arXiv:2604.24517cs.LGcs.GT2026-04被引 1

提出无需先验的预测聚合方法,可应对未知状态空间的最坏情况。

Prior-Agnostic Robust Forecast Aggregation

  • 在未知状态空间下,采用对数几率线性融合专家预测。
  • 最坏情况下后悔度低至0.0255,优于已有方法。
  • 适合对鲁棒性要求高的决策场景,如金融或风险评估。

稳健预测聚合旨在结合多个信息源的预测,在所有可能的信息结构中最优表现。以往研究多限于已知二元状态空间(0或1)的情形。本文研究先验无关的稳健预测聚合,即聚合器仅观测专家报告,却不知底层联合信息结构和完整先验,包括状态空间本身。不同于固定{0,1}状态空间的标准模型,我们允许未知二元状态值为[0,1]中任意实数,导致相同报告概率对应不同真实发生频率。核心贡献是一种简单、显式、闭式表达的对数几率聚合器,通过在logit空间线性池化预测,实现三种知识条件下近乎紧的极小极大后悔保证。我们证明:在条件独立信号下,未知状态空间情形比已知状态更难,且下界更高;所提规则可达到最坏后悔度0.0255。同时刻画了黑威尔序结构与一般信息结构的紧后悔界。在经典已知状态{0,1}设置下,该聚合器对条件独立结构的后悔度严格低于0.0226。据我们所知,这是首个实现后悔上界严格低于0.0226的显式闭式聚合器。最后,扩展到聚合器额外知晓每位专家边际预测分布的情形,在条件独立结构下,广义对数几率规则达到0.0228的后悔度,并给出0.0225的下界。

原文摘要 · Abstract (English)

Robust forecast aggregation combines the predictions of multiple information sources to perform well in the worst case across all possible information structures. Previous work largely focuses on settings with a known binary state space, where the state is either 0 or 1. We study prior-agnostic robust forecast aggregation in which the aggregator observes only experts' reports, yet is ignorant of both the underlying joint information structure and the full prior, including the underlying state space. Unlike the standard model that fixes the binary state space {0, 1}, we allow the (binary) unknown state values to be arbitrary numbers in [0, 1], so the same reported probability may correspond to very different realized outcome frequencies across environments. Our main contribution is a simple, explicit, closed-form log-odds aggregator that linearly pools forecasts in logit space, together with (nearly-)tight minimax-regret guarantees across three knowledge regimes. We first show that under conditionally independent (CI) signals, robust aggregation with an unknown state space is strictly harder than in the known-state setting by establishing a larger lower bound, and our aggregation rule can achieve a worst-case regret of 0.0255. Along the way, we also characterize tight regret bounds for Blackwell-ordered structures and for general information structures. In the classical setting with known state space {0,1}, our aggregator achieves regret strictly below 0.0226 for CI structures. To the best of our knowledge, this is the first explicit closed-form aggregator that achieves a regret upper bound strictly less than 0.0226. Finally, we extend the model where the aggregator additionally knows each expert's marginal forecast distribution; in this setting, with the CI structures, we show that a generalized log-odds rule achieves regret of 0.0228, complementing with a lower bound of 0.0225.

预测聚合鲁棒学习信息理论

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