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Robustness Verification of Deep Reinforcement Learning Based Control Systems using Reward Martingales

arXiv 2312.09695 ↗First posted 15 Dec 2023cs.AIcited by 0

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Abstract (arXiv)

Deep Reinforcement Learning (DRL) has gained prominence as an effective approach for control systems. However, its practical deployment is impeded by state perturbations that can severely impact system performance. Addressing this critical challenge requires robustness verification about system performance, which involves tackling two quantitative questions: (i) how to establish guaranteed bounds for expected cumulative rewards, and (ii) how to determine tail bounds for cumulative rewards. In this work, we present the first approach for robustness verification of DRL-based control systems by introducing reward martingales, which offer a rigorous mathematical foundation to characterize the impact of state perturbations on system performance in terms of cumulative rewards. Our verified results provide provably quantitative certificates for the two questions. We then show that reward martingales can be implemented and trained via neural networks, against different types of control policies. Experimental results demonstrate that our certified bounds tightly enclose simulation outcomes on various DRL-based control systems, indicating the effectiveness and generality of the proposed approach.

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References · 14

  1. 2015Continuous control with deep reinforcement learningcited by 3,407
  2. 2013Playing Atari with Deep Reinforcement Learningcited by 3,274
  3. 2017Safe Model-based Reinforcement Learning with Stability Guaranteescited by 366
  4. 2018On the Effectiveness of Interval Bound Propagation for Training Verifiably Robust Modelscited by 328
  5. 2020Robust Deep Reinforcement Learning against Adversarial Perturbations on State Observationscited by 238
  6. 2022Safe Control with Learned Certificates: A Survey of Neural Lyapunov, Barrier, and Contraction methodscited by 151
  7. 2018Reachability Analysis of Deep Neural Networks with Provable Guaranteescited by 93
  8. 2020Robust Deep Reinforcement Learning through Adversarial Losscited by 75
  9. 2019Certified Adversarial Robustness for Deep Reinforcement Learningcited by 47
  10. 2021Policy Smoothing for Provably Robust Reinforcement Learningcited by 40
  11. 2021Stability Verification in Stochastic Control Systems via Neural Network Supermartingalescited by 26
  12. 2022Learning Control Policies for Stochastic Systems with Reach-avoid Guaranteescited by 23
2 more
  1. 2023Neural Episodic Control with State Abstractioncited by 7
  2. 2019Cost Analysis of Nondeterministic Probabilistic Programscited by 2

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