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.
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.
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.
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.
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.
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.
In an offline reinforcement learning setting, the safe policy improvement (SPI) problem aims to improve the performance of a behavior policy according to which sample data has been generated. State-of-the-art approaches to SPI require a high number of samples to provide practical probabilistic guarantees on the improved policy's performance. We present a novel approach to the SPI problem that provides the means to require less data for such guarantees. Specifically, to prove the correctness of these guarantees, we devise implicit transformations on the data set and the underlying environment model that serve as theoretical foundations to derive tighter improvement bounds for SPI. Our empirical evaluation, using the well-established SPI with baseline bootstrapping (SPIBB) algorithm, on standard benchmarks shows that our method indeed significantly reduces the sample complexity of the SPIBB algorithm.
We provide a novel method for sensitivity analysis of parametric robust Markov chains. These models incorporate parameters and sets of probability distributions to alleviate the often unrealistic assumption that precise probabilities are available. We measure sensitivity in terms of partial derivatives with respect to the uncertain transition probabilities regarding measures such as the expected reward. As our main contribution, we present an efficient method to compute these partial derivatives. To scale our approach to models with thousands of parameters, we present an extension of this method that selects the subset of $k$ parameters with the highest partial derivative. Our methods are based on linear programming and differentiating these programs around a given value for the parameters. The experiments show the applicability of our approach on models with over a million states and thousands of parameters. Moreover, we embed the results within an iterative learning scheme that profits from having access to a dedicated sensitivity analysis.
We study Markov decision processes (MDPs), where agents have direct control over when and how they gather information, as formalized by action-contingent noiselessly observable MDPs (ACNO-MPDs). In these models, actions consist of two components: a control action that affects the environment, and a measurement action that affects what the agent can observe. To solve ACNO-MDPs, we introduce the act-then-measure (ATM) heuristic, which assumes that we can ignore future state uncertainty when choosing control actions. We show how following this heuristic may lead to shorter policy computation times and prove a bound on the performance loss incurred by the heuristic. To decide whether or not to take a measurement action, we introduce the concept of measuring value. We develop a reinforcement learning algorithm based on the ATM heuristic, using a Dyna-Q variant adapted for partially observable domains, and showcase its superior performance compared to prior methods on a number of partially-observable environments.
This position paper reflects on the state-of-the-art in decision-making under uncertainty. A classical assumption is that probabilities can sufficiently capture all uncertainty in a system. In this paper, the focus is on the uncertainty that goes beyond this classical interpretation, particularly by employing a clear distinction between aleatoric and epistemic uncertainty. The paper features an overview of Markov decision processes (MDPs) and extensions to account for partial observability and adversarial behavior. These models sufficiently capture aleatoric uncertainty but fail to account for epistemic uncertainty robustly. Consequently, we present a thorough overview of so-called uncertainty models that exhibit uncertainty in a more robust interpretation. We show several solution techniques for both discrete and continuous models, ranging from formal verification, over control-based abstractions, to reinforcement learning. As an integral part of this paper, we list and discuss several key challenges that arise when dealing with rich types of uncertainty in a model-based fashion.