Title: Conformal Regression under Distribution Shift: A Reinforcement Learning Method for Adaptive Uncertainty Quantification
Primary area: learning on time series and dynamical systems
Keywords: Conformal Prediction, Reinforcement Learning, Uncertainty Quantification, Time-series Forecasting

Abstract: Conformal prediction (CP) offers distribution-free uncertainty quantification with formal coverage guarantees, and has been widely applied to regression tasks, including time-series forecasting. However, in time-series settings, the exchangeability assumption underlying CP is often violated due to temporal dependencies. To address this, recent adaptive CP methods mitigate distributional shifts by dynamically calibrating intervals based on recent residuals and adaptive weighting strategies. However, these methods remain limited by their sensitivity to outliers, inability to detect systematic prediction bias, and the decoupling of calibration from model learning. In this work, we introduce CORE that establishes a mutual feedback loop between reinforcement learning (RL) and conformal prediction for adaptive uncertainty quantification. The method leverages RL's exploration capability to better cover uncertain or outlier regions, adapts calibration through exploration feedback, and designs uncertainty-guided rewards, enabling dynamically improved prediction and interval quality through policy interaction and feedback. We conduct extensive experiments to validate its effectiveness across 8 time-series standard datasets. The results demonstrate that our approach achieves superior accuracy and calibration, consistently outperforming 6 state-of-the-art baselines, with an average improvement of 1.36% in coverage rate and 5.03% in interval length.