Uncertainty Quantification with Statistical Guarantees in End-to-End Autonomous Driving Control
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Abstract (arXiv)
Deep neural network controllers for autonomous driving have recently benefited from significant performance improvements, and have begun deployment in the real world. Prior to their widespread adoption, safety guarantees are needed on the controller behaviour that properly take account of the uncertainty within the model as well as sensor noise. Bayesian neural networks, which assume a prior over the weights, have been shown capable of producing such uncertainty measures, but properties surrounding their safety have not yet been quantified for use in autonomous driving scenarios. In this paper, we develop a framework based on a state-of-the-art simulator for evaluating end-to-end Bayesian controllers. In addition to computing pointwise uncertainty measures that can be computed in real time and with statistical guarantees, we also provide a method for estimating the probability that, given a scenario, the controller keeps the car safe within a finite horizon. We experimentally evaluate the quality of uncertainty computation by several Bayesian inference methods in different scenarios and show how the uncertainty measures can be combined and calibrated for use in collision avoidance. Our results suggest that uncertainty estimates can greatly aid decision making in autonomous driving.
Key facts. Cited by 60 papers in the map (data through 7 Oct 2026). First posted on arXiv 21 Sep 2019.
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Citing papers per year: 2021: 12; 2022: 5; 2023: 15; 2024: 13; 2025: 9; 2026: 6.
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- 2021Efficient Deep Reinforcement Learning with Imitative Expert Priors for Autonomous Drivingcited by 46
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- 2021Mind the Gap! A Study on the Transferability of Virtual vs Physical-world Testing of Autonomous Driving Systemscited by 36
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- 2023Learning Sample Difficulty from Pre-trained Models for Reliable Predictioncited by 15
- 2025UncAD: Towards Safe End-to-end Autonomous Driving via Online Map Uncertaintycited by 14
- 2021The Vulnerability of Semantic Segmentation Networks to Adversarial Attacks in Autonomous Driving: Enhancing Extensive Environment Sensingcited by 12
- 2021Infinite Time Horizon Safety of Bayesian Neural Networkscited by 12
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- 2021Statistical Perspectives on Reliability of Artificial Intelligence Systemscited by 10
- 2023Efficient Uncertainty Quantification and Reduction for Over-Parameterized Neural Networkscited by 10
- 2023SMARLA: A Safety Monitoring Approach for Deep Reinforcement Learning Agentscited by 9
- 2024Explaining Predictive Uncertainty by Exposing Second-Order Effectscited by 9
- 2021Certification of Iterative Predictions in Bayesian Neural Networkscited by 8
- 2023Clarifying Trust of Materials Property Predictions using Neural Networks with Distribution-Specific Uncertainty Quantificationcited by 8
- 2023How Safe Am I Given What I See? Calibrated Prediction of Safety Chances for Image-Controlled Autonomycited by 8
- 2023Adversarial Robustness Certification for Bayesian Neural Networkscited by 7
- 2024Safety Implications of Explainable Artificial Intelligence in End-to-End Autonomous Drivingcited by 7
- 2021Reliability Analysis of Artificial Intelligence Systems Using Recurrent Events Data from Autonomous Vehiclescited by 6
- 2023When to Trust AI: Advances and Challenges for Certification of Neural Networkscited by 6
- 2022Discrete-Event Controller Synthesis for Autonomous Systems with Deep-Learning Perception Componentscited by 5
- 2024Streamlining Prediction in Bayesian Deep Learningcited by 5
- 2022Variational Inference of overparameterized Bayesian Neural Networks: a theoretical and empirical studycited by 4
- 2023Probabilistic Reach-Avoid for Bayesian Neural Networkscited by 4
- 2024Inferring the Langevin Equation with Uncertainty via Bayesian Neural Networkscited by 4
- 2025SafePath: Conformal Prediction for Safe LLM-Based Autonomous Navigationcited by 4
- 2024Partial-Label Learning with a Reject Optioncited by 3
- 2025Mimir: Hierarchical Goal-Driven Diffusion with Uncertainty Propagation for End-to-End Autonomous Drivingcited by 3
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- 2023Dealing with uncertainty: balancing exploration and exploitation in deep recurrent reinforcement learningcited by 1
