Complexity of Solving Decision Trees with Skew-Symmetric Bilinear Utility

Hugo Gilbert, Olivier Spanjaard
Proceedings of the 33rd Conference on Uncertainty in Artificial Intelligence, PMLR R15:181-190, 2017.

Abstract

We study the complexity of solving decision trees with a Skew-Symmetric Bilinear (SSB) utility function. The SSB model is an exten- sion of Expected Utility (EU) with enhanced descriptive possibilities. Unlike EU, the opti- mality principle does not hold for SSB, which makes its optimization trickier. We show that determining an SSB optimal plan is NP-hard if one only considers deterministic plans while it is polynomial time if one allows randomized plans. With the Weighted EU model (a spe- cial case of SSB), the problem becomes poly- nomial in both settings. Our numerical tests show the operationality of the methods.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR15-gilbert17a, title = {Complexity of Solving Decision Trees with Skew-Symmetric Bilinear Utility}, author = {Gilbert, Hugo and Spanjaard, Olivier}, booktitle = {Proceedings of the 33rd Conference on Uncertainty in Artificial Intelligence}, pages = {181--190}, year = {2017}, editor = {Elidan, Gal and Kersting, Kristian}, volume = {R15}, series = {Proceedings of Machine Learning Research}, month = {11--15 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r15/main/assets/gilbert17a/gilbert17a.pdf}, url = {https://proceedings.mlr.press/r15/gilbert17a.html}, abstract = {We study the complexity of solving decision trees with a Skew-Symmetric Bilinear (SSB) utility function. The SSB model is an exten- sion of Expected Utility (EU) with enhanced descriptive possibilities. Unlike EU, the opti- mality principle does not hold for SSB, which makes its optimization trickier. We show that determining an SSB optimal plan is NP-hard if one only considers deterministic plans while it is polynomial time if one allows randomized plans. With the Weighted EU model (a spe- cial case of SSB), the problem becomes poly- nomial in both settings. Our numerical tests show the operationality of the methods.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Complexity of Solving Decision Trees with Skew-Symmetric Bilinear Utility %A Hugo Gilbert %A Olivier Spanjaard %B Proceedings of the 33rd Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2017 %E Gal Elidan %E Kristian Kersting %F pmlr-vR15-gilbert17a %I PMLR %P 181--190 %U https://proceedings.mlr.press/r15/gilbert17a.html %V R15 %X We study the complexity of solving decision trees with a Skew-Symmetric Bilinear (SSB) utility function. The SSB model is an exten- sion of Expected Utility (EU) with enhanced descriptive possibilities. Unlike EU, the opti- mality principle does not hold for SSB, which makes its optimization trickier. We show that determining an SSB optimal plan is NP-hard if one only considers deterministic plans while it is polynomial time if one allows randomized plans. With the Weighted EU model (a spe- cial case of SSB), the problem becomes poly- nomial in both settings. Our numerical tests show the operationality of the methods. %Z Reissued by PMLR on 04 October 2026.
APA
Gilbert, H. & Spanjaard, O.. (2017). Complexity of Solving Decision Trees with Skew-Symmetric Bilinear Utility. Proceedings of the 33rd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R15:181-190 Available from https://proceedings.mlr.press/r15/gilbert17a.html. Reissued by PMLR on 04 October 2026.

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