Approximation of Lorenz-Optimal Solutions in Multiobjective Markov Decision Processes

Judy Goldsmith, Josiah Hanna, Patrice Perny, Paul Weng
Proceedings of the 29th Conference on Uncertainty in Artificial Intelligence, PMLR R11:125-134, 2013.

Abstract

This paper is devoted to fair optimization in Multiobjective Markov Decision Processes (MOMDPs). A MOMDP is an extension of the MDP model for planning under uncer- tainty while trying to optimize several re- ward functions simultaneously. This applies to multiagent problems when rewards define individual utility functions, or in multicrite- ria problems when rewards refer to different features. In this setting, we study the deter- mination of policies leading to Lorenz-non- dominated tradeoffs. Lorenz dominance is a refinement of Pareto dominance that was in- troduced in Social Choice for the measure- ment of inequalities. In this paper, we in- troduce methods to efficiently approximate the sets of Lorenz-non-dominated solutions of infinite-horizon, discounted MOMDPs. The approximations are polynomial-sized subsets of those solutions.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR11-goldsmith13a, title = {Approximation of Lorenz-Optimal Solutions in Multiobjective {M}arkov Decision Processes}, author = {Goldsmith, Judy and Hanna, Josiah and Perny, Patrice and Weng, Paul}, booktitle = {Proceedings of the 29th Conference on Uncertainty in Artificial Intelligence}, pages = {125--134}, year = {2013}, editor = {Nicholson, Ann and Smyth, Padhraic}, volume = {R11}, series = {Proceedings of Machine Learning Research}, month = {12--14 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r11/main/assets/goldsmith13a/goldsmith13a.pdf}, url = {https://proceedings.mlr.press/r11/goldsmith13a.html}, abstract = {This paper is devoted to fair optimization in Multiobjective Markov Decision Processes (MOMDPs). A MOMDP is an extension of the MDP model for planning under uncer- tainty while trying to optimize several re- ward functions simultaneously. This applies to multiagent problems when rewards define individual utility functions, or in multicrite- ria problems when rewards refer to different features. In this setting, we study the deter- mination of policies leading to Lorenz-non- dominated tradeoffs. Lorenz dominance is a refinement of Pareto dominance that was in- troduced in Social Choice for the measure- ment of inequalities. In this paper, we in- troduce methods to efficiently approximate the sets of Lorenz-non-dominated solutions of infinite-horizon, discounted MOMDPs. The approximations are polynomial-sized subsets of those solutions.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Approximation of Lorenz-Optimal Solutions in Multiobjective Markov Decision Processes %A Judy Goldsmith %A Josiah Hanna %A Patrice Perny %A Paul Weng %B Proceedings of the 29th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2013 %E Ann Nicholson %E Padhraic Smyth %F pmlr-vR11-goldsmith13a %I PMLR %P 125--134 %U https://proceedings.mlr.press/r11/goldsmith13a.html %V R11 %X This paper is devoted to fair optimization in Multiobjective Markov Decision Processes (MOMDPs). A MOMDP is an extension of the MDP model for planning under uncer- tainty while trying to optimize several re- ward functions simultaneously. This applies to multiagent problems when rewards define individual utility functions, or in multicrite- ria problems when rewards refer to different features. In this setting, we study the deter- mination of policies leading to Lorenz-non- dominated tradeoffs. Lorenz dominance is a refinement of Pareto dominance that was in- troduced in Social Choice for the measure- ment of inequalities. In this paper, we in- troduce methods to efficiently approximate the sets of Lorenz-non-dominated solutions of infinite-horizon, discounted MOMDPs. The approximations are polynomial-sized subsets of those solutions. %Z Reissued by PMLR on 04 October 2026.
APA
Goldsmith, J., Hanna, J., Perny, P. & Weng, P.. (2013). Approximation of Lorenz-Optimal Solutions in Multiobjective Markov Decision Processes. Proceedings of the 29th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R11:125-134 Available from https://proceedings.mlr.press/r11/goldsmith13a.html. Reissued by PMLR on 04 October 2026.

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