Approximation of Lorenz-Optimal Solutions in Multiobjective Markov Decision Processes
This addresses fairness in multiagent or multicriteria planning under uncertainty, but is incremental as it builds on existing Lorenz dominance concepts.
The paper tackles the problem of fair optimization in Multiobjective Markov Decision Processes (MOMDPs) by introducing methods to efficiently approximate sets of Lorenz-non-dominated solutions, producing polynomial-sized subsets.
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.