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Learning from Yesterday's Error: An Efficient Online Learning Method for Traffic Demand Prediction

Xiannan Huang, Quan Yuan, Chao Yang

TL;DR

This work proposes FORESEE (Forecasting Online with Residual Smoothing and Ensemble Experts), a lightweight online adaptation framework that is accurate, robust, and computationally efficient and enables real-time adaptation of traffic forecasting models with negligible computational cost.

Abstract

Accurately predicting short-term traffic demand is critical for intelligent transportation systems. While deep learning models achieve strong performance under stationary conditions, their accuracy often degrades significantly when faced with distribution shifts caused by external events or evolving urban dynamics. Frequent model retraining to adapt to such changes incurs prohibitive computational costs, especially for large-scale or foundation models. To address this challenge, we propose FORESEE (Forecasting Online with Residual Smoothing and Ensemble Experts), a lightweight online adaptation framework that is accurate, robust, and computationally efficient. FORESEE operates without any parameter updates to the base model. Instead, it corrects today's forecast in each region using yesterday's prediction error, stabilized through exponential smoothing guided by a mixture-of-experts mechanism that adapts to recent error dynamics. Moreover, an adaptive spatiotemporal smoothing component propagates error signals across neighboring regions and time slots, capturing coherent shifts in demand patterns. Extensive experiments on seven real-world datasets with three backbone models demonstrate that FORESEE consistently improves prediction accuracy, maintains robustness even when distribution shifts are minimal (avoiding performance degradation), and achieves the lowest computational overhead among existing online methods. By enabling real-time adaptation of traffic forecasting models with negligible computational cost, FORESEE paves the way for deploying reliable, up-to-date prediction systems in dynamic urban environments. Code and data are available at https://github.com/xiannanhuang/FORESEE

Learning from Yesterday's Error: An Efficient Online Learning Method for Traffic Demand Prediction

TL;DR

This work proposes FORESEE (Forecasting Online with Residual Smoothing and Ensemble Experts), a lightweight online adaptation framework that is accurate, robust, and computationally efficient and enables real-time adaptation of traffic forecasting models with negligible computational cost.

Abstract

Accurately predicting short-term traffic demand is critical for intelligent transportation systems. While deep learning models achieve strong performance under stationary conditions, their accuracy often degrades significantly when faced with distribution shifts caused by external events or evolving urban dynamics. Frequent model retraining to adapt to such changes incurs prohibitive computational costs, especially for large-scale or foundation models. To address this challenge, we propose FORESEE (Forecasting Online with Residual Smoothing and Ensemble Experts), a lightweight online adaptation framework that is accurate, robust, and computationally efficient. FORESEE operates without any parameter updates to the base model. Instead, it corrects today's forecast in each region using yesterday's prediction error, stabilized through exponential smoothing guided by a mixture-of-experts mechanism that adapts to recent error dynamics. Moreover, an adaptive spatiotemporal smoothing component propagates error signals across neighboring regions and time slots, capturing coherent shifts in demand patterns. Extensive experiments on seven real-world datasets with three backbone models demonstrate that FORESEE consistently improves prediction accuracy, maintains robustness even when distribution shifts are minimal (avoiding performance degradation), and achieves the lowest computational overhead among existing online methods. By enabling real-time adaptation of traffic forecasting models with negligible computational cost, FORESEE paves the way for deploying reliable, up-to-date prediction systems in dynamic urban environments. Code and data are available at https://github.com/xiannanhuang/FORESEE
Paper Structure (29 sections, 4 theorems, 47 equations, 9 figures, 6 tables, 2 algorithms)

This paper contains 29 sections, 4 theorems, 47 equations, 9 figures, 6 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Short-term traffic prediction
  4. Online prediction
  5. Test-Time Adaptation
  6. Limitations of Existing Approaches
  7. Method
  8. Temporal Bias Correction via Exponential Smoothing and Expert Ensembling
  9. Leveraging Spatiotemporal Coherence for Robust Adjustment
  10. The FORESEE Frame work: Integration and Deployment
  11. Theoretical analysis
  12. Data generation mechanism
  13. Theorems
  14. Experiments
  15. Setup
  16. ...and 14 more sections

Key Result

Theorem 1

If we let $\hat{y}_t=f(x_t)$, then the prediction error during a period of $T$ days will be:

Figures (9)

  • Figure 1: The motivation of our method
  • Figure 2: The prediction errors of taxi usage in New York City
  • Figure 3: The prediction errors of taxi usage in Chicago City
  • Figure 4: The workflow of our method
  • Figure 5: The zones in New York and Chicago
  • ...and 4 more figures

Theorems & Definitions (8)

  • Theorem 1: The performance of original model
  • Theorem 2: The performance of using errors in the proceeding day to adjust the prediction in the next day
  • Theorem 3: The performance of using EMA errors in the proceeding days to adjust the prediction on the next day
  • Theorem 4: The performance of using multiple EMAs and mixture of experts
  • proof
  • proof
  • proof
  • proof