Multitask learning is a powerful framework that enables one to simultaneously learn multiple related tasks by sharing information between them. Quantifying uncertainty in the estimated tasks is of pivotal importance for many downstream applications, such as online or active learning. In this work, we provide novel multitask confidence intervals in the challenging agnostic setting, i.e., when neither the similarity between tasks nor the tasks' features are available to the learner. The obtained intervals do not require i.i.d. data and can be directly applied to bound the regret in online learning. Through a refined analysis of the multitask information gain, we obtain new regret guarantees that, depending on a task similarity parameter, can significantly improve over treating tasks independently. We further propose a novel online learning algorithm that achieves such improved regret without knowing this parameter in advance, i.e., automatically adapting to task similarity. As a second key application of our results, we introduce a novel multitask active learning setup where several tasks must be simultaneously optimized, but only one of them can be queried for feedback by the learner at each round. For this problem, we design a no-regret algorithm that uses our confidence intervals to decide which task should be queried. Finally, we empirically validate our bounds and algorithms on synthetic and real-world (drug discovery) data.

该研究提出了在缺乏任务相似性和任务特征的条件下，通过多任务学习获得的置信区间，可以有效地估计多个相关任务的不确定性，并且可以应用于在线学习中，进一步提出了一种新颖的多任务主动学习算法来同时优化多个任务，通过使用置信区间决定选择哪个任务进行查询，并通过合成和真实世界数据验证了算法和界限的有效性。

无悔的多任务学习：从改进的置信界到主动学习