mlsanityData to 14 Oct 2026

Certification of Iterative Predictions in Bayesian Neural Networks

arXiv 2105.10134 ↗First posted 21 May 2021cs.LGcited by 8

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Abstract (arXiv)

We consider the problem of computing reach-avoid probabilities for iterative predictions made with Bayesian neural network (BNN) models. Specifically, we leverage bound propagation techniques and backward recursion to compute lower bounds for the probability that trajectories of the BNN model reach a given set of states while avoiding a set of unsafe states. We use the lower bounds in the context of control and reinforcement learning to provide safety certification for given control policies, as well as to synthesize control policies that improve the certification bounds. On a set of benchmarks, we demonstrate that our framework can be employed to certify policies over BNNs predictions for problems of more than 10 dimensions, and to effectively synthesize policies that significantly increase the lower bound on the satisfaction probability.

Key facts. Cited by 8 papers in the map (data through 14 Oct 2026). Builds on 26 of its 54 references that are in the map. First posted on arXiv 21 May 2021.

Builds on

26 of 54 references.

References · 26

  1. 2016Asynchronous Methods for Deep Reinforcement Learningcited by 2,258
  2. 2018Obfuscated Gradients Give a False Sense of Security: Circumventing Defenses to Adversarial Examplescited by 1,268
  3. 2018Deep Reinforcement Learning in a Handful of Trials using Probabilistic Dynamics Modelscited by 774
  4. 2017Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networkscited by 744
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  11. 2019Uncertainty Quantification with Statistical Guarantees in End-to-End Autonomous Driving Controlcited by 61
  12. 2016Learning and Policy Search in Stochastic Dynamical Systems with Bayesian Neural Networkscited by 49
14 more
  1. 2020Robustness of Bayesian Neural Networks to Gradient-Based Attackscited by 48
  2. 2020Probabilistic Safety for Bayesian Neural Networkscited by 42
  3. 2018Formal Verification of Neural Network Controlled Autonomous Systemscited by 41
  4. 2019Certified Reinforcement Learning with Logic Guidancecited by 36
  5. 2019Statistical Guarantees for the Robustness of Bayesian Neural Networkscited by 35
  6. 2021Bayesian Inference with Certifiable Adversarial Robustnesscited by 26
  7. 2018Robustness Guarantees for Bayesian Inference with Gaussian Processescited by 23
  8. 2020Probabilistic Guarantees for Safe Deep Reinforcement Learningcited by 15
  9. 2019Efficiency through Uncertainty: Scalable Formal Synthesis for Stochastic Hybrid Systemscited by 11
  10. 2019Adversarial Robustness Guarantees for Classification with Gaussian Processescited by 11
  11. 2017Safe Policy Search with Gaussian Process Modelscited by 9
  12. 2020Safety Verification of Unknown Dynamical Systems via Gaussian Process Regressioncited by 9
  13. 2017How Wrong Am I? - Studying Adversarial Examples and their Impact on Uncertainty in Gaussian Process Machine Learning Modelscited by 3
  14. 2016Data-Efficient Reinforcement Learning in Continuous-State POMDPscited by 2

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 3; 2024: 1; 2025: 2; 2026: 2.

8 papers.

  1. 2023Adversarial Robustness Certification for Bayesian Neural Networkscited by 7
  2. 2023When to Trust AI: Advances and Challenges for Certification of Neural Networkscited by 6
  3. 2023Probabilistic Reach-Avoid for Bayesian Neural Networkscited by 5
  4. 2025Provably Safe Model Updatescited by 3
  5. 2024Risk-Averse Certification of Bayesian Neural Networkscited by 0
  6. 2025LTL Verification of Memoryful Neural Agentscited by 0
  7. 2026SafeAdapt: Provably Safe Policy Updates in Deep Reinforcement Learningcited by 0
  8. 2026Hybrid Robustness Verification for Spatio-Temporal Neural Networkscited by 0