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：鲁棒预测聚合通过整合多个信息源的预测，在所有可能的信息结构下实现最坏情况下的良好性能。此前的工作主要集中于已知二元状态空间（即状态为0或1）的场景。我们研究先验无关的鲁棒预测聚合问题，其中聚合器仅观测到专家的报告，但对底层联合信息结构、完整先验以及状态空间本身一无所知。与固定二元状态空间{0,1}的标准模型不同，我们允许（二元）未知状态值为[0,1]中的任意数，因此相同报告的概率在不同环境下可能对应截然不同的实际结果频率。我们的主要贡献是一个简单、显式、闭合形式的对数几率聚合器，该聚合器在逻辑空间中线性汇集预测，同时在三个知识体系下提供了（近似）紧的极小极大遗憾保证。我们首先证明，在条件独立信号下，未知状态空间的鲁棒聚合比已知状态设置严格更困难——通过建立更大的下界——而我们的聚合规则可实现0.0255的最坏情况遗憾。在此过程中，我们还刻画了布莱克威尔有序结构以及一般信息结构的紧遗憾界。在已知状态空间{0,1}的经典设置下，针对条件独立结构，我们的聚合器实现的遗憾严格低于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：针对条件独立结构，我们证明广义对数几率规则可实现0.0228的遗憾，同时辅以0.0225的下界。