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.

Approximate Dec-POMDP Solving Using Multi-Agent A*

We present an A*-based algorithm to compute policies for finite-horizon Dec-POMDPs. Our goal is to sacrifice optimality in favor of scalability for larger horizons. The main ingredients of our approach are (1) using clustered sliding window memory, (2) pruning the A* search tree, and (3) using novel A* heuristics. Our experiments show competitive performance to the state-of-the-art. Moreover, for multiple benchmarks, we achieve superior performance. In addition, we provide an A* algorithm that finds upper bounds for the optimum, tailored towards problems with long horizons. The main ingredient is a new heuristic that periodically reveals the state, thereby limiting the number of reachable beliefs. Our experiments demonstrate the efficacy and scalability of the approach.

Imprecise Probabilities Meet Partial Observability: Game Semantics for Robust POMDPs

Partially observable Markov decision processes (POMDPs) rely on the key assumption that probability distributions are precisely known. Robust POMDPs (RPOMDPs) alleviate this concern by defining imprecise probabilities, referred to as uncertainty sets. While robust MDPs have been studied extensively, work on RPOMDPs is limited and primarily focuses on algorithmic solution methods. We expand the theoretical understanding of RPOMDPs by showing that 1) different assumptions on the uncertainty sets affect optimal policies and values; 2) RPOMDPs have a partially observable stochastic game (POSG) semantic; and 3) the same RPOMDP with different assumptions leads to semantically different POSGs and, thus, different policies and values. These novel semantics for RPOMDPS give access to results for the widely studied POSG model; concretely, we show the existence of a Nash equilibrium. Finally, we classify the existing RPOMDP literature using our semantics, clarifying under which uncertainty assumptions these existing works operate.

Factored Online Planning in Many-Agent POMDPs

In centralized multi-agent systems, often modeled as multi-agent partially observable Markov decision processes (MPOMDPs), the action and observation spaces grow exponentially with the number of agents, making the value and belief estimation of single-agent online planning ineffective. Prior work partially tackles value estimation by exploiting the inherent structure of multi-agent settings via so-called coordination graphs. Additionally, belief estimation has been improved by incorporating the likelihood of observations into the approximation. However, the challenges of value estimation and belief estimation have only been tackled individually, which prevents existing methods from scaling to many agents. Therefore, we address these challenges simultaneously. First, we introduce weighted particle filtering to a sample-based online planner for MPOMDPs. Second, we present a scalable approximation of the belief. Third, we bring an approach that exploits the typical locality of agent interactions to novel online planning algorithms for MPOMDPs operating on a so-called sparse particle filter tree. Our experimental evaluation against several state-of-the-art baselines shows that our methods (1) are competitive in settings with only a few agents and (2) improve over the baselines in the presence of many agents.

Robust Active Measuring under Model Uncertainty

Partial observability and uncertainty are common problems in sequential decision-making that particularly impede the use of formal models such as Markov decision processes (MDPs). However, in practice, agents may be able to employ costly sensors to measure their environment and resolve partial observability by gathering information. Moreover, imprecise transition functions can capture model uncertainty. We combine these concepts and extend MDPs to robust active-measuring MDPs (RAM-MDPs). We present an active-measure heuristic to solve RAM-MDPs efficiently and show that model uncertainty can, counterintuitively, let agents take fewer measurements. We propose a method to counteract this behavior while only incurring a bounded additional cost. We empirically compare our methods to several baselines and show their superior scalability and performance.

Correct-by-Construction Control for Stochastic and Uncertain Dynamical Models via Formal Abstractions

Automated synthesis of correct-by-construction controllers for autonomous systems is crucial for their deployment in safety-critical scenarios. Such autonomous systems are naturally modeled as stochastic dynamical models. The general problem is to compute a controller that provably satisfies a given task, represented as a probabilistic temporal logic specification. However, factors such as stochastic uncertainty, imprecisely known parameters, and hybrid features make this problem challenging. We have developed an abstraction framework that can be used to solve this problem under various modeling assumptions. Our approach is based on a robust finite-state abstraction of the stochastic dynamical model in the form of a Markov decision process with intervals of probabilities (iMDP). We use state-of-the-art verification techniques to compute an optimal policy on the iMDP with guarantees for satisfying the given specification. We then show that, by construction, we can refine this policy into a feedback controller for which these guarantees carry over to the dynamical model. In this short paper, we survey our recent research in this area and highlight two challenges (related to scalability and dealing with nonlinear dynamics) that we aim to address with our ongoing research.

Reinforcement Learning by Guided Safe Exploration

Safety is critical to broadening the application of reinforcement learning (RL). Often, we train RL agents in a controlled environment, such as a laboratory, before deploying them in the real world. However, the real-world target task might be unknown prior to deployment. Reward-free RL trains an agent without the reward to adapt quickly once the reward is revealed. We consider the constrained reward-free setting, where an agent (the guide) learns to explore safely without the reward signal. This agent is trained in a controlled environment, which allows unsafe interactions and still provides the safety signal. After the target task is revealed, safety violations are not allowed anymore. Thus, the guide is leveraged to compose a safe behaviour policy. Drawing from transfer learning, we also regularize a target policy (the student) towards the guide while the student is unreliable and gradually eliminate the influence of the guide as training progresses. The empirical analysis shows that this method can achieve safe transfer learning and helps the student solve the target task faster.