Blackwell's Approachability for Sequential Conformal Inference
This addresses the challenge of reliable uncertainty quantification in sequential or adversarial settings for statisticians and machine learning practitioners, though it is incremental as it builds on existing adaptive conformal inference methods.
The paper tackles the problem of conformal inference in non-exchangeable environments by applying Blackwell's approachability theory, recasting adaptive conformal inference as a game to characterize coverage-efficiency tradeoffs and designing a calibration-based strategy with strong theoretical guarantees.
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 Candès, 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.