- 2024Pretraining with random noise for uncertainty calibrationcited by 1
- 2025Combining Bayesian Inference and Reinforcement Learning for Agent Decision Making: A Reviewcited by 1
- 2025How Safe Will I Be Given What I Saw? Calibrated Prediction of Safety Chances for Image-Controlled Autonomycited by 1
- 2022Safer Autonomous Driving in a Stochastic, Partially-Observable Environment by Hierarchical Contingency Planningcited by 0
- 2023Meta-learning to Calibrate Gaussian Processes with Deep Kernels for Regression Uncertainty Estimationcited by 0
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50 most cited of 60 All 60 (JSON)
- 2026Testing Between the Test Cases: Proving End-to-End Steering in Conditions You Never Drove10 Sep 2026
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- 2026Clustered Randomized Smoothing for Stochastic Prediction Functions12 Aug 2026
- 2026UECP: Uncertainty-Enhanced Collaborative Perception22 Jun 2026
- 2026SPACR: Single-Pass Adaptive Training of Uncertainty-Aware Conformal Regressors9 Jun 2026
- 2026Uncertainty-Guided Label Rebalancing for CPS Safety Monitoring26 Mar 2026
- 2025Mimir: Hierarchical Goal-Driven Diffusion with Uncertainty Propagation for End-to-End Autonomous Driving8 Dec 2025
- 2025How Safe Will I Be Given What I Saw? Calibrated Prediction of Safety Chances for Image-Controlled Autonomy12 Aug 2025
- 2025Stochastic Weight Sharing for Bayesian Neural Networks23 May 2025
- 2025SafePath: Conformal Prediction for Safe LLM-Based Autonomous Navigation14 May 2025
- 2025Combining Bayesian Inference and Reinforcement Learning for Agent Decision Making: A Review12 May 2025
- 2025Probabilistic Interactive 3D Segmentation with Hierarchical Neural Processes3 May 2025
38 more
- 2025Model uncertainty quantification using feature confidence sets for outcome excursions28 Apr 2025
- 2025UncAD: Towards Safe End-to-end Autonomous Driving via Online Map Uncertainty17 Apr 2025
- 2025Support is All You Need for Certified VAE Training16 Apr 2025
- 2024Pretraining with random noise for uncertainty calibration23 Dec 2024
- 2024Risk-Averse Certification of Bayesian Neural Networks29 Nov 2024
- 2024Streamlining Prediction in Bayesian Deep Learning27 Nov 2024
- 2024Good Data Is All Imitation Learning Needs26 Sep 2024
- 2024Achieving Well-Informed Decision-Making in Drug Discovery: A Comprehensive Calibration Study using Neural Network-Based Structure-Activity Models19 Jul 2024
- 2024Full-ECE: A Metric For Token-level Calibration on Large Language Models17 Jun 2024
- 2024Central Limit Theorem for Bayesian Neural Network trained with Variational Inference10 Jun 2024
- 2024Accurate and Reliable Predictions with Mutual-Transport Ensemble30 May 2024
- 2024Predicting Safety Misbehaviours in Autonomous Driving Systems using Uncertainty Quantification29 Apr 2024
- 2024Safety Implications of Explainable Artificial Intelligence in End-to-End Autonomous Driving18 Mar 2024
- 2024Inferring the Langevin Equation with Uncertainty via Bayesian Neural Networks2 Feb 2024
- 2024Partial-Label Learning with a Reject Option1 Feb 2024
- 2024Explaining Predictive Uncertainty by Exposing Second-Order Effects30 Jan 2024
- 2023Meta-learning to Calibrate Gaussian Processes with Deep Kernels for Regression Uncertainty Estimation13 Dec 2023
- 2023Dealing with uncertainty: balancing exploration and exploitation in deep recurrent reinforcement learning12 Oct 2023
- 2023Probabilistic Reach-Avoid for Bayesian Neural Networks3 Oct 2023
- 2023When to Trust AI: Advances and Challenges for Certification of Neural Networks20 Sep 2023
- 2023Distributionally Robust Statistical Verification with Imprecise Neural Networks28 Aug 2023
- 2023How Safe Am I Given What I See? Calibrated Prediction of Safety Chances for Image-Controlled Autonomy23 Aug 2023
- 2023SMARLA: A Safety Monitoring Approach for Deep Reinforcement Learning Agents3 Aug 2023
- 2023Bayesian inference for data-efficient, explainable, and safe robotic motion planning: A review16 Jul 2023
- 2023Law of Large Numbers for Bayesian two-layer Neural Network trained with Variational Inference10 Jul 2023
- 2023Adversarial Robustness Certification for Bayesian Neural Networks23 Jun 2023
- 2023Hyperbolic Active Learning for Semantic Segmentation under Domain Shift19 Jun 2023
- 2023Efficient Uncertainty Quantification and Reduction for Over-Parameterized Neural Networks9 Jun 2023
- 2023Learning Sample Difficulty from Pre-trained Models for Reliable Prediction20 Apr 2023
- 2023Uncertainty Calibration for Counterfactual Propensity Estimation in Recommendation23 Mar 2023
- 2023Clarifying Trust of Materials Property Predictions using Neural Networks with Distribution-Specific Uncertainty Quantification6 Feb 2023
