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Enhanced Route Planning with Calibrated Uncertainty Set

Lingxuan Tang, Rui Luo, Zhixin Zhou, Nicolo Colombo

TL;DR

The paper addresses route planning under uncertainty in road networks by learning edge-weight uncertainty sets with calibrated probabilistic predictions. It introduces Conformalized Quantile Regression for Graph Autoencoders (CQR-GAE), which outputs a mean and two quantiles for each edge and provides a coverage guarantee $P(W_e\in C_e)\ge 1-\alpha$, enabling robust optimization. The work adds an ERC enhancement to adapt intervals to heteroscedastic residuals and integrates these calibrated sets into risk-aware route planning, including contextual covariates via VaR-based objectives. Experiments on the Chicago traffic network demonstrate improved coverage and lower robust costs compared with baselines, highlighting practical benefits for intelligent transportation systems.

Abstract

This paper investigates the application of probabilistic prediction methodologies in route planning within a road network context. Specifically, we introduce the Conformalized Quantile Regression for Graph Autoencoders (CQR-GAE), which leverages the conformal prediction technique to offer a coverage guarantee, thus improving the reliability and robustness of our predictions. By incorporating uncertainty sets derived from CQR-GAE, we substantially improve the decision-making process in route planning under a robust optimization framework. We demonstrate the effectiveness of our approach by applying the CQR-GAE model to a real-world traffic scenario. The results indicate that our model significantly outperforms baseline methods, offering a promising avenue for advancing intelligent transportation systems.

Enhanced Route Planning with Calibrated Uncertainty Set

TL;DR

The paper addresses route planning under uncertainty in road networks by learning edge-weight uncertainty sets with calibrated probabilistic predictions. It introduces Conformalized Quantile Regression for Graph Autoencoders (CQR-GAE), which outputs a mean and two quantiles for each edge and provides a coverage guarantee , enabling robust optimization. The work adds an ERC enhancement to adapt intervals to heteroscedastic residuals and integrates these calibrated sets into risk-aware route planning, including contextual covariates via VaR-based objectives. Experiments on the Chicago traffic network demonstrate improved coverage and lower robust costs compared with baselines, highlighting practical benefits for intelligent transportation systems.

Abstract

This paper investigates the application of probabilistic prediction methodologies in route planning within a road network context. Specifically, we introduce the Conformalized Quantile Regression for Graph Autoencoders (CQR-GAE), which leverages the conformal prediction technique to offer a coverage guarantee, thus improving the reliability and robustness of our predictions. By incorporating uncertainty sets derived from CQR-GAE, we substantially improve the decision-making process in route planning under a robust optimization framework. We demonstrate the effectiveness of our approach by applying the CQR-GAE model to a real-world traffic scenario. The results indicate that our model significantly outperforms baseline methods, offering a promising avenue for advancing intelligent transportation systems.

Paper Structure

This paper contains 18 sections, 1 theorem, 17 equations, 6 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Works
  3. Robust Optimization for Networks
  4. Traffic Prediction
  5. Conformal Prediction
  6. GNN-Based Traffic Prediction
  7. GAE-Based Point Prediction
  8. CQR-Based Set Prediction
  9. ERC-Enhanced Set Prediction
  10. Robust Optimization for Route Planning
  11. Robust Optimization with Predicted Uncertainty Sets
  12. Contextual Risk-sensitive Robust Optimization
  13. Experiments
  14. Traffic Network Analysis
  15. Baseline
  16. ...and 3 more sections

Key Result

Theorem 1

Given any score $V$ satisfying the permutation invariance condition and any confidence level $\alpha\in (0,1)$, $V_{e}$ is a simple random sample from $\{V_{e}\}_{e\in \{\mathcal{E}^{\textrm{calib}} \cup \mathcal{E}^{\textrm{test}}\}}$. We define the split conformal prediction set as $\hat{C}_e =\{W

Figures (6)

  • Figure 1: Training settings for edge weight prediction in a conventional data split. Different colors indicate the availability of the nodes during training, calibration or testing. Solid and dashed lines represent edges used for training and edges within the test and calibration set. Predicting (1) corresponds to the transductive setting considered here. (2) and (3) are examples of the inductive setting. In road traffic forecasting, (1) may be the undetected traffic flow between two existing road junctions, e.g. for a (new) road where a traffic detector has not yet been installed. (2) and (3) represent scenarios where new road junctions are constructed, connecting to existing ones or forming connections with each other to create new roads.
  • Figure 2: The figure demonstrates the application of our proposed prediction models, which provide a coverage guarantee, using a snapshot of road network and traffic flow data from Chicago, IL, United States bar2021transportation. The road network is divided into training roads (represented by black solid lines) and test roads (represented by red dashed lines). Our CQR-GAE model (Algorithm \ref{['alg: CQR']}) is developed to generate a prediction interval with a user-specified error rate of $\alpha=0.05$. The middle plot displays the predicted edge weights $\hat{W}$, where the line thickness increases proportionally with the predicted edge weights. The right plot illustrates the lengths of the prediction intervals, with darker lines indicating wider intervals or higher inefficiency.
  • Figure 3: The figure illustrates various decision paths generated for a given source-target pair under Baseline, QR, CQR, CQR-ERC (training info from general information). Each subplot is accompanied by a descriptive title indicating the algorithm responsible for generating the respective path, along with the actual cost associated with it.
  • Figure 4: The figure illustrates various decision paths generated for a given source-target pair under Baseline, QR, CQR, CQR-ERC (training info from the neighborhood). Each subplot is accompanied by a descriptive title indicating the algorithm responsible for generating the respective path, along with the actual cost associated with it.
  • Figure 5: This figure compares the prediction intervals generated by the QR, CQR, and CQR-ERC methods (training info from general information) at $\alpha=0.05$ with the true edge weights.
  • ...and 1 more figures

Theorems & Definitions (2)

  • Theorem 1
  • proof