Over the past couple of decades, many active learning acquisition functions have been proposed, leaving practitioners with an unclear choice of which to use. Bayesian Decision Theory (BDT) offers a universal principle to guide decision-making. In this work, we derive BDT for (Bayesian) active learning in the myopic framework, where we imagine we only have one more point to label. This derivation leads to effective algorithms such as Expected Error Reduction (EER), Expected Predictive Information Gain (EPIG), and other algorithms that appear in the literature. A key challenge of such methods is the difficult scaling to large batch sizes, leading to either computational challenges (BatchBALD) or dramatic performance drops (top-$B$ selection). Here, using a particular formulation of the decision process, we derive Partial Batch Label Sampling (ParBaLS) for the EPIG algorithm. We show experimentally for several datasets that ParBaLS EPIG gives superior performance for a fixed budget and Bayesian Logistic Regression on Neural Embeddings. Our code is available at https://github.com/ADDAPT-ML/ParBaLS.

翻译：过去几十年间，众多主动学习获取函数被提出，使得实践者在选择使用时面临困惑。贝叶斯决策理论为决策制定提供了普适性指导原则。本研究在近视框架下推导了（贝叶斯）主动学习的BDT理论体系，该框架假设我们仅能再标注一个数据点。此推导过程衍生出预期误差缩减、预期预测信息增益等文献中已存在的有效算法，以及其他相关算法。此类方法面临的关键挑战在于难以扩展至大批量规模，导致计算复杂度激增或性能急剧下降。本文通过特定决策过程建模，为EPIG算法推导出部分批量标签采样方法。在多数据集实验表明，在固定预算和基于神经嵌入的贝叶斯逻辑回归条件下，ParBaLS EPIG算法展现出优越性能。代码已开源：https://github.com/ADDAPT-ML/ParBaLS。