- 2022On the Robustness of Bayesian Neural Networks to Adversarial Attacks13 Jul 2022
- 2022Variational Inference of overparameterized Bayesian Neural Networks: a theoretical and empirical study8 Jul 2022
- 2022Improving Trustworthiness of AI Disease Severity Rating in Medical Imaging with Ordinal Conformal Prediction Sets5 Jul 2022
- 2022Safer Autonomous Driving in a Stochastic, Partially-Observable Environment by Hierarchical Contingency Planning13 Apr 2022
- 2022Discrete-Event Controller Synthesis for Autonomous Systems with Deep-Learning Perception Components7 Feb 2022
- 2021Mind the Gap! A Study on the Transferability of Virtual vs Physical-world Testing of Autonomous Driving Systems21 Dec 2021
- 2021Statistical Perspectives on Reliability of Artificial Intelligence Systems9 Nov 2021
50 newest of 60 All 60 (JSON)
- 2021Efficient Deep Reinforcement Learning with Imitative Expert Priors for Autonomous Drivingcited by 46
- 2025UncAD: Towards Safe End-to-end Autonomous Driving via Online Map Uncertaintycited by 14
- 2024Safety Implications of Explainable Artificial Intelligence in End-to-End Autonomous Drivingcited by 7
- 2025Mimir: Hierarchical Goal-Driven Diffusion with Uncertainty Propagation for End-to-End Autonomous Drivingcited by 3
- 2022Safer Autonomous Driving in a Stochastic, Partially-Observable Environment by Hierarchical Contingency Planningcited by 0
- 2026Variance-Guided Spatial Attention Fusion for Robust End-to-End Driving under Asymmetric Sensor Degradationcited by 0
- 2026Variance-Guided Spatial Attention Fusion for Robust End-to-End Driving under Asymmetric Sensor Degradation25 Aug 2026
- 2025Mimir: Hierarchical Goal-Driven Diffusion with Uncertainty Propagation for End-to-End Autonomous Driving8 Dec 2025
- 2025UncAD: Towards Safe End-to-end Autonomous Driving via Online Map Uncertainty17 Apr 2025
- 2024Safety Implications of Explainable Artificial Intelligence in End-to-End Autonomous Driving18 Mar 2024
- 2022Safer Autonomous Driving in a Stochastic, Partially-Observable Environment by Hierarchical Contingency Planning13 Apr 2022
- 2021Efficient Deep Reinforcement Learning with Imitative Expert Priors for Autonomous Driving19 Mar 2021
- 2024Good Data Is All Imitation Learning Needscited by 2
- 2024Good Data Is All Imitation Learning Needs26 Sep 2024
- 2022Improving Trustworthiness of AI Disease Severity Rating in Medical Imaging with Ordinal Conformal Prediction Setscited by 38
- 2021Mind the Gap! A Study on the Transferability of Virtual vs Physical-world Testing of Autonomous Driving Systemscited by 36
- 2021Dangers of Bayesian Model Averaging under Covariate Shiftcited by 31
- 2021Valid prediction intervals for regression problemscited by 28
- 2021Deep Ensembles from a Bayesian Perspectivecited by 27
- 2021Make Sure You're Unsure: A Framework for Verifying Probabilistic Specificationscited by 18
- 2023Hyperbolic Active Learning for Semantic Segmentation under Domain Shiftcited by 18
- 2023Learning Sample Difficulty from Pre-trained Models for Reliable Predictioncited by 15
- 2021The Vulnerability of Semantic Segmentation Networks to Adversarial Attacks in Autonomous Driving: Enhancing Extensive Environment Sensingcited by 12
- 2021Infinite Time Horizon Safety of Bayesian Neural Networkscited by 12
- 2022On the Robustness of Bayesian Neural Networks to Adversarial Attackscited by 12
- 2023Distributionally Robust Statistical Verification with Imprecise Neural Networkscited by 12
12 most cited of 52 All 52 (JSON)
- 2026Testing Between the Test Cases: Proving End-to-End Steering in Conditions You Never Drove10 Sep 2026
- 2026Clustered Randomized Smoothing for Stochastic Prediction Functions12 Aug 2026
- 2026UECP: Uncertainty-Enhanced Collaborative Perception22 Jun 2026
- 2026SPACR: Single-Pass Adaptive Training of Uncertainty-Aware Conformal Regressors9 Jun 2026
- 2026Uncertainty-Guided Label Rebalancing for CPS Safety Monitoring26 Mar 2026
- 2025Stochastic Weight Sharing for Bayesian Neural Networks23 May 2025
- 2025SafePath: Conformal Prediction for Safe LLM-Based Autonomous Navigation14 May 2025
- 2025Combining Bayesian Inference and Reinforcement Learning for Agent Decision Making: A Review12 May 2025
- 2025Probabilistic Interactive 3D Segmentation with Hierarchical Neural Processes3 May 2025
- 2025Model uncertainty quantification using feature confidence sets for outcome excursions28 Apr 2025
- 2025Support is All You Need for Certified VAE Training16 Apr 2025
- 2024Pretraining with random noise for uncertainty calibration23 Dec 2024
12 newest of 52 All 52 (JSON)