We show that in pool-based active classification without assumptions on the underlying distribution, if the learner is given the power to abstain from some predictions by paying the price marginally smaller than the average loss $1/2$ of a random guess, exponential savings in the number of label requests are possible whenever they are possible in the corresponding realizable problem. We extend this result to provide a necessary and sufficient condition for exponential savings in pool-based active classification under the model misspecification.

翻译：我们表明,在基于集合的积极分类中,不假定基本分布,如果学习者有权通过支付略小于随机猜测平均损失1/2美元的价格而放弃某些预测,只要在相应的可实现问题中有可能,标签要求的数量就有可能指数性地节省。 我们扩大这一结果,为在模型误差下根据基于集合的积极分类指数性储蓄提供了必要和充分的条件。