# Distributional Multi-Objective Decision Making

arXiv: https://arxiv.org/abs/2305.05560 · HTML: https://mlsanity.com/paper/2305.05560/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 37 references that are in the map.
- First posted on arXiv 9 May 2023.

## Builds on (most cited first, 6 of 6)

- [A Practical Guide to Multi-Objective Reinforcement Learning and Planning](https://mlsanity.com/paper/2103.09568/) (2021)
- [A Survey of Multi-Objective Sequential Decision-Making](https://mlsanity.com/paper/1402.0590/) (2014)
- [An Analysis of Categorical Distributional Reinforcement Learning](https://mlsanity.com/paper/1802.08163/) (2018)
- [Stochastically Dominant Distributional Reinforcement Learning](https://mlsanity.com/paper/1905.07318/) (2019)
- [Expected Scalarised Returns Dominance: A New Solution Concept for Multi-Objective Decision Making](https://mlsanity.com/paper/2106.01048/) (2021)
- [Multi-objective dynamic programming with limited precision](https://mlsanity.com/paper/2009.08198/) (2020)

## Built on by (most cited first, 2 of 2)

- [Multi-Objective Reinforcement Learning Based on Decomposition: A Taxonomy and Framework](https://mlsanity.com/paper/2311.12495/) (2023)
- [It's a matter of timescale: non-linear utility in successor features and multi-objective planning and learning](https://mlsanity.com/paper/2608.25723/) (2026)

## Abstract (arXiv)

For effective decision support in scenarios with conflicting objectives, sets of potentially optimal solutions can be presented to the decision maker. We explore both what policies these sets should contain and how such sets can be computed efficiently. With this in mind, we take a distributional approach and introduce a novel dominance criterion relating return distributions of policies directly. Based on this criterion, we present the distributional undominated set and show that it contains optimal policies otherwise ignored by the Pareto front. In addition, we propose the convex distributional undominated set and prove that it comprises all policies that maximise expected utility for multivariate risk-averse decision makers. We propose a novel algorithm to learn the distributional undominated set and further contribute pruning operators to reduce the set to the convex distributional undominated set. Through experiments, we demonstrate the feasibility and effectiveness of these methods, making this a valuable new approach for decision support in real-world problems.