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.

通过观察决策者过去的决策，能否理解或模拟他们的决策理念？我们将这个问题形式化为学习社会福利函数的问题，属于广为研究的幂均值函数家族。我们专注于两个学习任务：第一个任务的输入是群体中个体采取行动（决策或政策）的效用向量以及由决策者判断的与之关联的社会福利，而第二个任务的输入是给定一对效用向量关联的福利的两两比较。我们证明了在两种情况下，即使比较的社会福利信息是噪声的，幂均值函数也能够在多项式样本复杂度下进行学习。最后，我们设计了实用的算法来解决这些任务并评估它们的性能。