[论文] Defensive Boosting for Online Probabilistic Forecasting
论文概要
研究领域: ML 作者: Georgy Noarov, Aaron Roth 发布时间: 2026-08-13 arXiv: 2608.13554中文摘要
我们研究由自适应对抗者选择的二元结果的在线概率预测。给定一个针对弱假设类H的在线学习算法，我们希望高效地同时获得现有在线提升技术分别提供的两个不可比较的保证。在线梯度提升在Brier分数上与H的张成所诱导的最佳预测器竞争，但当张成不包含准确预测器时则不提供任何保证。在线弱到强提升在弱学习条件下将分类误差驱动至零，但当该条件失败时几乎不提供保证。我们给出一个简单的防御性预测算法——Defensive Booster，同时获得这两个保证。在每个自适应序列上，其Brier分数与在线梯度提升以相同速率与H张成诱导的最佳预测竞争；同时，当实现的历史满足平滑弱学习条件时，其Brier分数和随机分类误差满足与在线分类提升相同的速率保证。这通过将提升的"对偶视角"操作化实现：当算法的随机分类误差持续较高时，其错误权重形成一种平滑重加权，使每个弱假设都具有低边缘，从而产生弱学习条件失败的事后硬核证书。我们还开发了一个强自适应变体，在每个时间间隔上满足两个保证。Defensive Booster非常高效：它只访问一个弱分类学习器，而我们比较的先前在线提升方法则维护大型弱学习器集成。在合成和真实数据流上的实验表明，它具有强大的预测性能（有时大幅改进所有先前基线），同时运行速度快几个数量级。原文摘要
We study online probabilistic forecasting of binary outcomes chosen by an adaptive adversary. Given an online learning algorithm for a weak hypothesis class H, we would like to efficiently obtain two incomparable guarantees that existing online boosting techniques provide separately. Online gradient boosting competes in Brier score with the best predictor induced by the span of H on every sequence, but promises nothing when the span does not contain an accurate predictor. Online weak-to-strong boosting drives classification error to zero under a weak-learning condition, but promises little when that condition fails. We give a simple defensive forecasting algorithm, the Defensive Booster, that obtains both guarantees. On every adaptive sequence, its Brier score is competitive with the best prediction induced by the span of H at the same rate as online gradient boosting; simultaneously, whenever the realized transcript satisfies the smooth weak-learning condition, its Brier score and randomized classification error satisfy the same rate guarantee as online classification boosting. This is achieved by operationalizing the "dual view" of boosting: When the algorithm's randomized classification error is persistently high, its mistake weights form a smooth reweighting on which every weak hypothesis has low edge, yielding an ex-post hard-core certificate that the weak-learning condition fails. We also develop a strongly adaptive variant, which satisfies both guarantees on every time interval. The Defensive Booster is very efficient: it accesses just one weak-class learner, whereas the prior online boosting methods we compare against maintain large weak-learner ensembles. Experiments on synthetic and real data streams demonstrate its strong predictive performance (sometimes substantially improving over all prior baselines) coupled with orders-of-magnitude faster runtime.--- *自动采集于 2026-08-15*
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