We consider a batch active learning scenario where the learner adaptively
issues batches of points to a labeling oracle. Sampling labels in batches is
highly desirable in practice due to the smaller number of interactive rounds
with the labeling oracle (often human beings). However, batch active learning
typically pays the price of a reduced adaptivity, leading to suboptimal
results. In this paper we propose a solution which requires a careful trade off
between the informativeness of the queried points and their diversity. We
theoretically investigate batch active learning in the practically relevant
scenario where the unlabeled pool of data is available beforehand ({\em
pool-based} active learning). We analyze a novel stage-wise greedy algorithm
and show that, as a function of the label complexity, the excess risk of this
algorithm matches the known minimax rates in standard statistical learning
settings. Our results also exhibit a mild dependence on the batch size. These
are the first theoretical results that employ careful trade offs between
informativeness and diversity to rigorously quantify the statistical
performance of batch active learning in the pool-based scenario.

本文在 batch active learning 场景下，提出了一种解决 informativeness 和 diversity 之间权衡问题的算法，理论上可以在 pool-based active learning 中得到最优结果，并且这也是第一篇使用这种方式明确量化在 pool-based 场景中 batch active learning 统计表现的论文。

基于池的批次主动学习中的快速速率

Fast Rates in Pool-Based Batch Active Learning

The disagreement coefficient of Hanneke has become a central data independent
invariant in proving active learning rates. It has been shown in various ways
that a concept class with low complexity together with a bound on the
disagreement coefficient at an optimal solution allows active learning rates
that are superior to passive learning ones.
We present a different tool for pool based active learning which follows from
the existence of a certain uniform version of low disagreement coefficient, but
is not equivalent to it. In fact, we present two fundamental active learning
problems of significant interest for which our approach allows nontrivial
active learning bounds. However, any general purpose method relying on the
disagreement coefficient bounds only fails to guarantee any useful bounds for
these problems.
The tool we use is based on the learner's ability to compute an estimator of
the difference between the loss of any hypotheses and some fixed "pivotal"
hypothesis to within an absolute error of at most $\eps$ times the

我们提出了一种基于池泛型主动学习的不同工具，该工具基于学习器计算假设损失和某个固定 “关键” 假设之间差异的估计器能力，进而得到一些显著意义上的主动学习界限，尤其对于那些只依赖于不一致性系数限制的方法在某些问题上无法提供有用边界的情况下。