We present an efficient reduction that converts any machine learning algorithm into an interactive protocol, enabling collaboration with another party (e.g., a human) to achieve consensus on predictions and improve accuracy. This approach imposes calibration conditions on each party, which are computationally and statistically tractable relaxations of Bayesian rationality. These conditions are sensible even in prior-free settings, representing a significant generalization of Aumann's classic "agreement theorem." In our protocol, the model first provides a prediction. The human then responds by either agreeing or offering feedback. The model updates its state and revises its prediction, while the human may adjust their beliefs. This iterative process continues until the two parties reach agreement. Initially, we study a setting that extends Aumann's Agreement Theorem, where parties aim to agree on a one-dimensional expectation by iteratively sharing their current estimates. Here, we recover the convergence theorem of Aaronson'05 under weaker assumptions. We then address the case where parties hold beliefs over distributions with d outcomes, exploring two feedback mechanisms. The first involves vector-valued estimates of predictions, while the second adopts a decision-theoretic approach: the human, needing to take an action from a finite set based on utility, communicates their utility-maximizing action at each round. In this setup, the number of rounds until agreement remains independent of d. Finally, we generalize to scenarios with more than two parties, where computational complexity scales linearly with the number of participants. Our protocols rely on simple, efficient conditions and produce predictions that surpass the accuracy of any individual party's alone.

翻译：我们提出一种高效约简方法，可将任意机器学习算法转化为交互式协议，使其能够与另一方（例如人类）协作达成预测共识并提升准确率。该方法对各方施加校准条件，这些条件是贝叶斯理性在计算与统计意义上可处理的松弛形式。即使在无先验设定中，这些条件仍具有合理性，这构成了对奥曼经典"共识定理"的重要推广。在我们的协议中，模型首先提供预测，人类随后通过同意或提供反馈进行响应。模型更新其状态并修正预测，同时人类可调整其信念。此迭代过程持续至双方达成共识。首先，我们研究扩展奥曼共识定理的设定：各方通过迭代共享当前估计值来就一维期望达成共识。在此框架下，我们在更弱假设下恢复了Aaronson'05的收敛定理。随后我们处理各方持有d种结果分布信念的情形，探索两种反馈机制：第一种采用预测的向量值估计，第二种采用决策论方法——需要基于效用从有限集合中选择行动的人类，在每轮中传递其效用最大化行动。在此设置下，达成共识所需轮数与d无关。最后，我们将框架推广至多方参与场景，其计算复杂度随参与者数量线性增长。我们的协议依赖简洁高效的条件，产生的预测结果优于任何单方独立预测的准确率。