The Multi-Agent Pathfinding (MAPF) problem involves finding a set of conflict-free paths for a group of agents confined to a graph. In typical MAPF scenarios, the graph and the agents' starting and ending vertices are known beforehand, allowing the use of centralized planning algorithms. However, in this study, we focus on the decentralized MAPF setting, where the agents may observe the other agents only locally and are restricted in communications with each other. Specifically, we investigate the lifelong variant of MAPF, where new goals are continually assigned to the agents upon completion of previous ones. Drawing inspiration from the successful AlphaZero approach, we propose a decentralized multi-agent Monte Carlo Tree Search (MCTS) method for MAPF tasks. Our approach utilizes the agent's observations to recreate the intrinsic Markov decision process, which is then used for planning with a tailored for multi-agent tasks version of neural MCTS. The experimental results show that our approach outperforms state-of-the-art learnable MAPF solvers. The source code is available at https://github.com/AIRI-Institute/mats-lp.

In this work, we revisit the marking decisions made in the standard adaptive finite element method (AFEM). Experience shows that a na\"{i}ve marking policy leads to inefficient use of computational resources for adaptive mesh refinement (AMR). Consequently, using AFEM in practice often involves ad-hoc or time-consuming offline parameter tuning to set appropriate parameters for the marking subroutine. To address these practical concerns, we recast AMR as a Markov decision process in which refinement parameters can be selected on-the-fly at run time, without the need for pre-tuning by expert users. In this new paradigm, the refinement parameters are also chosen adaptively via a marking policy that can be optimized using methods from reinforcement learning. We use the Poisson equation to demonstrate our techniques on $h$- and $hp$-refinement benchmark problems, and our experiments suggest that superior marking policies remain undiscovered for many classical AFEM applications. Furthermore, an unexpected observation from this work is that marking policies trained on one family of PDEs are sometimes robust enough to perform well on problems far outside the training family. For illustration, we show that a simple $hp$-refinement policy trained on 2D domains with only a single re-entrant corner can be deployed on far more complicated 2D domains, and even 3D domains, without significant performance loss. For reproduction and broader adoption, we accompany this work with an open-source implementation of our methods.

Designing better deep networks and better reinforcement learning (RL) algorithms are both important for deep RL. This work studies the former. Specifically, the Perception and Decision-making Interleaving Transformer (PDiT) network is proposed, which cascades two Transformers in a very natural way: the perceiving one focuses on \emph{the environmental perception} by processing the observation at the patch level, whereas the deciding one pays attention to \emph{the decision-making} by conditioning on the history of the desired returns, the perceiver's outputs, and the actions. Such a network design is generally applicable to a lot of deep RL settings, e.g., both the online and offline RL algorithms under environments with either image observations, proprioception observations, or hybrid image-language observations. Extensive experiments show that PDiT can not only achieve superior performance than strong baselines in different settings but also extract explainable feature representations. Our code is available at \url{https://github.com/maohangyu/PDiT}.

Traditional clustering algorithms often struggle to capture the complex relationships within graphs and generalise to arbitrary clustering criteria. The emergence of graph neural networks (GNNs) as a powerful framework for learning representations of graph data provides new approaches to solving the problem. Previous work has shown GNNs to be capable of proposing partitionings using a variety of criteria, however, these approaches have not yet been extended to work on Markov chains or kinetic networks. These arise frequently in the study of molecular systems and are of particular interest to the biochemical modelling community. In this work, we propose several GNN-based architectures to tackle the graph partitioning problem for Markov Chains described as kinetic networks. This approach aims to minimize how much a proposed partitioning changes the Kemeny constant. We propose using an encoder-decoder architecture and show how simple GraphSAGE-based GNNs with linear layers can outperform much larger and more expressive attention-based models in this context. As a proof of concept, we first demonstrate the method's ability to cluster randomly connected graphs. We also use a linear chain architecture corresponding to a 1D free energy profile as our kinetic network. Subsequently, we demonstrate the effectiveness of our method through experiments on a data set derived from molecular dynamics. We compare the performance of our method to other partitioning techniques such as PCCA+. We explore the importance of feature and hyperparameter selection and propose a general strategy for large-scale parallel training of GNNs for discovering optimal graph partitionings.

Multi-agent reinforcement learning shines as the pinnacle of multi-agent systems, conquering intricate real-world challenges, fostering collaboration and coordination among agents, and unleashing the potential for intelligent decision-making across domains. However, training a multi-agent reinforcement learning network is a formidable endeavor, demanding substantial computational resources to interact with diverse environmental variables, extract state representations, and acquire decision-making knowledge. The recent breakthroughs in large-scale pre-trained models ignite our curiosity: Can we uncover shared knowledge in multi-agent reinforcement learning and leverage pre-trained models to expedite training for future tasks? Addressing this issue, we present an innovative multi-task learning approach that aims to extract and harness common decision-making knowledge, like cooperation and competition, across different tasks. Our approach involves concurrent training of multiple multi-agent tasks, with each task employing independent front-end perception layers while sharing back-end decision-making layers. This effective decoupling of state representation extraction from decision-making allows for more efficient training and better transferability. To evaluate the efficacy of our proposed approach, we conduct comprehensive experiments in two distinct environments: the StarCraft Multi-agent Challenge (SMAC) and the Google Research Football (GRF) environments. The experimental results unequivocally demonstrate the smooth transferability of the shared decision-making network to other tasks, thereby significantly reducing training costs and improving final performance. Furthermore, visualizations authenticate the presence of general multi-agent decision-making knowledge within the shared network layers, further validating the effectiveness of our approach.

