We propose a multi-agent variant of the classical multi-armed bandit problem, in which there are N agents and K arms, and pulling an arm generates a (possibly different) stochastic reward to each agent. Unlike the classical multi-armed bandit problem, the goal is not to learn the "best arm", as each agent may perceive a different arm as best for her. Instead, we seek to learn a fair distribution over arms. Drawing on a long line of research in economics and computer science, we use the Nash social welfare as our notion of fairness. We design multi-agent variants of three classic multi-armed bandit algorithms, and show that they achieve sublinear regret, now measured in terms of the Nash social welfare.

中文翻译：

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Multi-Agent Multi-Armed Bandits 的公平算法

我们提出了经典多臂老虎机问题的多智能体变体，其中有 N 个智能体和 K 个臂，并且拉动一只臂会为每个智能体生成（可能不同的）随机奖励。与经典的多臂老虎机问题不同，目标不是学习“最好的手臂”，因为每个智能体可能认为不同的手臂最适合她。相反，我们寻求学习武器的公平分配。借鉴经济学和计算机科学的长期研究，我们使用纳什社会福利作为我们的公平概念。我们设计了三种经典多臂老虎机算法的多智能体变体，并表明它们实现了亚线性后悔，现在用纳什社会福利来衡量。