Resilient Strategies for Stochastic Systems: How Much Does It Take to Break a Winning Strategy?

We study the problem of resilient strategies in the presence of uncertainty. Resilient strategies enable an agent to make decisions that are robust against disturbances. In particular, we are interested in those disturbances that are able to flip a decision made by the agent. Such a disturbance may, for instance, occur when the intended action of the agent cannot be executed due to a malfunction of an actuator in the environment. In this work, we introduce the concept of resilience in the stochastic setting and present a comprehensive set of fundamental problems. Specifically, we discuss such problems for Markov decision processes with reachability and safety objectives, which also smoothly extend to stochastic games. To account for the stochastic setting, we provide various ways of aggregating the amounts of disturbances that may have occurred, for instance, in expectation or in the worst case. Moreover, to reason about infinite disturbances, we use quantitative measures, like their frequency of occurrence.

Finite-State Controllers for (Hidden-Model) POMDPs using Deep Reinforcement Learning

Solving partially observable Markov decision processes (POMDPs) requires computing policies under imperfect state information. Despite recent advances, the scalability of existing POMDP solvers remains limited. Moreover, many settings require a policy that is robust across multiple POMDPs, further aggravating the scalability issue. We propose the Lexpop framework for POMDP solving. Lexpop (1) employs deep reinforcement learning to train a neural policy, represented by a recurrent neural network, and (2) constructs a finite-state controller mimicking the neural policy through efficient extraction methods. Crucially, unlike neural policies, such controllers can be formally evaluated, providing performance guarantees. We extend Lexpop to compute robust policies for hidden-model POMDPs (HM-POMDPs), which describe finite sets of POMDPs. We associate every extracted controller with its worst-case POMDP. Using a set of such POMDPs, we iteratively train a robust neural policy and consequently extract a robust controller. Our experiments show that on problems with large state spaces, Lexpop outperforms state-of-the-art solvers for POMDPs as well as HM-POMDPs.

Perception-Based Beliefs for POMDPs with Visual Observations

Partially observable Markov decision processes (POMDPs) are a principled planning model for sequential decision-making under uncertainty. Yet, real-world problems with high-dimensional observations, such as camera images, remain intractable for traditional belief- and filtering-based solvers. To tackle this problem, we introduce the Perception-based Beliefs for POMDPs framework (PBP), which complements such solvers with a perception model. This model takes the form of an image classifier which maps visual observations to probability distributions over states. PBP incorporates these distributions directly into belief updates, so the underlying solver does not need to reason explicitly over high-dimensional observation spaces. We show that the belief update of PBP coincides with the standard belief update if the image classifier is exact. Moreover, to handle classifier imprecision, we incorporate uncertainty quantification and introduce two methods to adjust the belief update accordingly. We implement PBP using two traditional POMDP solvers and empirically show that (1) it outperforms existing end-to-end deep RL methods and (2) uncertainty quantification improves robustness of PBP against visual corruption.

\textsc{rfPG}: Robust Finite-Memory Policy Gradients for Hidden-Model POMDPs

Partially observable Markov decision processes (POMDPs) model specific environments in sequential decision-making under uncertainty. Critically, optimal policies for POMDPs may not be robust against perturbations in the environment. Hidden-model POMDPs (HM-POMDPs) capture sets of different environment models, that is, POMDPs with a shared action and observation space. The intuition is that the true model is hidden among a set of potential models, and it is unknown which model will be the environment at execution time. A policy is robust for a given HM-POMDP if it achieves sufficient performance for each of its POMDPs. We compute such robust policies by combining two orthogonal techniques: (1) a deductive formal verification technique that supports tractable robust policy evaluation by computing a worst-case POMDP within the HM-POMDP and (2) subgradient ascent to optimize the candidate policy for a worst-case POMDP. The empirical evaluation shows that, compared to various baselines, our approach (1) produces policies that are more robust and generalize better to unseen POMDPs and (2) scales to HM-POMDPs that consist of over a hundred thousand environments.

Does Knowledge About Perceptual Uncertainty Help an Agent in Automated Driving?

Agents in real-world scenarios like automated driving deal with uncertainty in their environment, in particular due to perceptual uncertainty. Although, reinforcement learning is dedicated to autonomous decision-making under uncertainty these algorithms are typically not informed about the uncertainty currently contained in their environment. On the other hand, uncertainty estimation for perception itself is typically directly evaluated in the perception domain, e.g., in terms of false positive detection rates or calibration errors based on camera images. Its use for deciding on goal-oriented actions remains largely unstudied. In this paper, we investigate how an agent's behavior is influenced by an uncertain perception and how this behavior changes if information about this uncertainty is available. Therefore, we consider a proxy task, where the agent is rewarded for driving a route as fast as possible without colliding with other road users. For controlled experiments, we introduce uncertainty in the observation space by perturbing the perception of the given agent while informing the latter. Our experiments show that an unreliable observation space modeled by a perturbed perception leads to a defensive driving behavior of the agent. Furthermore, when adding the information about the current uncertainty directly to the observation space, the agent adapts to the specific situation and in general accomplishes its task faster while, at the same time, accounting for risks.

