Improving Algorithms for Decision Making with the Hurwicz Criterion

Nawapon Nakharutai, Matthias Troffaes
Proceedings of the Twelveth International Symposium on Imprecise Probability: Theories and Applications, PMLR 147:235-243, 2021.

Abstract

We propose two improved algorithms for evaluating the Hurwicz criterion in the context of decision making with lower previsions, along with a new benchmarking algorithm for measuring these improvements. The Hurwicz criterion is a well-known criterion for decision making with lower previsions under severe uncertainty when decision makers want to balance between pessimistic and optimistic extremes. When the domain of the lower prevision, the set of possible outcomes and the set of possible decisions are all finite, the classic method for applying this criterion goes by solving a sequence of linear programs. We show how to improve this classic algorithm, based on similar improvements that we have proposed for other decision criteria. Additionally, to allow benchmarking these improvements, we provide a new algorithm for randomly generating artificial decision problems with a set number of Hurwicz gambles. In our simulation, our proposed algorithms for Hurwicz outperform the standard algorithm in most scenarios except when the set of outcomes is small, the domain of the lower prevision is large, and there are many Hurwicz optimal decisions at once, in which case our proposed algorithms are slightly slower.

Cite this Paper

BibTeX
@InProceedings{pmlr-v147-nakharutai21a, title = {Improving Algorithms for Decision Making with the Hurwicz Criterion}, author = {Nakharutai, Nawapon and Troffaes, Matthias}, booktitle = {Proceedings of the Twelveth International Symposium on Imprecise Probability: Theories and Applications}, pages = {235--243}, year = {2021}, editor = {Cano, Andrés and De Bock, Jasper and Miranda, Enrique and Moral, Serafı́n}, volume = {147}, series = {Proceedings of Machine Learning Research}, month = {06--09 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v147/nakharutai21a/nakharutai21a.pdf}, url = {https://proceedings.mlr.press/v147/nakharutai21a.html}, abstract = {We propose two improved algorithms for evaluating the Hurwicz criterion in the context of decision making with lower previsions, along with a new benchmarking algorithm for measuring these improvements. The Hurwicz criterion is a well-known criterion for decision making with lower previsions under severe uncertainty when decision makers want to balance between pessimistic and optimistic extremes. When the domain of the lower prevision, the set of possible outcomes and the set of possible decisions are all finite, the classic method for applying this criterion goes by solving a sequence of linear programs. We show how to improve this classic algorithm, based on similar improvements that we have proposed for other decision criteria. Additionally, to allow benchmarking these improvements, we provide a new algorithm for randomly generating artificial decision problems with a set number of Hurwicz gambles. In our simulation, our proposed algorithms for Hurwicz outperform the standard algorithm in most scenarios except when the set of outcomes is small, the domain of the lower prevision is large, and there are many Hurwicz optimal decisions at once, in which case our proposed algorithms are slightly slower.} }
Endnote
%0 Conference Paper %T Improving Algorithms for Decision Making with the Hurwicz Criterion %A Nawapon Nakharutai %A Matthias Troffaes %B Proceedings of the Twelveth International Symposium on Imprecise Probability: Theories and Applications %C Proceedings of Machine Learning Research %D 2021 %E Andrés Cano %E Jasper De Bock %E Enrique Miranda %E Serafı́n Moral %F pmlr-v147-nakharutai21a %I PMLR %P 235--243 %U https://proceedings.mlr.press/v147/nakharutai21a.html %V 147 %X We propose two improved algorithms for evaluating the Hurwicz criterion in the context of decision making with lower previsions, along with a new benchmarking algorithm for measuring these improvements. The Hurwicz criterion is a well-known criterion for decision making with lower previsions under severe uncertainty when decision makers want to balance between pessimistic and optimistic extremes. When the domain of the lower prevision, the set of possible outcomes and the set of possible decisions are all finite, the classic method for applying this criterion goes by solving a sequence of linear programs. We show how to improve this classic algorithm, based on similar improvements that we have proposed for other decision criteria. Additionally, to allow benchmarking these improvements, we provide a new algorithm for randomly generating artificial decision problems with a set number of Hurwicz gambles. In our simulation, our proposed algorithms for Hurwicz outperform the standard algorithm in most scenarios except when the set of outcomes is small, the domain of the lower prevision is large, and there are many Hurwicz optimal decisions at once, in which case our proposed algorithms are slightly slower.
APA
Nakharutai, N. & Troffaes, M.. (2021). Improving Algorithms for Decision Making with the Hurwicz Criterion. Proceedings of the Twelveth International Symposium on Imprecise Probability: Theories and Applications, in Proceedings of Machine Learning Research 147:235-243 Available from https://proceedings.mlr.press/v147/nakharutai21a.html.

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