The theoretical analysis of Markov Decision Processes (MDPs) is commonly split into two cases - the average-reward case and the discounted-reward case - which, while sharing similarities, are typically analyzed separately. In this work, we extend a recently introduced geometric interpretation of MDPs for the discounted-reward case to the average-reward case, thereby unifying both. This allows us to extend a major result known for the discounted-reward case to the average-reward case: under a unique and ergodic optimal policy, the Value Iteration algorithm achieves a geometric convergence rate.

This paper studies group target trajectory intent as the outcome of a cooperative game where the complex-spatio trajectories are modeled using an NLP-based generative model. In our framework, the group intent is specified by the characteristic function of a cooperative game, and allocations for players in the cooperative game are specified by either the core, the Shapley value, or the nucleolus. The resulting allocations induce probability distributions that govern the coordinated spatio-temporal trajectories of the targets that reflect the group's underlying intent. We address two key questions: (1) How can the intent of a group trajectory be optimally formalized as the characteristic function of a cooperative game? (2) How can such intent be inferred from noisy observations of the targets? To answer the first question, we introduce a Fisher-information-based characteristic function of the cooperative game, which yields probability distributions that generate coordinated spatio-temporal patterns. As a generative model for these patterns, we develop an NLP-based generative model built on formal grammar, enabling the creation of realistic multi-target trajectory data. To answer the second question, we train a Graph Transformer Neural Network (GTNN) to infer group trajectory intent-expressed as the characteristic function of the cooperative game-from observational data with high accuracy. The self-attention function of the GTNN depends on the track estimates. Thus, the formulation and algorithms provide a multi-layer approach that spans target tracking (Bayesian signal processing) and the GTNN (for group intent inference).

Autonomous drone technology holds significant promise for enhancing search and rescue operations during evacuations by guiding humans toward safety and supporting broader emergency response efforts. However, their application in dynamic, real-time evacuation support remains limited. Existing models often overlook the psychological and emotional complexity of human behavior under extreme stress. In real-world fire scenarios, evacuees frequently deviate from designated safe routes due to panic and uncertainty. To address these challenges, this paper presents a multi-agent coordination framework in which autonomous Unmanned Aerial Vehicles (UAVs) assist human evacuees in real-time by locating, intercepting, and guiding them to safety under uncertain conditions. We model the problem as a Partially Observable Markov Decision Process (POMDP), where two heterogeneous UAV agents, a high-level rescuer (HLR) and a low-level rescuer (LLR), coordinate through shared observations and complementary capabilities. Human behavior is captured using an agent-based model grounded in empirical psychology, where panic dynamically affects decision-making and movement in response to environmental stimuli. The environment features stochastic fire spread, unknown evacuee locations, and limited visibility, requiring UAVs to plan over long horizons to search for humans and adapt in real-time. Our framework employs the Proximal Policy Optimization (PPO) algorithm with recurrent policies to enable robust decision-making in partially observable settings. Simulation results demonstrate that the UAV team can rapidly locate and intercept evacuees, significantly reducing the time required for them to reach safety compared to scenarios without UAV assistance.

Multi-environment POMDPs (ME-POMDPs) extend standard POMDPs with discrete model uncertainty. ME-POMDPs represent a finite set of POMDPs that share the same state, action, and observation spaces, but may arbitrarily vary in their transition, observation, and reward models. Such models arise, for instance, when multiple domain experts disagree on how to model a problem. The goal is to find a single policy that is robust against any choice of POMDP within the set, i.e., a policy that maximizes the worst-case reward across all POMDPs. We generalize and expand on existing work in the following way. First, we show that ME-POMDPs can be generalized to POMDPs with sets of initial beliefs, which we call adversarial-belief POMDPs (AB-POMDPs). Second, we show that any arbitrary ME-POMDP can be reduced to a ME-POMDP that only varies in its transition and reward functions or only in its observation and reward functions, while preserving (optimal) policies. We then devise exact and approximate (point-based) algorithms to compute robust policies for AB-POMDPs, and thus ME-POMDPs. We demonstrate that we can compute policies for standard POMDP benchmarks extended to the multi-environment setting.

This paper presents an approach for accelerated learning of optimal plans for a given task represented using Linear Temporal Logic (LTL) in multi-agent systems. Given a set of options (temporally abstract actions) available to each agent, we convert the task specification into the corresponding Buchi Automaton and proceed with a model-free approach which collects transition samples and constructs a product Semi Markov Decision Process (SMDP) on-the-fly. Value-based Reinforcement Learning algorithms can then be used to synthesize a correct-by-design controller without learning the underlying transition model of the multi-agent system. The exponential sample complexity due to multiple agents is dealt with using a novel reward shaping approach. We test the proposed algorithm in a deterministic gridworld simulation for different tasks and find that the reward shaping results in significant reduction in convergence times. We also infer that using options becomes increasing more relevant as the state and action space increases in multi-agent systems.