Tighter Value-Function Approximations for POMDPs

Solving partially observable Markov decision processes (POMDPs) typically requires reasoning about the values of exponentially many state beliefs. Towards practical performance, state-of-the-art solvers use value bounds to guide this reasoning. However, sound upper value bounds are often computationally expensive to compute, and there is a tradeoff between the tightness of such bounds and their computational cost. This paper introduces new and provably tighter upper value bounds than the commonly used fast informed bound. Our empirical evaluation shows that, despite their additional computational overhead, the new upper bounds accelerate state-of-the-art POMDP solvers on a wide range of benchmarks.

Robust Markov Decision Processes: A Place Where AI and Formal Methods Meet

Markov decision processes (MDPs) are a standard model for sequential decision-making problems and are widely used across many scientific areas, including formal methods and artificial intelligence (AI). MDPs do, however, come with the restrictive assumption that the transition probabilities need to be precisely known. Robust MDPs (RMDPs) overcome this assumption by instead defining the transition probabilities to belong to some uncertainty set. We present a gentle survey on RMDPs, providing a tutorial covering their fundamentals. In particular, we discuss RMDP semantics and how to solve them by extending standard MDP methods such as value iteration and policy iteration. We also discuss how RMDPs relate to other models and how they are used in several contexts, including reinforcement learning and abstraction techniques. We conclude with some challenges for future work on RMDPs.

Pessimistic Iterative Planning for Robust POMDPs

Robust partially observable Markov decision processes (robust POMDPs) extend classical POMDPs to handle additional uncertainty on the transition and observation probabilities via so-called uncertainty sets. Policies for robust POMDPs must not only be memory-based to account for partial observability but also robust against model uncertainty to account for the worst-case instances from the uncertainty sets. We propose the pessimistic iterative planning (PIP) framework, which finds robust memory-based policies for robust POMDPs. PIP alternates between two main steps: (1) selecting an adversarial (non-robust) POMDP via worst-case probability instances from the uncertainty sets; and (2) computing a finite-state controller (FSC) for this adversarial POMDP. We evaluate the performance of this FSC on the original robust POMDP and use this evaluation in step (1) to select the next adversarial POMDP. Within PIP, we propose the rFSCNet algorithm. In each iteration, rFSCNet finds an FSC through a recurrent neural network trained using supervision policies optimized for the adversarial POMDP. The empirical evaluation in four benchmark environments showcases improved robustness against a baseline method in an ablation study and competitive performance compared to a state-of-the-art robust POMDP solver.

Maintenance Strategies for Sewer Pipes with Multi-State Degradation and Deep Reinforcement Learning

Large-scale infrastructure systems are crucial for societal welfare, and their effective management requires strategic forecasting and intervention methods that account for various complexities. Our study addresses two challenges within the Prognostics and Health Management (PHM) framework applied to sewer assets: modeling pipe degradation across severity levels and developing effective maintenance policies. We employ Multi-State Degradation Models (MSDM) to represent the stochastic degradation process in sewer pipes and use Deep Reinforcement Learning (DRL) to devise maintenance strategies. A case study of a Dutch sewer network exemplifies our methodology. Our findings demonstrate the model's effectiveness in generating intelligent, cost-saving maintenance strategies that surpass heuristics. It adapts its management strategy based on the pipe's age, opting for a passive approach for newer pipes and transitioning to active strategies for older ones to prevent failures and reduce costs. This research highlights DRL's potential in optimizing maintenance policies. Future research will aim improve the model by incorporating partial observability, exploring various reinforcement learning algorithms, and extending this methodology to comprehensive infrastructure management.

Learning-Based Verification of Stochastic Dynamical Systems with Neural Network Policies

We consider the verification of neural network policies for reach-avoid control tasks in stochastic dynamical systems. We use a verification procedure that trains another neural network, which acts as a certificate proving that the policy satisfies the task. For reach-avoid tasks, it suffices to show that this certificate network is a reach-avoid supermartingale (RASM). As our main contribution, we significantly accelerate algorithmic approaches for verifying that a neural network is indeed a RASM. The main bottleneck of these approaches is the discretization of the state space of the dynamical system. The following two key contributions allow us to use a coarser discretization than existing approaches. First, we present a novel and fast method to compute tight upper bounds on Lipschitz constants of neural networks based on weighted norms. We further improve these bounds on Lipschitz constants based on the characteristics of the certificate network. Second, we integrate an efficient local refinement scheme that dynamically refines the state space discretization where necessary. Our empirical evaluation shows the effectiveness of our approach for verifying neural network policies in several benchmarks and trained with different reinforcement learning algorithms.