Wasserstein Auto-encoded MDPs: Formal Verification of Efficiently Distilled RL Policies with Many-sided Guarantees

Florent Delgrange, Ann Nowe, Guillermo A. Pérez

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Although deep reinforcement learning (DRL) has many success stories, the large-scale deployment of policies learned through these advanced techniques in safety-critical scenarios is hindered by their lack of formal guarantees. Variational Markov Decision Processes (VAE-MDPs) are discrete latent space models that provide a reliable framework for distilling formally verifiable controllers from any RL policy. While the related guarantees address relevant practical aspects such as the satisfaction of performance and safety properties, the VAE approach suffers from several learning flaws (posterior collapse, slow learning speed, poor dynamics estimates), primarily due to the absence of abstraction and representation guarantees to support latent optimization. We introduce the Wasserstein auto-encoded MDP (WAE-MDP), a latent space model that fixes those issues by minimizing a penalized form of the optimal transport between the behaviors of the agent executing the original policy and the distilled policy, for which the formal guarantees apply. Our approach yields bisimulation guarantees while learning the distilled policy, allowing concrete optimization of the abstraction and representation model quality. Our experiments show that, besides distilling policies up to 10 times faster, the latent model quality is indeed better in general. Moreover, we present experiments from a simple time-to-failure verification algorithm on the latent space. The fact that our approach enables such simple verification techniques highlights its applicability.
Original languageEnglish
Title of host publicationThe Eleventh International Conference on Learning Representations
Subtitle of host publicationICLR 2023
Place of PublicationKigali, Rwanda
Number of pages30
Publication statusPublished - 1 Feb 2023
EventThe Eleventh International Conference on Learning Representations: ICLR 2023 - Kigali Convention Centre, Kigali, Rwanda
Duration: 1 May 20235 May 2023
Conference number: 11


ConferenceThe Eleventh International Conference on Learning Representations
Abbreviated titleICLR 2023
Internet address


  • Reinforcement learning
  • Formal Verification
  • Representation Learning


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