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.

翻译：鲁棒性预测聚合将多个信息源的预测结果进行组合，以在所有可能的信息结构下实现最坏情况下的优异表现。以往的研究主要关注已知二元状态空间（状态为0或1）的场景。本文研究先验无关的鲁棒性预测聚合，其中聚合器仅能观察到专家报告，但对底层的联合信息结构以及完整先验（包括潜在的状态空间）一无所知。与固定二元状态空间{0, 1}的标准模型不同，我们允许（二元的）未知状态值为[0,1]区间内的任意数值，因此相同的报告概率在不同环境下可能对应截然不同的实际结果频率。我们的主要贡献在于提出了一种简洁、显式且闭合形式的对数几率聚合器，该聚合器在对数几率空间中对预测进行线性池化，并针对三种知识体系提供了（近乎）紧的最小最大遗憾保证。我们首先证明，在条件独立（CI）信号下，与已知状态空间场景相比，未知状态空间的鲁棒聚合难度严格更高（通过确立更大的下界），而我们的聚合规则可实现0.0255的最坏情况遗憾值。此外，我们还刻画了Blackwell序结构和一般信息结构下的紧遗憾界。在经典已知状态空间{0,1}场景中，我们的聚合器在CI结构下的遗憾值严格低于0.0226。据我们所知，这是首个实现遗憾上界严格小于0.0226的显式闭合形式聚合器。最后，我们将模型扩展至聚合器额外知晓每位专家边际预测分布的场景；在此设置下（针对CI结构），我们证明广义对数几率规则可实现0.0228的遗憾值，并补充了0.0225的下界。