Beginning with Witkowski et al. [2022], recent work on forecasting competitions has addressed incentive problems with the common winner-take-all mechanism. Frongillo et al. [2021] propose a competition mechanism based on follow-the-regularized-leader (FTRL), an online learning framework. They show that their mechanism selects an $\epsilon$-optimal forecaster with high probability using only $O(\log(n)/\epsilon^2)$ events. These works, together with all prior work on this problem thus far, assume that events are independent. We initiate the study of forecasting competitions for correlated events. To quantify correlation, we introduce a notion of block correlation, which allows each event to be strongly correlated with up to $b$ others. We show that under distributions with this correlation, the FTRL mechanism retains its $\epsilon$-optimal guarantee using $O(b^2 \log(n)/\epsilon^2)$ events. Our proof involves a novel concentration bound for correlated random variables which may be of broader interest.

翻译：摘要：从Witkowski et al. [2022]开始，最近的预测竞赛研究已经解决了使用常见的赢者通吃机制带来的激励问题。Frongillo et al. [2021]提出了一种基于follow-the-regularized-leader (FTRL)，一种在线学习框架的竞赛机制。他们表明，在仅使用$O(\log(n)/\epsilon^2)$事件的情况下，他们的机制可以选择一个$\epsilon$最优的预测者的概率很高。这些工作以及迄今为止针对该问题的所有先前工作都假定事件是独立的。我们开始研究相关事件的预测竞赛。为了量化相关性，我们引入了一个块相关性的概念，它允许每个事件与多达b个其他事件强相关。我们证明，在具有这种相关性的分布下，FTRL机制可保持其$\epsilon$-最优性保证，只需使用$O(b^2 \log(n)/\epsilon^2)$个事件。我们的证明涉及一种新的相关随机变量的浓度边界，可能具有更广泛的兴趣。