We consider the problem of online stochastic optimization in a distributed setting with $M$ clients connected through a central server. We develop a distributed online learning algorithm that achieves order-optimal cumulative regret with low communication cost measured in the total number of bits transmitted over the entire learning horizon. This is in contrast to existing studies which focus on the offline measure of simple regret for learning efficiency. The holistic measure for communication cost also departs from the prevailing approach that \emph{separately} tackles the communication frequency and the number of bits in each communication round.

翻译：我们研究通过中央服务器连接的$M$个客户端在分布式环境下的在线随机优化问题。我们提出一种分布式在线学习算法，该算法在总传输比特数衡量的整个学习周期内实现通信成本极低、阶最优的累积遗憾。这不同于现有研究聚焦于离线简单遗憾指标的学习效率。这种通信成本的全局性度量也告别了当前分别处理通信频率与每轮通信比特数的主流方法。