This paper addresses a key limitation in existing counterfactual inference methods for Markov Decision Processes (MDPs). Current approaches assume a specific causal model to make counterfactuals identifiable. However, there are usually many causal models that align with the observational and interventional distributions of an MDP, each yielding different counterfactual distributions, so fixing a particular causal model limits the validity (and usefulness) of counterfactual inference. W e propose a novel non-parametric approach that computes tight bounds on counterfactual transition probabilities across all compatible causal models. Unlike previous methods that require solving prohibitively large optimisation problems (with variables that grow exponentially in the size of the MDP), our approach provides closed-form expressions for these bounds, making computation highly efficient and scalable for non-trivial MDPs. Once such an interval counterfactual MDP is constructed, our method identifies robust counterfactual policies that optimise the worst-case reward w.r.t. the uncertain interval MDP probabilities. W e evaluate our method on various case studies, demonstrating improved robustness over existing methods.

Multi-agent planning under stochastic dynamics is usually formalised using decentralized (partially observable) Markov decision processes ( MDPs) and reachability or expected reward specifications. In this paper, we propose a different approach: we use an MDP describing how a single agent operates in an environment and probabilistic hyperproperties to capture desired temporal objectives for a set of decentralized agents operating in the environment. We extend existing approaches for model checking probabilistic hyperproperties to handle temporal formulae relating paths of different agents, thus requiring the self-composition between multiple MDPs. Using several case studies, we demonstrate that our approach provides a flexible and expressive framework to broaden the specification capabilities with respect to existing planning techniques. Additionally, we establish a close connection between a subclass of probabilistic hyperproperties and planning for a particular type of Dec-MDPs, for both of which we show undecidability. This lays the ground for the use of existing decentralized planning tools in the field of probabilistic hyperproperty verification.

Imitation learning techniques have been shown to be highly effective in real-world control scenarios, such as robotics. However, these approaches not only suffer from compounding error issues but also require human experts to provide complete trajectories. Although there exist interactive methods where an expert oversees the robot and intervenes if needed, these extensions usually only utilize the data collected during intervention periods and ignore the feedback signal hidden in non-intervention timesteps. In this work, we create a model to formulate how the interventions occur in such cases, and show that it is possible to learn a policy with just a handful of expert interventions. Our key insight is that it is possible to get crucial information about the quality of the current state and the optimality of the chosen action from expert feedback, regardless of the presence or the absence of intervention. We evaluate our method on various discrete and continuous simulation environments, a real-world robotic manipulation task, as well as a human subject study. Videos and the code can be found at https://liralab.usc.edu/mile .

We introduce a novel topology, called Kernel Mean Embedding Topology, for stochastic kernels, in a weak and strong form. This topology, defined on the spaces of Bochner integrable functions from a signal space to a space of probability measures endowed with a Hilbert space structure, allows for a versatile formulation. This construction allows one to obtain both a strong and weak formulation. (i) For its weak formulation, we highlight the utility on relaxed policy spaces, and investigate connections with the Young narrow topology and Borkar (or $w^*$)-topology, and establish equivalence properties. We report that, while both the $w^*$-topology and kernel mean embedding topology are relatively compact, they are not closed. Conversely, while the Young narrow topology is closed, it lacks relative compactness. (ii) We show that the strong form provides an appropriate formulation for placing topologies on spaces of models characterized by stochastic kernels with explicit robustness and learning theoretic implications on optimal stochastic control under discounted or average cost criteria. (iii) We show that this topology possesses several properties making it ideal to study optimality, approximations, robustness and continuity properties. In particular, the kernel mean embedding topology has a Hilbert space structure, which is particularly useful for approximating stochastic kernels through simulation data.

Guiding the policy of multi-agent reinforcement learning to align with human common sense is a difficult problem, largely due to the complexity of modeling common sense as a reward, especially in complex and long-horizon multi-agent tasks. Recent works have shown the effectiveness of reward shaping, such as potential-based rewards, to enhance policy alignment. The existing works, however, primarily rely on experts to design rule-based rewards, which are often labor-intensive and lack a high-level semantic understanding of common sense. To solve this problem, we propose a hierarchical vision-based reward shaping method. At the bottom layer, a visual-language model (VLM) serves as a generic potential function, guiding the policy to align with human common sense through its intrinsic semantic understanding. To help the policy adapts to uncertainty and changes in long-horizon tasks, the top layer features an adaptive skill selection module based on a visual large language model (vLLM). The module uses instructions, video replays, and training records to dynamically select suitable potential function from a pre-designed pool. Besides, our method is theoretically proven to preserve the optimal policy. Extensive experiments conducted in the Google Research Football environment demonstrate that our method not only achieves a higher win rate but also effectively aligns the policy with human common sense.

