In this paper, we investigate the concentration properties of cumulative rewards in Markov Decision Processes (MDPs), focusing on both asymptotic and non-asymptotic settings. We introduce a unified approach to characterize reward concentration in MDPs, covering both infinite-horizon settings (i.e., average and discounted reward frameworks) and finite-horizon setting. Our asymptotic results include the law of large numbers, the central limit theorem, and the law of iterated logarithms, while our non-asymptotic bounds include Azuma-Hoeffding-type inequalities and a non-asymptotic version of the law of iterated logarithms. Additionally, we explore two key implications of our results. First, we analyze the sample path behavior of the difference in rewards between any two stationary policies. Second, we show that two alternative definitions of regret for learning policies proposed in the literature are rate-equivalent. Our proof techniques rely on a novel martingale decomposition of cumulative rewards, properties of the solution to the policy evaluation fixed-point equation, and both asymptotic and non-asymptotic concentration results for martingale difference sequences.

Markov chains are simple yet powerful mathematical structures to model temporally dependent processes. They generally assume stationary data, i.e., fixed transition probabilities between observations/states. However, live, real-world processes, like in the context of activity tracking, biological time series, or industrial monitoring, often switch behavior over time. Such behavior switches can be modeled as transitions between higher-level \emph{modes} (e.g., running, walking, etc.). Yet all modes are usually not previously known, often exhibit vastly differing transition probabilities, and can switch unpredictably. Thus, to track behavior changes of live, real-world processes, this study proposes an online and efficient method to construct Evolving Markov chains (EMCs). EMCs adaptively track transition probabilities, automatically discover modes, and detect mode switches in an online manner. In contrast to previous work, EMCs are of arbitrary order, the proposed update scheme does not rely on tracking windows, only updates the relevant region of the probability tensor, and enjoys geometric convergence of the expected estimates. Our evaluation of synthetic data and real-world applications on human activity recognition, electric motor condition monitoring, and eye-state recognition from electroencephalography (EEG) measurements illustrates the versatility of the approach and points to the potential of EMCs to efficiently track, model, and understand live, real-world processes.

Intention recognition, or the ability to anticipate the actions of another agent, plays a vital role in the design and development of automated assistants that can support humans in their daily tasks. In particular, industrial settings pose interesting challenges that include potential distractions for a decision-maker as well as noisy or incomplete observations. In such a setting, a robotic assistant tasked with helping and supporting a human worker must interleave information gathering actions with proactive tasks of its own, an approach that has been referred to as active goal recognition. In this paper we describe a partially observable model for online intention recognition, show some preliminary experimental results and discuss some of the challenges present in this family of problems.

This paper studies the multi-robot reliable navigation problem in uncertain topological networks, which aims at maximizing the robot team's on-time arrival probabilities in the face of road network uncertainties. The uncertainty in these networks stems from the unknown edge traversability, which is only revealed to the robot upon its arrival at the edge's starting node. Existing approaches often struggle to adapt to real-time network topology changes, making them unsuitable for varying topological environments. To address the challenge, we reformulate the problem into a Partially Observable Markov Decision Process (POMDP) framework and introduce the Dynamic Adaptive Graph Embedding method to capture the evolving nature of the navigation task. We further enhance each robot's policy learning process by integrating deep reinforcement learning with Graph Attention Networks (GATs), leveraging self-attention to focus on critical graph features. The proposed approach, namely Multi-Agent Routing in Variable Environments with Learning (MARVEL) employs the generalized policy gradient algorithm to optimize the robots' real-time decision-making process iteratively. We compare the performance of MARVEL with state-of-the-art reliable navigation algorithms as well as Canadian traveller problem solutions in a range of canonical transportation networks, demonstrating improved adaptability and performance in uncertain topological networks. Additionally, real-world experiments with two robots navigating within a self-constructed indoor environment with uncertain topological structures demonstrate MARVEL's practicality.

Efficient traffic control (TSC) is essential for urban mobility, but traditional systems struggle to handle the complexity of real-world traffic. Multi-agent Reinforcement Learning (MARL) offers adaptive solutions, but online MARL requires extensive interactions with the environment, making it costly and impractical. Offline MARL mitigates these challenges by using historical traffic data for training but faces significant difficulties with heterogeneous behavior policies in real-world datasets, where mixed-quality data complicates learning. We introduce OffLight, a novel offline MARL framework designed to handle heterogeneous behavior policies in TSC datasets. To improve learning efficiency, OffLight incorporates Importance Sampling (IS) to correct for distributional shifts and Return-Based Prioritized Sampling (RBPS) to focus on high-quality experiences. OffLight utilizes a Gaussian Mixture Variational Graph Autoencoder (GMM-VGAE) to capture the diverse distribution of behavior policies from local observations. Extensive experiments across real-world urban traffic scenarios show that OffLight outperforms existing offline RL methods, achieving up to a 7.8% reduction in average travel time and 11.2% decrease in queue length. Ablation studies confirm the effectiveness of OffLight's components in handling heterogeneous data and improving policy performance. These results highlight OffLight's scalability and potential to improve urban traffic management without the risks of online learning.

