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.

Bayesian Knowledge Tracing (BKT) is a probabilistic model of a learner's state of mastery corresponding to a knowledge component. It considers the learner's state of mastery as a "hidden" or latent binary variable and updates this state based on the observed correctness of the learner's response using parameters that represent transition probabilities between states. BKT is often represented as a Hidden Markov Model and the Expectation-Maximization (EM) algorithm is used to infer these parameters. However, this algorithm can suffer from several issues including producing multiple viable sets of parameters, settling into a local minima, producing degenerate parameter values, and a high computational cost during fitting. This paper takes a "from first principles" approach to deriving constraints that can be imposed on the BKT parameter space. Starting from the basic mathematical truths of probability and building up to the behaviors expected of the BKT parameters in real systems, this paper presents a mathematical derivation that results in succinct constraints that can be imposed on the BKT parameter space. Since these constraints are necessary conditions, they can be applied prior to fitting in order to reduce computational cost and the likelihood of issues that can emerge from the EM procedure. In order to see that promise through, the paper further introduces a novel algorithm for estimating BKT parameters subject to the newly defined constraints. While the issue of degenerate parameter values has been reported previously, this paper is the first, to our best knowledge, to derive the constrains from first principles while also presenting an algorithm that respects those constraints.

We study a majority based preference diffusion model in which the members of a social network update their preferences based on those of their connections. Consider an undirected graph where each node has a strict linear order over a set of $\alpha$ alternatives. At each round, a node randomly selects two adjacent alternatives and updates their relative order with the majority view of its neighbors. We bound the convergence time of the process in terms of the number of nodes/edges and $\alpha$. Furthermore, we study the minimum cost to ensure that a desired alternative will ``win'' the process, where occupying each position in a preference order of a node has a cost. We prove tight bounds on the minimum cost for general graphs and graphs with strong expansion properties. Furthermore, we investigate a more light-weight process where each node chooses one of its neighbors uniformly at random and copies its order fully with some fixed probability and remains unchanged otherwise. We characterize the convergence properties of this process, namely convergence time and stable states, using Martingale and reversible Markov chain analysis. Finally, we present the outcomes of our experiments conducted on different synthetic random graph models and graph data from online social platforms. These experiments not only support our theoretical findings, but also shed some light on some other fundamental problems, such as designing powerful countermeasures.

In centralized multi-agent systems, often modeled as multi-agent partially observable Markov decision processes (MPOMDPs), the action and observation spaces grow exponentially with the number of agents, making the value and belief estimation of single-agent online planning ineffective. Prior work partially tackles value estimation by exploiting the inherent structure of multi-agent settings via so-called coordination graphs. Additionally, belief estimation has been improved by incorporating the likelihood of observations into the approximation. However, the challenges of value estimation and belief estimation have only been tackled individually, which prevents existing methods from scaling to many agents. Therefore, we address these challenges simultaneously. First, we introduce weighted particle filtering to a sample-based online planner for MPOMDPs. Second, we present a scalable approximation of the belief. Third, we bring an approach that exploits the typical locality of agent interactions to novel online planning algorithms for MPOMDPs operating on a so-called sparse particle filter tree. Our experimental evaluation against several state-of-the-art baselines shows that our methods (1) are competitive in settings with only a few agents and (2) improve over the baselines in the presence of many agents.

In recent years, machine learning (ML) has brought effective approaches and novel techniques to economic decision, investment forecasting, and risk management, etc., coping the variable and intricate nature of economic and financial environments. For the investment in stock market, this research introduces a pioneering quantitative fusion model combining stock timing and picking strategy by leveraging the Multivariate Gaussian-Hidden Markov Model (MGHMM) and Back Propagation Neural Network optimized by Particle Swarm (PSO-BPNN). After the information coefficients (IC) between fifty-two factors that have been winsorized, neutralized and standardized and the return of CSI 300 index are calculated, a given amount of factors that rank ahead are choose to be candidate factors heading for the input of PSO-BPNN after dimension reduction by Principal Component Analysis (PCA), followed by a certain amount of constituent stocks outputted. Subsequently, we conduct the prediction and trading on the basis of the screening stocks and stock market state outputted by MGHMM trained using inputting CSI 300 index data after Box-Cox transformation, bespeaking eximious performance during the period of past four years. Ultimately, some conventional forecast and trading methods are compared with our strategy in Chinese stock market. Our fusion strategy incorporating stock picking and timing presented in this article provide a innovative technique for financial analysis.