Reinforcement Learning (RL) from raw visual input has achieved impressive successes in recent years, yet it remains fragile to out-of-distribution variations such as changes in lighting, color, and viewpoint. Point Cloud Reinforcement Learning (PC-RL) offers a promising alternative by mitigating appearance-based brittleness, but its sensitivity to camera pose mismatches continues to undermine reliability in realistic settings. To address this challenge, we propose PCA Point Cloud (PPC), a canonicalization framework specifically tailored for downstream robotic control. PPC maps point clouds under arbitrary rigid-body transformations to a unique canonical pose, aligning observations to a consistent frame, thereby substantially decreasing viewpoint-induced inconsistencies. In our experiments, we show that PPC improves robustness to unseen camera poses across challenging robotic tasks, providing a principled alternative to domain randomization.

The p-persistent CSMA protocol is central to random-access MAC analysis, but predicting saturation throughput in heterogeneous multi-hop wireless networks remains a hard problem. Simplified models that assume a single, shared interference domain can underestimate throughput by 48-62% in sparse topologies. Exact Markov-chain analyses are accurate but scale exponentially in computation time, making them impractical for large networks. These computational barriers motivate structural machine learning approaches like GNNs for scalable throughput prediction in general network topologies. Yet off-the-shelf GNNs struggle here: a standard GCN yields 63.94% normalized mean absolute error (NMAE) on heterogeneous networks because symmetric normalization conflates a node's direct interference with higher-order, cascading effects that pertain to how interference propagates over the network graph. Building on these insights, we propose the Decoupled Graph Convolutional Network (D-GCN), a novel architecture that explicitly separates processing of a node's own transmission probability from neighbor interference effects. D-GCN replaces mean aggregation with learnable attention, yielding interpretable, per-neighbor contribution weights while capturing complex multihop interference patterns. D-GCN attains 3.3% NMAE, outperforms strong baselines, remains tractable even when exact analytical methods become computationally infeasible, and enables gradient-based network optimization that achieves within 1% of theoretical optima.

Solving quantum many-body problems is one of the most challenging tasks in modern physics, and tensor network states have been widely used to efficiently represent quantum many-body states in recent years. Matrix product states (MPSs) [1-10], often specialized in one spatial dimension, and their generalizations to higher dimensions, such as projected entangled pair states (PEPSs) [9-14] and tree tensor networks [15-18], have been successfully applied to various quantum many-body problems in low-dimensional quantum systems by keeping the entanglement entropy of the wave function as low as possible. The number of variational parameters in tensor network states remains relatively small and grows only polynomially with the number of sites in most of quantum many-body systems. Recently, neural network quantum states (NNQSs) have been proposed as a new class of variational wave functions for quantum many-body systems [19-26]. One of the basic NNQSs is the restricted Boltzmann machine (RBM) wave function [19, 27-38].

Hidden Quantum Markov Models (HQMMs) extend classical Hidden Markov Models to the quantum domain, offering a powerful probabilistic framework for modeling sequential data with quantum coherence. However, existing HQMM learning algorithms are highly sensitive to data corruption and lack mechanisms to ensure robustness under adversarial perturbations. In this work, we introduce the Adversarially Corrupted HQMM (AC-HQMM), which formalizes robustness analysis by allowing a controlled fraction of observation sequences to be adversarially corrupted. To learn AC-HQMMs, we propose the Robust Iterative Learning Algorithm (RILA), a derivative-free method that integrates a Remove Corrupted Rows by Entropy Filtering (RCR-EF) module with an iterative stochastic resampling procedure for physically valid Kraus operator updates. RILA incorporates L1-penalized likelihood objectives to enhance stability, resist overfitting, and remain effective under non-differentiable conditions. Across multiple HQMM and HMM benchmarks, RILA demonstrates superior convergence stability, corruption resilience, and preservation of physical validity compared to existing algorithms, establishing a principled and efficient approach for robust quantum sequential learning.

Urban micromobility applications, such as delivery robots, demand reliable navigation across large-scale urban environments while following long-horizon route instructions. This task is particularly challenging due to the dynamic and unstructured nature of real-world city areas, yet most existing navigation methods remain tailored to short-scale and controllable scenarios. Effective urban micromobility requires two complementary levels of navigation skills: low-level capabilities such as point-goal reaching and obstacle avoidance, and high-level capabilities, such as route-visual alignment. To this end, we propose UrbanVLA, a route-conditioned Vision-Language-Action (VLA) framework designed for scalable urban navigation. Our method explicitly aligns noisy route waypoints with visual observations during execution, and subsequently plans trajectories to drive the robot. To enable UrbanVLA to master both levels of navigation, we employ a two-stage training pipeline. The process begins with Supervised Fine-Tuning (SFT) using simulated environments and trajectories parsed from web videos. This is followed by Reinforcement Fine-Tuning (RFT) on a mixture of simulation and real-world data, which enhances the model's safety and adaptability in real-world settings. Experiments demonstrate that UrbanVLA surpasses strong baselines by more than 55% in the SocialNav task on MetaUrban. Furthermore, UrbanVLA achieves reliable real-world navigation, showcasing both scalability to large-scale urban environments and robustness against real-world uncertainties.