We study the problem of solving fixed-point equations for seminorm-contractive operators and establish foundational results on the non-asymptotic behavior of iterative algorithms in both deterministic and stochastic settings. Specifically, in the deterministic setting, we prove a fixed-point theorem for seminorm-contractive operators, showing that iterates converge geometrically to the kernel of the seminorm. In the stochastic setting, we analyze the corresponding stochastic approximation (SA) algorithm under seminorm-contractive operators and Markovian noise, providing a finite-sample analysis for various stepsize choices. A benchmark for equation solving is linear systems of equations, where the convergence behavior of fixed-point iteration is closely tied to the stability of linear dynamical systems. In this special case, our results provide a complete characterization of system stability with respect to a seminorm, linking it to the solution of a Lyapunov equation in terms of positive semi-definite matrices. In the stochastic setting, we establish a finite-sample analysis for linear Markovian SA without requiring the Hurwitzness assumption. Our theoretical results offer a unified framework for deriving finite-sample bounds for various reinforcement learning algorithms in the average reward setting, including TD($\lambda$) for policy evaluation (which is a special case of solving a Poisson equation) and Q-learning for control.

Markov chains are fundamental to statistical machine learning, underpinning key methodologies such as Markov Chain Monte Carlo (MCMC) sampling and temporal difference (TD) learning in reinforcement learning (RL). Given their widespread use, it is crucial to establish rigorous probabilistic guarantees on their convergence, uncertainty, and stability. In this work, we develop novel, high-dimensional concentration inequalities and Berry-Esseen bounds for vector- and matrix-valued functions of Markov chains, addressing key limitations in existing theoretical tools for handling dependent data. We leverage these results to analyze the TD learning algorithm, a widely used method for policy evaluation in RL. Our analysis yields a sharp high-probability consistency guarantee that matches the asymptotic variance up to logarithmic factors. Furthermore, we establish a $O(T^{-\frac{1}{4}}\log T)$ distributional convergence rate for the Gaussian approximation of the TD estimator, measured in convex distance. These findings provide new insights into statistical inference for RL algorithms, bridging the gaps between classical stochastic approximation theory and modern reinforcement learning applications.

In our increasingly interconnected world, Cyber-Physical Systems (CPS) play a crucial role in industries like healthcare, transportation, and manufacturing by combining physical processes with computing power. These systems, however, face many challenges, especially regarding security and system faults. Anomalies in CPS may indicate unexpected problems, from sensor malfunctions to cyber-attacks, and must be detected to prevent failures that can cause harm or disrupt services. This paper provides an overview of the different ways researchers have approached anomaly detection in CPS. We categorize and compare methods like machine learning, deep learning, mathematical models, invariant, and hybrid techniques. Our goal is to help readers understand the strengths and weaknesses of these methods and how they can be used to create safer, more reliable CPS. By identifying the gaps in current solutions, we aim to encourage future research that will make CPS more secure and adaptive in our increasingly automated world.

As machine learning-based prediction systems are increasingly used in high-stakes situations, it is important to understand how such predictive models will perform upon deployment. Distribution-free uncertainty quantification techniques such as conformal prediction provide guarantees about the loss black-box models will incur even when the details of the models are hidden. However, such methods are based on frequentist probability, which unduly limits their applicability. We revisit the central aspects of conformal prediction from a Bayesian perspective and thereby illuminate the shortcomings of frequentist guarantees. We propose a practical alternative based on Bayesian quadrature that provides interpretable guarantees and offers a richer representation of the likely range of losses to be observed at test time.

Adaptive Traffic Signal Control (ATSC) has become a popular research topic in intelligent transportation systems. Regional Traffic Signal Control (RTSC) using the Multi-agent Deep Reinforcement Learning (MADRL) technique has become a promising approach for ATSC due to its ability to achieve the optimum trade-off between scalability and optimality. Most existing RTSC approaches partition a traffic network into several disjoint regions, followed by applying centralized reinforcement learning techniques to each region. However, the pursuit of cooperation among RTSC agents still remains an open issue and no communication strategy for RTSC agents has been investigated. In this paper, we propose communication strategies to capture the correlation of micro-traffic states among lanes and the correlation of macro-traffic states among intersections. We first justify the evolution equation of the RTSC process is Markovian via a system of store-and-forward queues. Next, based on the evolution equation, we propose two GAT-Aggregated (GA2) communication modules--GA2-Naive and GA2-Aug to extract both intra-region and inter-region correlations between macro and micro traffic states. While GA2-Naive only considers the movements at each intersection, GA2-Aug also considers the lane-changing behavior of vehicles. Two proposed communication modules are then aggregated into two existing novel RTSC frameworks--RegionLight and Regional-DRL. Experimental results demonstrate that both GA2-Naive and GA2-Aug effectively improve the performance of existing RTSC frameworks under both real and synthetic scenarios. Hyperparameter testing also reveals the robustness and potential of our communication modules in large-scale traffic networks.