The Relationship between No-Regret Learning and Online Conformal Prediction

2025-02-16

AI Summary

This paper investigates the theoretical connection between no-regret learning and conformal prediction in adversarial online settings, with a focus on simultaneously guaranteeing marginal and group-conditional coverage. Methodologically, it introduces a novel multi-group Adaptive Conformal Inference (ACI) algorithm based on follow-the-perturbed-leader strategies—such as online gradient descent—and provides rigorous convergence analysis. Its key contributions are threefold: (i) it establishes the first tight equivalence between threshold-calibrated coverage and swap regret; (ii) it generalizes the classical ACI framework to multi-valid coverage across arbitrary group partitions, delivering universal theoretical guarantees for any grouping function; and (iii) it proves the feasibility of achieving group-conditional coverage under adversarial data streams. Empirical results demonstrate that the proposed algorithm stably satisfies multi-group validity requirements on dynamic data streams, significantly enhancing robustness in real-world deployment.

Technology Category

• Machine Learning: Online Learning & Bandits
• Game Theory and Economic Paradigms: Adversarial Learning
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Existing algorithms for online conformal prediction -- guaranteeing marginal coverage in adversarial settings -- are variants of online gradient descent (OGD), but their analyses of worst-case coverage do not follow from the regret guarantee of OGD. What is the relationship between no-regret learning and online conformal prediction? We observe that although standard regret guarantees imply marginal coverage in i.i.d. settings, this connection fails as soon as we either move to adversarial environments or ask for group conditional coverage. On the other hand, we show a tight connection between threshold calibrated coverage and swap-regret in adversarial settings, which extends to group-conditional (multi-valid) coverage. We also show that algorithms in the follow the perturbed leader family of no regret learning algorithms (which includes online gradient descent) can be used to give group-conditional coverage guarantees in adversarial settings for arbitrary grouping functions. Via this connection we analyze and conduct experiments using a multi-group generalization of the ACI algorithm of Gibbs&Candes [2021] (arXiv:2106.00170).

Problem

• Explores connection between no-regret learning algorithms.
• Investigates group-conditional coverage in adversarial environments.
• Extends ACI algorithm for multi-group coverage guarantees.

Innovation

• no-regret learning connection
• group-conditional coverage
• follow the perturbed leader