Multi-Agent Reinforcement Learning (MARL) methods have shown promise in enabling agents to learn a shared communication protocol from scratch and accomplish challenging team tasks. However, the learned language is usually not interpretable to humans or other agents not co-trained together, limiting its applicability in ad-hoc teamwork scenarios. In this work, we propose a novel computational pipeline that aligns the communication space between MARL agents with an embedding space of human natural language by grounding agent communications on synthetic data generated by embodied Large Language Models (LLMs) in interactive teamwork scenarios. Our results demonstrate that introducing language grounding not only maintains task performance but also accelerates the emergence of communication. Furthermore, the learned communication protocols exhibit zero-shot generalization capabilities in ad-hoc teamwork scenarios with unseen teammates and novel task states. This work presents a significant step toward enabling effective communication and collaboration between artificial agents and humans in real-world teamwork settings.

Large-scale generative models have achieved remarkable success in a number of domains. However, for sequential decision-making problems, such as robotics, action-labelled data is often scarce and therefore scaling-up foundation models for decision-making remains a challenge. A potential solution lies in leveraging widely-available unlabelled videos to train world models that simulate the consequences of actions. If the world model is accurate, it can be used to optimize decision-making in downstream tasks. Image-to-video diffusion models are already capable of generating highly realistic synthetic videos. However, these models are not action-conditioned, and the most powerful models are closedsource which means they cannot be finetuned. In this work, we propose to adapt pretrained video diffusion models to action-conditioned world models, without access to the parameters of the pretrained model. Our approach, AVID, trains an adapter on a small domain-specific dataset of action-labelled videos. AVID uses a learned mask to modify the intermediate outputs of the pretrained model and generate accurate action-conditioned videos. We evaluate AVID on video game and real-world robotics data, and show that it outperforms existing baselines for diffusion model adaptation. Our results demonstrate that if utilized correctly, pretrained video models have the potential to be powerful tools for embodied AI. Large generative models trained on web-scale data have driven rapid improvement in natural language processing (Brown, 2020; Touvron et al., 2023; Achiam et al., 2023), image generation (Rombach et al., 2022), and video generation (OpenAI, 2024).

Effective extraction of the world knowledge in LLMs for complex decision-making tasks remains a challenge. We propose a framework PIANIST for decomposing the world model into seven intuitive components conducive to zero-shot LLM generation. Given only the natural language description of the game and how input observations are formatted, our method can generate a working world model for fast and efficient MCTS simulation. We show that our method works well on two different games that challenge the planning and decision making skills of the agent for both language and non-language based action taking, without any training on domain-specific training data or explicitly defined world model.

Precision matrix estimation is essential in various fields, yet it is challenging when samples for the target study are limited. Transfer learning can enhance estimation accuracy by leveraging data from related source studies. We propose Trans-Glasso, a two-step transfer learning method for precision matrix estimation. First, we obtain initial estimators using a multi-task learning objective that captures shared and unique features across studies. Then, we refine these estimators through differential network estimation to adjust for structural differences between the target and source precision matrices. Under the assumption that most entries of the target precision matrix are shared with source matrices, we derive non-asymptotic error bounds and show that Trans-Glasso achieves minimax optimality under certain conditions. Extensive simulations demonstrate Trans Glasso's superior performance compared to baseline methods, particularly in small-sample settings. We further validate Trans-Glasso in applications to gene networks across brain tissues and protein networks for various cancer subtypes, showcasing its effectiveness in biological contexts. Additionally, we derive the minimax optimal rate for differential network estimation, representing the first such guarantee in this area.

This paper proposes a novel analytical framework: Transition Network Analysis (TNA), an approach that integrates Stochastic Process Mining and probabilistic graph representation to model, visualize, and identify transition patterns in the learning process data. Combining the relational and temporal aspects into a single lens offers capabilities beyond either framework, including centralities to capture important learning events, community finding to identify patterns of behavior, and clustering to reveal temporal patterns. This paper introduces the theoretical and mathematical foundations of TNA. To demonstrate the functionalities of TNA, we present a case study with students (n=191) engaged in small-group collaboration to map patterns of group dynamics using the theories of co-regulation and socially-shared regulated learning. The analysis revealed that TNA could reveal the regulatory processes and identify important events, temporal patterns and clusters. Bootstrap validation established the significant transitions and eliminated spurious transitions. In doing so, we showcase TNA's utility to capture learning dynamics and provide a robust framework for investigating the temporal evolution of learning processes. Future directions include advancing estimation methods, expanding reliability assessment, exploring longitudinal TNA, and comparing TNA networks using permutation tests.