Florent Delgrange

Raphael Avalos, Florent Delgrange, Ann Nowé et al.

Partially Observable Markov Decision Processes (POMDPs) are used to model environments where the full state cannot be perceived by an agent. As such the agent needs to reason taking into account the past observations and actions. However, simply remembering the full history is generally intractable due to the exponential growth in the history space. Maintaining a probability distribution that models the belief over what the true state is can be used as a sufficient statistic of the history, but its computation requires access to the model of the environment and is often intractable. While SOTA algorithms use Recurrent Neural Networks to compress the observation-action history aiming to learn a sufficient statistic, they lack guarantees of success and can lead to sub-optimal policies. To overcome this, we propose the Wasserstein Belief Updater, an RL algorithm that learns a latent model of the POMDP and an approximation of the belief update. Our approach comes with theoretical guarantees on the quality of our approximation ensuring that our outputted beliefs allow for learning the optimal value function.

Florent Delgrange, Ann Nowé, Guillermo A. Pérez

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.

Florent Delgrange, Guy Avni, Anna Lukina et al.

We propose a novel framework to controller design in environments with a two-level structure: a known high-level graph ("map") in which each vertex is populated by a Markov decision process, called a "room". The framework "separates concerns" by using different design techniques for low- and high-level tasks. We apply reactive synthesis for high-level tasks: given a specification as a logical formula over the high-level graph and a collection of low-level policies obtained together with "concise" latent structures, we construct a "planner" that selects which low-level policy to apply in each room. We develop a reinforcement learning procedure to train low-level policies on latent structures, which unlike previous approaches, circumvents a model distillation step. We pair the policy with probably approximately correct guarantees on its performance and on the abstraction quality, and lift these guarantees to the high-level task. These formal guarantees are the main advantage of the framework. Other advantages include scalability (rooms are large and their dynamics are unknown) and reusability of low-level policies. We demonstrate feasibility in challenging case studies where an agent navigates environments with moving obstacles and visual inputs.

Florent Delgrange, Raphael Avalos, Willem Röpke

Safe policy improvement (SPI) offers theoretical control over policy updates, yet existing guarantees largely concern offline, tabular reinforcement learning (RL). We study SPI in general online settings, when combined with world model and representation learning. We develop a theoretical framework showing that restricting policy updates to a well-defined neighborhood of the current policy ensures monotonic improvement and convergence. This analysis links transition and reward prediction losses to representation quality, yielding online, "deep" analogues of classical SPI theorems from the offline RL literature. Building on these results, we introduce DeepSPI, a principled on-policy algorithm that couples local transition and reward losses with regularised policy updates. On the ALE-57 benchmark, DeepSPI matches or exceeds strong baselines, including PPO and DeepMDPs, while retaining theoretical guarantees.

Florent Delgrange, Ann Nowé, Guillermo A. Pérez

We consider the challenge of policy simplification and verification in the context of policies learned through reinforcement learning (RL) in continuous environments. In well-behaved settings, RL algorithms have convergence guarantees in the limit. While these guarantees are valuable, they are insufficient for safety-critical applications. Furthermore, they are lost when applying advanced techniques such as deep-RL. To recover guarantees when applying advanced RL algorithms to more complex environments with (i) reachability, (ii) safety-constrained reachability, or (iii) discounted-reward objectives, we build upon the DeepMDP framework introduced by Gelada et al. to derive new bisimulation bounds between the unknown environment and a learned discrete latent model of it. Our bisimulation bounds enable the application of formal methods for Markov decision processes. Finally, we show how one can use a policy obtained via state-of-the-art RL to efficiently train a variational autoencoder that yields a discrete latent model with provably approximately correct bisimulation guarantees. Additionally, we obtain a distilled version of the policy for the latent model.

Florent Delgrange, Joost-Pieter Katoen, Tim Quatmann et al.

We consider the verification of multiple expected reward objectives at once on Markov decision processes (MDPs). This enables a trade-off analysis among multiple objectives by obtaining the Pareto front. We focus on strategies that are easy to employ and implement. That is, strategies that are pure (no randomization) and have bounded memory. We show that checking whether a point is achievable by a pure stationary strategy is NP-complete, even for two objectives, and we provide an MILP encoding to solve the corresponding problem. The bounded memory case can be reduced to the stationary one by a product construction. Experimental results using \Storm and Gurobi show the feasibility of our algorithms.

Thomas Brihaye, Florent Delgrange, Youssouf Oualhadj et al.

The window mechanism was introduced by Chatterjee et al. to strengthen classical game objectives with time bounds. It permits to synthesize system controllers that exhibit acceptable behaviors within a configurable time frame, all along their infinite execution, in contrast to the traditional objectives that only require correctness of behaviors in the limit. The window concept has proved its interest in a variety of two-player zero-sum games because it enables reasoning about such time bounds in system specifications, but also thanks to the increased tractability that it usually yields. In this work, we extend the window framework to stochastic environments by considering Markov decision processes. A fundamental problem in this context is the threshold probability problem: given an objective it aims to synthesize strategies that guarantee satisfying runs with a given probability. We solve it for the usual variants of window objectives, where either the time frame is set as a parameter, or we ask if such a time frame exists. We develop a generic approach for window-based objectives and instantiate it for the classical mean-payoff and parity objectives, already considered in games. Our work paves the way to a wide use of the window mechanism in stochastic models.