This paper studies a discrete-time mean-variance model based on reinforcement learning. Compared with its continuous-time counterpart in \cite{zhou2020mv}, the discrete-time model makes more general assumptions about the asset's return distribution. Using entropy to measure the cost of exploration, we derive the optimal investment strategy, whose density function is also Gaussian type. Additionally, we design the corresponding reinforcement learning algorithm. Both simulation experiments and empirical analysis indicate that our discrete-time model exhibits better applicability when analyzing real-world data than the continuous-time model.

As artificial intelligence (AI) systems become increasingly integrated into various domains, ensuring that they align with human values becomes critical. This paper introduces a novel formalism to quantify the alignment between AI systems and human values, using Markov Decision Processes (MDPs) as the foundational model. We delve into the concept of values as desirable goals tied to actions and norms as behavioral guidelines, aiming to shed light on how they can be used to guide AI decisions. This framework offers a mechanism to evaluate the degree of alignment between norms and values by assessing preference changes across state transitions in a normative world. By utilizing this formalism, AI developers and ethicists can better design and evaluate AI systems to ensure they operate in harmony with human values. The proposed methodology holds potential for a wide range of applications, from recommendation systems emphasizing well-being to autonomous vehicles prioritizing safety.

The task of collision-free navigation (CFN) of self-driving cars is an NP-hard problem usually tackled using Deep Reinforcement Learning (DRL). While DRL methods have proven to be effective, their implementation requires substantial computing resources and extended training periods to develop a robust agent. On the other hand, quantum reinforcement learning has recently demonstrated faster convergence and improved stability in simple, non-real-world environments. In this work, we propose Nav-Q, the first quantum-supported DRL algorithm for CFN of self-driving cars, that leverages quantum computation for improving the training performance without the requirement for onboard quantum hardware. Nav-Q is based on the actor-critic approach, where the critic is implemented using a hybrid quantum-classical algorithm suitable for near-term quantum devices. We assess the performance of Nav-Q using the CARLA driving simulator, a de facto standard benchmark for evaluating state-of-the-art DRL methods. Our empirical evaluations showcase that Nav-Q surpasses its classical counterpart in terms of training stability and, in certain instances, with respect to the convergence rate. Furthermore, we assess Nav-Q in relation to effective dimension, unveiling that the incorporation of a quantum component results in a model with greater descriptive power compared to classical baselines. Finally, we evaluate the performance of Nav-Q using noisy quantum simulation, observing that the quantum noise deteriorates the training performances but enhances the exploratory tendencies of the agent during training.

Although the applications of artificial intelligence especially deep learning had greatly improved various aspects of intelligent manufacturing, they still face challenges for wide employment due to the poor generalization ability, difficulties to establish high-quality training datasets, and unsatisfactory performance of deep learning methods. The emergence of large scale foundational models(LSFMs) had triggered a wave in the field of artificial intelligence, shifting deep learning models from single-task, single-modal, limited data patterns to a paradigm encompassing diverse tasks, multimodal, and pre-training on massive datasets. Although LSFMs had demonstrated powerful generalization capabilities, automatic high-quality training dataset generation and superior performance across various domains, applications of LSFMs on intelligent manufacturing were still in their nascent stage. A systematic overview of this topic was lacking, especially regarding which challenges of deep learning can be addressed by LSFMs and how these challenges can be systematically tackled. To fill this gap, this paper systematically expounded current statue of LSFMs and their advantages in the context of intelligent manufacturing. and compared comprehensively with the challenges faced by current deep learning models in various intelligent manufacturing applications. We also outlined the roadmaps for utilizing LSFMs to address these challenges. Finally, case studies of applications of LSFMs in real-world intelligent manufacturing scenarios were presented to illustrate how LSFMs could help industries, improve their efficiency.

Error bounds are derived for sampling and estimation using a discretization of an intrinsically defined Langevin diffusion with invariant measure $d\mu_\phi \propto e^{-\phi} \mathrm{dvol}_g $ on a compact Riemannian manifold. Two estimators of linear functionals of $\mu_\phi $ based on the discretized Markov process are considered: a time-averaging estimator based on a single trajectory and an ensemble-averaging estimator based on multiple independent trajectories. Imposing no restrictions beyond a nominal level of smoothness on $\phi$, first-order error bounds, in discretization step size, on the bias and variances of both estimators are derived. The order of error matches the optimal rate in Euclidean and flat spaces, and leads to a first-order bound on distance between the invariant measure $\mu_\phi$ and a stationary measure of the discretized Markov process. Generality of the proof techniques, which exploit links between two partial differential equations and the semigroup of operators corresponding to the Langevin diffusion, renders them amenable for the study of a more general class of sampling algorithms related to the Langevin diffusion. Conditions for extending analysis to the case of non-compact manifolds are discussed. Numerical illustrations with distributions, log-concave and otherwise, on the manifolds of positive and negative curvature elucidate on the derived bounds and demonstrate practical utility of the sampling algorithm.