We study multitask online learning in a setting where agents can only exchange information with their neighbors on an arbitrary communication network. We introduce $\texttt{MT-CO}_2\texttt{OL}$, a decentralized algorithm for this setting whose regret depends on the interplay between the task similarities and the network structure. Our analysis shows that the regret of $\texttt{MT-CO}_2\texttt{OL}$ is never worse (up to constants) than the bound obtained when agents do not share information. On the other hand, our bounds significantly improve when neighboring agents operate on similar tasks. In addition, we prove that our algorithm can be made differentially private with a negligible impact on the regret when the losses are linear. Finally, we provide experimental support for our theory.

我们在一个能够通过网络与邻居交换信息的设定中研究多任务在线学习。我们介绍了一种分散算法 $	exttt{MT-CO}_2	exttt{OL}$，其遗憾度取决于任务相似性和网络结构之间的相互作用。我们的分析表明，$	exttt{MT-CO}_2	exttt{OL}$的遗憾度（在常数范围内）永远不会比没有信息共享的情况更糟。另一方面，在邻近代理在相似任务上操作时，我们的边界显著改进。此外，我们证明了当损失是线性的时候，我们的算法可以以微不足道的遗憾影响实现差分隐私。最后，我们提供对我们理论的实验支持。

多任务在线学习：聆听邻域嗡嗡声