Approximation of Lorenz-Optimal Solutions in Multiobjective Markov Decision Processes
Patrice Perny, Paul Weng, Judy Goldsmith, Josiah Hanna
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.
PDF Link: /papers/13/p508-perny.pdf
AUTHOR = "Patrice Perny
and Paul Weng and Judy Goldsmith and Josiah Hanna",
TITLE = "Approximation of Lorenz-Optimal Solutions in Multiobjective Markov Decision Processes",
BOOKTITLE = "Proceedings of the Twenty-Ninth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-13)",
PUBLISHER = "AUAI Press",
ADDRESS = "Corvallis, Oregon",
YEAR = "2013",
PAGES = "508--517"