Iterated risk measures for risk-sensitive Markov decision processes with discounted cost

Takayuki Osogami
Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence, PMLR R9:639-646, 2011.

Abstract

We demonstrate a limitation of discounted expected utility, a standard approach for representing the preference to risk when future cost is discounted. Specifically, we provide an example of the preference of a decision maker that appears to be rational but cannot be represented with any discounted expected utility. A straightforward modification to discounted expected utility leads to inconsistent decision making over time. We will show that an iterated risk measure can represent the preference that cannot be represented by any discounted expected utility and that the decisions based on the iterated risk measure are consistent over time.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR9-osogami11a, title = {Iterated risk measures for risk-sensitive {M}arkov decision processes with discounted cost}, author = {Osogami, Takayuki}, booktitle = {Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence}, pages = {639--646}, year = {2011}, editor = {Cozman, Fabio and Pfeffer, Avi}, volume = {R9}, series = {Proceedings of Machine Learning Research}, month = {14--17 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r9/main/assets/osogami11a/osogami11a.pdf}, url = {https://proceedings.mlr.press/r9/osogami11a.html}, abstract = {We demonstrate a limitation of discounted expected utility, a standard approach for representing the preference to risk when future cost is discounted. Specifically, we provide an example of the preference of a decision maker that appears to be rational but cannot be represented with any discounted expected utility. A straightforward modification to discounted expected utility leads to inconsistent decision making over time. We will show that an iterated risk measure can represent the preference that cannot be represented by any discounted expected utility and that the decisions based on the iterated risk measure are consistent over time.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Iterated risk measures for risk-sensitive Markov decision processes with discounted cost %A Takayuki Osogami %B Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2011 %E Fabio Cozman %E Avi Pfeffer %F pmlr-vR9-osogami11a %I PMLR %P 639--646 %U https://proceedings.mlr.press/r9/osogami11a.html %V R9 %X We demonstrate a limitation of discounted expected utility, a standard approach for representing the preference to risk when future cost is discounted. Specifically, we provide an example of the preference of a decision maker that appears to be rational but cannot be represented with any discounted expected utility. A straightforward modification to discounted expected utility leads to inconsistent decision making over time. We will show that an iterated risk measure can represent the preference that cannot be represented by any discounted expected utility and that the decisions based on the iterated risk measure are consistent over time. %Z Reissued by PMLR on 04 October 2026.
APA
Osogami, T.. (2011). Iterated risk measures for risk-sensitive Markov decision processes with discounted cost. Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R9:639-646 Available from https://proceedings.mlr.press/r9/osogami11a.html. Reissued by PMLR on 04 October 2026.

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