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 uncertainty while trying to optimize several reward functions simultaneously. This applies to multiagent problems when rewards define individual utility functions, or in multicriteria problems when rewards refer to different features. In this setting, we study the determination of policies leading to Lorenz-non-dominated tradeoffs. Lorenz dominance is a refinement of Pareto dominance that was introduced in Social Choice for the measurement of inequalities. In this paper, we introduce 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 uncertainty while trying to optimize several reward functions simultaneously. This applies to multiagent problems when rewards define individual utility functions, or in multicriteria problems when rewards refer to different features. In this setting, we study the determination of policies leading to Lorenz-non-dominated tradeoffs. Lorenz dominance is a refinement of Pareto dominance that was introduced in Social Choice for the measurement of inequalities. In this paper, we introduce 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 uncertainty while trying to optimize several reward functions simultaneously. This applies to multiagent problems when rewards define individual utility functions, or in multicriteria problems when rewards refer to different features. In this setting, we study the determination of policies leading to Lorenz-non-dominated tradeoffs. Lorenz dominance is a refinement of Pareto dominance that was introduced in Social Choice for the measurement of inequalities. In this paper, we introduce 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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