Blackwell's Approachability for Sequential Conformal Inference

2025-10-17

AI Summary

This paper addresses the fundamental trade-off between coverage validity and predictive efficiency in conformal inference under non-exchangeable data distributions. We propose an adaptive sequentialization framework grounded in Blackwell approachability theory, recasting conformal inference as a constrained two-player vector-valued game. To our knowledge, this is the first integration of Blackwell theory into the conformal inference paradigm, enabling joint optimization of coverage and efficiency under adversarial or distributionally restricted opponent behavior. We design a calibration-aware strategy that dynamically approaches the ideal performance frontier. The resulting algorithm enjoys rigorous theoretical guarantees—ensuring provably valid coverage and asymptotically tight prediction intervals across diverse non-i.i.d. and adversarial settings. While computational overhead is increased relative to standard conformal methods, our approach establishes a novel principled framework for robust uncertainty quantification beyond exchangeability assumptions.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Sequential Decision Making
• Game Theory and Economic Paradigms: Adversarial Learning

Application Category

• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

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.

Problem

• Achieving valid conformal inference under distribution shifts
• Characterizing attainable coverage-efficiency tradeoffs adaptively
• Designing calibration strategies with strong theoretical guarantees

Innovation

• Using Blackwell's approachability theory for conformal inference
• Designing calibration-based approachability strategy for coverage
• Achieving strong theoretical guarantees with practical insights