We consider an online estimation problem involving a set of agents. Each agent has access to a (personal) process that generates samples from a real-valued distribution and seeks to estimate its mean. We study the case where some of the distributions have the same mean, and the agents are allowed to actively query information from other agents. The goal is to design an algorithm that enables each agent to improve its mean estimate thanks to communication with other agents. The means as well as the number of distributions with same mean are unknown, which makes the task nontrivial. We introduce a novel collaborative strategy to solve this online personalized mean estimation problem. We analyze its time complexity and introduce variants that enjoy good performance in numerical experiments. We also extend our approach to the setting where clusters of agents with similar means seek to estimate the mean of their cluster.
翻译:我们考虑的是涉及一组代理商的在线估算问题。 每个代理商都可以进入一个( 个人) 过程, 从实际价值的分布中生成样本, 并试图估算其平均值。 我们研究一些分销商具有相同平均值的案例, 代理商可以积极向其他代理商查询信息。 我们的目标是设计一种算法, 使每个代理商能够通过与其他代理商的沟通来改进其中值估算。 使用同样平均值的分销方式和数量是未知的, 这使得任务变得无关紧要。 我们引入一种新的合作策略来解决这个在线个人化的中值估算问题。 我们分析了其时间复杂性, 并引入了在数字实验中表现良好的变量。 我们还将我们的方法扩大到拥有类似手段的代理商集群试图估算其组值的背景。