al [2017]. For benchmarking, we propose an algorithm for generating sets of gambles which have a precisely given number of maximal and interval dominant gambles.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Improving and benchmarking of algorithms for decision making with lower previsions

Nakharutai

Troffaes

Caiado

2019

International Journal of Approximate Reasoning

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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.

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Section: Lower Previsionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Improving and benchmarking of algorithms for decision making with lower previsions

Nakharutai

Troffaes

Caiado

2019

International Journal of Approximate Reasoning

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“…Further criteria for the case of cardinal utility and imprecise probabilities, each in its own way taking into account the whole set M of compatible probability measures, are reviewed in, e.g., Huntley et al (2014). Additionally, there exists a variety of efficient and powerful algorithms to deal with this kind of violation of the classical assumptions (see, e.g., Utkin and Augustin (2005); Kikuti et al (2011);Hable and Troffaes (2014);Jansen et al (2017a)). However, note that the assumption of a cardinal utility function u is essential for all these criteria in order to be applicable.…”

Section: Fundamentals Underlying Our Approach and Related Literaturementioning

confidence: 99%

Concepts for decision making under severe uncertainty with partial ordinal and partial cardinal preferences

Jansen¹,

Schollmeyer²,

Augustin³

2018

International Journal of Approximate Reasoning

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We introduce three different approaches for decision making under uncertainty if (I) there is only partial (both cardinally and ordinally scaled) information on an agent's preferences and (II) the uncertainty about the states of nature is described by a credal set (or some other imprecise probabilistic model). Particularly, situation (I) is modeled by a pair of binary relations, one specifying the partial rank order of the alternatives and the other modeling partial information on the strength of preference. Our first approach relies on decision criteria constructing complete rankings of the available acts that are based on generalized expectation intervals. Subsequently, we introduce different concepts of global admissibility that construct partial orders between the available acts by comparing them all simultaneously. Finally, we define criteria induced by suitable binary relations on the set of acts and, therefore, can be understood as concepts of local admissibility. For certain criteria, we provide linear programming based algorithms for checking optimality/admissibility of acts. Additionally, the paper includes a discussion of a prototypical situation by means of a toy example.

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Algorithms for Generating Sets of Gambles for Decision Making with Lower Previsions

Nakharutai

2020

Lecture Notes in Computer Science

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Decision Theory Meets Linear Optimization Beyond Computation

Cited by 8 publications

References 13 publications

Improving and benchmarking of algorithms for decision making with lower previsions

Improving and benchmarking of algorithms for decision making with lower previsions

Concepts for decision making under severe uncertainty with partial ordinal and partial cardinal preferences

Algorithms for Generating Sets of Gambles for Decision Making with Lower Previsions

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