Learning Control Policies for Stochastic Systems with Reach-Avoid Guarantees


  • Đorđe Žikelić IST Austria
  • Mathias Lechner MIT CSAIL
  • Thomas A. Henzinger IST Austria
  • Krishnendu Chatterjee IST Austria




PEAI: Safety, Robustness & Trustworthiness, ML: Adversarial Learning & Robustness, ML: Calibration & Uncertainty Quantification, ML: Probabilistic Methods, RU: Other Foundations of Reasoning Under Uncertainty


We study the problem of learning controllers for discrete-time non-linear stochastic dynamical systems with formal reach-avoid guarantees. This work presents the first method for providing formal reach-avoid guarantees, which combine and generalize stability and safety guarantees, with a tolerable probability threshold p in [0,1] over the infinite time horizon. Our method leverages advances in machine learning literature and it represents formal certificates as neural networks. In particular, we learn a certificate in the form of a reach-avoid supermartingale (RASM), a novel notion that we introduce in this work. Our RASMs provide reachability and avoidance guarantees by imposing constraints on what can be viewed as a stochastic extension of level sets of Lyapunov functions for deterministic systems. Our approach solves several important problems -- it can be used to learn a control policy from scratch, to verify a reach-avoid specification for a fixed control policy, or to fine-tune a pre-trained policy if it does not satisfy the reach-avoid specification. We validate our approach on 3 stochastic non-linear reinforcement learning tasks.




How to Cite

Žikelić, Đorđe, Lechner, M., Henzinger, T. A., & Chatterjee, K. (2023). Learning Control Policies for Stochastic Systems with Reach-Avoid Guarantees. Proceedings of the AAAI Conference on Artificial Intelligence, 37(10), 11926-11935. https://doi.org/10.1609/aaai.v37i10.26407



AAAI Technical Track on Philosophy and Ethics of AI