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：自Witkowski等人[2022]的研究以来，近期关于预测竞赛的工作已针对常见的“赢家通吃”机制中的激励问题展开探讨。Frongillo等人[2021]提出了一种基于“跟随正则化领导者”(FTRL)在线学习框架的竞赛机制。他们证明，该机制仅需使用$O(\log(n)/\epsilon^2)$个事件，就能以高概率选出$\epsilon$-最优预测者。这些研究以及此前所有关于该问题的成果均假设事件相互独立。本文开创性地研究了关联事件中的预测竞赛。为量化关联性，我们引入了“块关联”概念，该概念允许每个事件与至多$b$个其他事件存在强关联。我们证明：在具有此类关联性的分布下，FTRL机制仅需使用$O(b^2 \log(n)/\epsilon^2)$个事件即可保持其$\epsilon$-最优保证。本文的证明涉及一个可能具有更广泛意义的关联随机变量新型集中不等式。