We study conformal inference in non-exchangeable environments through the lens of Blackwell's theory of approachability. We first recast adaptive conformal inference (ACI, Gibbs and Cand\`es, 2021) as a repeated two-player vector-valued finite game and characterize attainable coverage--efficiency tradeoffs. We then construct coverage and efficiency objectives under potential restrictions on the adversary's play, and design a calibration-based approachability strategy to achieve these goals. The resulting algorithm enjoys strong theoretical guarantees and provides practical insights, though its computational burden may limit deployment in practice.

翻译：本文通过布莱克威尔可接近性理论研究了非可交换环境下的共形推断问题。我们首先将自适应共形推断（ACI，Gibbs与Candès，2021）重构为重复双人向量值有限博弈，并刻画了可达的覆盖效率权衡关系。随后在对手行为可能受限的条件下构建了覆盖度与效率目标，并设计了基于校准的可接近性策略来实现这些目标。所得算法具有坚实的理论保证并提供实用洞见，但其计算负担可能限制实际部署。