Is it possible to understand or imitate a policy maker's rationale by looking at past decisions they made? We formalize this question as the problem of learning social welfare functions belonging to the well-studied family of power mean functions. We focus on two learning tasks; in the first, the input is vectors of utilities of an action (decision or policy) for individuals in a group and their associated social welfare as judged by a policy maker, whereas in the second, the input is pairwise comparisons between the welfares associated with a given pair of utility vectors. We show that power mean functions are learnable with polynomial sample complexity in both cases, even if the comparisons are social welfare information is noisy. Finally, we design practical algorithms for these tasks and evaluate their performance.

翻译：是否可能通过观察决策者过去做出的决定来理解或模仿其决策逻辑？我们将这一问题形式化为学习属于被广泛研究的幂平均函数族的社会福利函数的问题。我们聚焦于两个学习任务：在第一个任务中，输入是行动（决策或政策）对群体中个体产生的效用向量及其对应的决策者判定的社会福利值；而在第二个任务中，输入则是给定效用向量对之间社会福利的比较结果。我们证明，在这两种情况下，即使比较结果或社会福利信息存在噪声，幂平均函数仍可通过多项式样本复杂度进行学习。最后，我们为这些任务设计了实用算法并评估其性能。