Online Conformal Prediction via Universal Portfolio Algorithms

2026-02-03

AI Summary

This work proposes UP-OCP, a parameter-free online conformal prediction method designed to handle arbitrary (including adversarial) data streams while simultaneously guaranteeing strict long-term coverage and producing highly informative prediction intervals. By introducing linearized regret as a core analytical tool, the authors establish a general regret-coverage theoretical framework and reformulate the online conformal prediction problem as a two-asset portfolio selection task, enabling adaptive parameter updates via universal portfolio algorithms. Theoretical analysis, leveraging Fenchel conjugacy and regret control, ensures finite-time miscoverage bounds. Empirical results demonstrate that UP-OCP consistently achieves nominal coverage while significantly narrowing prediction interval width, outperforming existing baseline methods.

Technology Category

• Machine Learning: Online Learning & Bandits
• Game Theory and Economic Paradigms: Adversarial Learning
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• User Modeling, Personalization and Recommendation: User modeling for targeted and personalized online advertising
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

Abstract

Online conformal prediction (OCP) seeks prediction intervals that achieve long-run $1-\alpha$ coverage for arbitrary (possibly adversarial) data streams, while remaining as informative as possible. Existing OCP methods often require manual learning-rate tuning to work well, and may also require algorithm-specific analyses. Here, we develop a general regret-to-coverage theory for interval-valued OCP based on the $(1-\alpha)$-pinball loss. Our first contribution is to identify \emph{linearized regret} as a key notion, showing that controlling it implies coverage bounds for any online algorithm. This relies on a black-box reduction that depends only on the Fenchel conjugate of an upper bound on the linearized regret. Building on this theory, we propose UP-OCP, a parameter-free method for OCP, via a reduction to a two-asset portfolio selection problem, leveraging universal portfolio algorithms. We show strong finite-time bounds on the miscoverage of UP-OCP, even for polynomially growing predictions. Extensive experiments support that UP-OCP delivers consistently better size/coverage trade-offs than prior online conformal baselines.

Problem

• Online Conformal Prediction
• Coverage
• Prediction Intervals
• Adversarial Data Streams
• Learning-rate Tuning

Innovation

• Online Conformal Prediction
• Universal Portfolio Algorithms
• Linearized Regret
• Parameter-Free Learning
• Coverage Guarantee