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

arXiv: https://arxiv.org/abs/1309.6856 · HTML: https://mlsanity.com/paper/1309.6856/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Sep 2013.

## Built on by (most cited first, 4 of 4)

- [A Practical Guide to Multi-Objective Reinforcement Learning and Planning](https://mlsanity.com/paper/2103.09568/) (2021)
- [Scalable Multi-Objective Reinforcement Learning with Fairness Guarantees using Lorenz Dominance](https://mlsanity.com/paper/2411.18195/) (2024)
- [Learning Fair Pareto-Optimal Policies in Multi-Objective Reinforcement Learning](https://mlsanity.com/paper/2606.18111/) (2026)
- [Multi-Objective Optimization Using Adaptive Distributed Reinforcement Learning](https://mlsanity.com/paper/2403.08879/) (2024)

## Abstract (arXiv)

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.