We develop a generic policy gradient method with the global optimality guarantee for robust Markov Decision Processes (MDPs). While policy gradient methods are widely used for solving dynamic decision problems due to their scalable and efficient nature, adapting these methods to account for model ambiguity has been challenging, often making it impractical to learn robust policies. This paper introduces a novel policy gradient method, Double-Loop Robust Policy Mirror Descent (DRPMD), for solving robust MDPs. DRPMD employs a general mirror descent update rule for the policy optimization with adaptive tolerance per iteration, guaranteeing convergence to a globally optimal policy. We provide a comprehensive analysis of DRPMD, including new convergence results under both direct and softmax parameterizations, and provide novel insights into the inner problem solution through Transition Mirror Ascent (TMA). Additionally, we propose innovative parametric transition kernels for both discrete and continuous state-action spaces, broadening the applicability of our approach.

Effective governance and steering of behavior in complex multi-agent systems (MAS) are essential for managing system-wide outcomes, particularly in environments where interactions are structured by dynamic networks. In many applications, the goal is to promote pro-social behavior among agents, where network structure plays a pivotal role in shaping these interactions. This paper introduces a Hierarchical Graph Reinforcement Learning (HGRL) framework that governs such systems through targeted interventions in the network structure. Operating within the constraints of limited managerial authority, the HGRL framework demonstrates superior performance across a range of environmental conditions, outperforming established baseline methods. Our findings highlight the critical influence of agent-to-agent learning (social learning) on system behavior: under low social learning, the HGRL manager preserves cooperation, forming robust core-periphery networks dominated by cooperators. In contrast, high social learning accelerates defection, leading to sparser, chain-like networks. Additionally, the study underscores the importance of the system manager's authority level in preventing system-wide failures, such as agent rebellion or collapse, positioning HGRL as a powerful tool for dynamic network-based governance.

We introduce a framework that integrates variational autoencoders (VAE) with reinforcement learning (RL) to balance system performance and resource usage in multi-agent systems by dynamically adjusting network structures over time. A key innovation of this method is its capability to handle the vast action space of the network structure. This is achieved by combining Variational Auto-Encoder and Deep Reinforcement Learning to control the latent space encoded from the network structures. The proposed method, evaluated on the modified OpenAI particle environment under various scenarios, not only demonstrates superior performance compared to baselines but also reveals interesting strategies and insights through the learned behaviors.

In restless multi-arm bandits, a central agent is tasked with optimally distributing limited resources across several bandits (arms), with each arm being a Markov decision process. In this work, we generalize the traditional restless multi-arm bandit problem with a risk-neutral objective by incorporating risk-awareness. We establish indexability conditions for the case of a risk-aware objective and provide a solution based on Whittle index. In addition, we address the learning problem when the true transition probabilities are unknown by proposing a Thompson sampling approach and show that it achieves bounded regret that scales sublinearly with the number of episodes and quadratically with the number of arms. The efficacy of our method in reducing risk exposure in restless multi-arm bandits is illustrated through a set of numerical experiments.

We study stochastic pairwise interaction network systems whereby a finite population of agents, identified with the nodes of a graph, update their states in response to both individual mutations and pairwise interactions with their neighbors. The considered class of systems include the main epidemic models -such as the SIS, SIR, and SIRS models-, certain social dynamics models -such as the voter and anti-voter models-, as well as evolutionary dynamics on graphs. Since these stochastic systems fall into the class of finite-state Markov chains, they always admit stationary distributions. We analyze the asymptotic behavior of these stationary distributions in the limit as the population size grows large while the interaction network maintains certain mixing properties. Our approach relies on the use of Lyapunov-type functions to obtain concentration results on these stationary distributions. Notably, our results are not limited to fully mixed population models, as they do apply to a much broader spectrum of interaction network structures, including, e.g., Erd\"oos-R\'enyi random graphs.

Recent advances in large language models have demonstrated promising capabilities in following simple instructions through instruction tuning. However, real-world tasks often involve complex, multi-step instructions that remain challenging for current NLP systems. Despite growing interest in this area, there lacks a comprehensive survey that systematically analyzes the landscape of complex instruction understanding and processing. Through a systematic review of the literature, we analyze available resources, representation schemes, and downstream tasks related to instructional text. Our study examines 177 papers, identifying trends, challenges, and opportunities in this emerging field. We provide AI/NLP researchers with essential background knowledge and a unified view of various approaches to complex instruction understanding, bridging gaps between different research directions and highlighting future research opportunities.

