Approximation of Lorenz-Optimal Solutions in Multiobjective Markov
  Decision Processes
  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.
