Improved Online Conformal Prediction via Strongly Adaptive Online Learning (2302.07869v1)

Abstract: We study the problem of uncertainty quantification via prediction sets, in an online setting where the data distribution may vary arbitrarily over time. Recent work develops online conformal prediction techniques that leverage regret minimization algorithms from the online learning literature to learn prediction sets with approximately valid coverage and small regret. However, standard regret minimization could be insufficient for handling changing environments, where performance guarantees may be desired not only over the full time horizon but also in all (sub-)intervals of time. We develop new online conformal prediction methods that minimize the strongly adaptive regret, which measures the worst-case regret over all intervals of a fixed length. We prove that our methods achieve near-optimal strongly adaptive regret for all interval lengths simultaneously, and approximately valid coverage. Experiments show that our methods consistently obtain better coverage and smaller prediction sets than existing methods on real-world tasks, such as time series forecasting and image classification under distribution shift.

Improved Online Conformal Prediction via Strongly Adaptive Online Learning

The paper "Improved Online Conformal Prediction via Strongly Adaptive Online Learning" addresses the challenge of uncertainty quantification in dynamic environments through online conformal prediction methods. Recognizing the limitation of standard regret minimization techniques in handling non-stationary data, the authors propose novel algorithms that incorporate strongly adaptive online learning to improve performance over both global and local intervals.

The core contribution of this paper is the development of the Strongly Adaptive Online Conformal Prediction (SAOCP) algorithm, designed to achieve near-optimal strongly adaptive regret across all possible time intervals. This enhancement is particularly pertinent in scenarios involving distribution shifts, such as time-series data or data subject to corruption, where traditional methods may underperform. SAOCP builds upon online learning techniques, specifically leveraging the concept of strongly adaptive regret introduced in the online learning literature, to guarantee robust performance across various sub-intervals of the sequence of data.

The authors integrate a several-armed approach, where multiple experts maintain separate intervals, into a cohesive meta-algorithm. This mechanism allows SAOCP to adaptively select experts based on their prediction performance. Using Scale-Free Online Gradient Descent (SF-OGD) for the expert implementation, the approach ensures that the prediction sets are not only valid in terms of coverage but also maintain efficiency by minimizing excess size. Empirical results featured in the paper demonstrate that SAOCP consistently provides superior coverage and generates narrower prediction intervals across diverse datasets, including time series forecasting and image classification tasks, compared to existing approaches such as FACI.

Theoretical analysis in the paper supports the empirical findings, offering bounds on strongly adaptive regret and coverage errors. In particular, the authors demonstrate that their methods align well with theoretical performance metrics, validating the adaptive capabilities of SAOCP in environments with abrupt or gradual data distribution shifts. The coverage bound analysis further relies on reasonable distributional assumptions, enhancing the practical applicability of these methods.

This paper makes significant progress in the field of online prediction under distribution instability, providing a foundation for advanced methods that ensure reliable uncertainty quantification across shifting domains. Given the rise of real-world applications with significant online data flows where data distributions are volatile, ensuring that predictive models can offer reliable predictions is crucial. Consequently, this work has implications for creating more robust AI systems capable of adapting in real-time to changing data patterns without sacrificing predictive certainty or efficiency.

Future research could explore expanding the range of data environments and exploring the generalized applicability of the SAOCP algorithm to other machine learning architectures or wider problem settings where uncertainty quantification remains a challenge. Additionally, further refining the theoretical underpinning of strongly adaptive online learning in the context of complex data transformations remains an intriguing area for exploration, potentially leading to broader applications in predictive analytics and AI-based decision-making systems.