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. Furthermore, we show that BAIT (active learning based on V-optimal experimental design) can be derived from BDT and asymptotic approximations. 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原则。本研究推导了（贝叶斯）主动学习在短视框架下的贝叶斯决策理论，该框架假设我们仅能再标注一个数据点。此推导产生了诸如期望误差减少、期望预测信息增益等有效算法，以及文献中出现的其他算法。此外，我们证明基于V最优实验设计的BAIT算法可通过贝叶斯决策理论与渐近近似推导得出。此类方法的关键挑战在于难以扩展至大批量规模，导致计算瓶颈或性能急剧下降。本文通过特定决策过程表述，为期望预测信息增益算法推导出部分批量标签采样方法。我们在多个数据集上的实验表明，对于固定预算和基于神经嵌入的贝叶斯逻辑回归任务，部分批量标签采样期望预测信息增益算法具有更优性能。代码发布于https://github.com/ADDAPT-ML/ParBaLS。