Many applications involve estimation of parameters that generalize across multiple diverse, but related, data-scarce task environments. Bayesian active meta-learning, a form of sequential optimal experimental design, provides a framework for solving such problems. The active meta-learner's goal is to gain transferable knowledge (estimate the transferable parameters) in the presence of idiosyncratic characteristics of the current task (task-specific parameters). We show that in such a setting, greedy pursuit of this goal can actually hurt estimation of the transferable parameters (induce so-called negative transfer). The learner faces a dilemma akin to but distinct from the exploration--exploitation dilemma: should they spend their acquisition budget pursuing transferable knowledge, or identifying the current task-specific parameters? We show theoretically that some tasks pose an inevitable and arbitrarily large threat of negative transfer, and that task identification is critical to reducing this threat. Our results generalize to analysis of prior misspecification over nuisance parameters. Finally, we empirically illustrate circumstances that lead to negative transfer.

翻译：许多应用涉及对跨多个多样但相关、数据稀缺任务环境泛化的参数估计。贝叶斯主动元学习作为序贯最优实验设计的一种形式，为求解此类问题提供了框架。主动元学习者的目标是在当前任务的特殊特征（任务特定参数）存在的情况下，获取可迁移知识（估计可迁移参数）。我们表明，在这种设定下，对这一目标的贪婪追求实际上可能损害可迁移参数的估计（引发所谓的负迁移）。学习者面临一个与探索-利用困境相似但不同的困境：应该将获取预算用于追求可迁移知识，还是用于识别当前的任务特定参数？我们从理论上证明，某些任务会构成不可避免且任意大的负迁移风险，而任务识别对于降低此类风险至关重要。我们的结果可推广至对先验误规范在多余参数上的分析。最后，我们通过实验说明了导致负迁移的具体情形。