Disease progression models infer group-level temporal trajectories of change in patients' features as a chronic degenerative condition plays out. They provide unique insight into disease biology and staging systems with individual-level clinical utility. Discrete models consider disease progression as a latent permutation of events, where each event corresponds to a feature becoming measurably abnormal. However, permutation inference using traditional maximum likelihood approaches becomes prohibitive due to combinatoric explosion, severely limiting model dimensionality and utility. Here we leverage ideas from optimal transport to model disease progression as a latent permutation matrix of events belonging to the Birkhoff polytope, facilitating fast inference via optimisation of the variational lower bound. This enables a factor of 1000 times faster inference than the current state of the art and, correspondingly, supports models with several orders of magnitude more features than the current state of the art can consider. Experiments demonstrate the increase in speed, accuracy and robustness to noise in simulation. Further experiments with real-world imaging data from two separate datasets, one from Alzheimer's disease patients, the other age-related macular degeneration, showcase, for the first time, pixel-level disease progression events in the brain and eye, respectively. Our method is low compute, interpretable and applicable to any progressive condition and data modality, giving it broad potential clinical utility.

Estimating the ground-state energy of Hamiltonians is a fundamental task for which it is believed that quantum computers can be helpful. Several approaches have been proposed toward this goal, including algorithms based on quantum phase estimation and hybrid quantum-classical optimizers involving parameterized quantum circuits, the latter falling under the umbrella of the variational quantum eigensolver. Here, we analyze the performance of quantum Boltzmann machines for this task, which is a less explored ansatz based on parameterized thermal states and which is not known to suffer from the barren-plateau problem. We delineate a hybrid quantum-classical algorithm for this task and rigorously prove that it converges to an $\varepsilon$-approximate stationary point of the energy function optimized over parameter space, while using a number of parameterized-thermal-state samples that is polynomial in $\varepsilon^{-1}$, the number of parameters, and the norm of the Hamiltonian being optimized. Our algorithm estimates the gradient of the energy function efficiently by means of a novel quantum circuit construction that combines classical sampling, Hamiltonian simulation, and the Hadamard test, thus overcoming a key obstacle to quantum Boltzmann machine learning that has been left open since [Amin et al., Phys. Rev. X 8, 021050 (2018)]. Additionally supporting our main claims are calculations of the gradient and Hessian of the energy function, as well as an upper bound on the matrix elements of the latter that is used in the convergence analysis.

Integrating symbolic techniques with statistical ones is a long-standing problem in artificial intelligence. The motivation is that the strengths of either area match the weaknesses of the other, and $\unicode{x2013}$ by combining the two $\unicode{x2013}$ the weaknesses of either method can be limited. Neuro-symbolic AI focuses on this integration where the statistical methods are in particular neural networks. In recent years, there has been significant progress in this research field, where neuro-symbolic systems outperformed logical or neural models alone. Yet, neuro-symbolic AI is, comparatively speaking, still in its infancy and has not been widely adopted by machine learning practitioners. In this survey, we present the first mapping of neuro-symbolic techniques into families of frameworks based on their architectures, with several benefits: Firstly, it allows us to link different strengths of frameworks to their respective architectures. Secondly, it allows us to illustrate how engineers can augment their neural networks while treating the symbolic methods as black-boxes. Thirdly, it allows us to map most of the field so that future researchers can identify closely related frameworks.

As reinforcement learning agents become increasingly deployed in real-world scenarios, predicting future agent actions and events during deployment is important for facilitating better human-agent interaction and preventing catastrophic outcomes. This paper experimentally evaluates and compares the effectiveness of future action and event prediction for three types of RL agents: explicitly planning, implicitly planning, and non-planning. We employ two approaches: the inner state approach, which involves predicting based on the inner computations of the agents (e.g., plans or neuron activations), and a simulation-based approach, which involves unrolling the agent in a learned world model. Our results show that the plans of explicitly planning agents are significantly more informative for prediction than the neuron activations of the other types. Furthermore, using internal plans proves more robust to model quality compared to simulation-based approaches when predicting actions, while the results for event prediction are more mixed. These findings highlight the benefits of leveraging inner states and simulations to predict future agent actions and events, thereby improving interaction and safety in real-world deployments.