We introduce and analyze AdaTask, a multitask online learning algorithm that adapts to the unknown structure of the tasks. When the $N$ tasks are stochastically activated, we show that the regret of AdaTask is better, by a factor that can be as large as $\sqrt{N}$, than the regret achieved by running $N$ independent algorithms, one for each task. AdaTask can be seen as a comparator-adaptive version of Follow-the-Regularized-Leader with a Mahalanobis norm potential. Through a variational formulation of this potential, our analysis reveals how AdaTask jointly learns the tasks and their structure. Experiments supporting our findings are presented.

翻译：我们引入并分析AdaTask, 这是一种适应任务未知结构的多任务在线学习算法。 当美元任务被快速启动时, 我们发现AdaTask的遗憾比每个任务都能运行美元独立算法的遗憾要大得多。 AdaTask可以被视为具有 Mahalanobis 规范潜力的“ 追踪目标” 的参照和适应版本。 通过对这一潜力的变式表述,我们的分析揭示了AdaTask 是如何共同学习任务及其结构的。 展示了支持我们发现的各种实验。