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.

翻译：针对存在冲突目标的决策支持场景，可向决策者呈现潜在的优化解集。本文探讨了这些解集应包含哪些策略，以及如何高效计算此类集合。基于此，我们采用分布式方法，引入一种直接关联策略回报分布的新型支配准则。依据该准则，我们提出分布非支配集，并证明该集合包含被帕累托前沿忽略的最优策略。此外，我们提出凸分布非支配集，并证明其包含所有使多变量风险厌恶决策者期望效用最大化的策略。我们设计了一种新颖算法来学习分布非支配集，并进一步提出剪枝算子以将该集合缩减为凸分布非支配集。通过实验验证了这些方法的可行性与有效性，为实际问题中的决策支持提供了有价值的新途径。