Decentralized partially observable Markov decision processes (Dec-POMDPs) formalize the problem of designing individual controllers for a group of collaborative agents under stochastic dynamics and partial observability. Seeking a global optimum is difficult (NEXP complete), but seeking a Nash equilibrium -- each agent policy being a best response to the other agents -- is more accessible, and allowed addressing infinite-horizon problems with solutions in the form of finite state controllers. In this paper, we show that this approach can be adapted to cases where only a generative model (a simulator) of the Dec-POMDP is available. This requires relying on a simulation-based POMDP solver to construct an agent's FSC node by node. A related process is used to heuristically derive initial FSCs. Experiment with benchmarks shows that MC-JESP is competitive with exisiting Dec-POMDP solvers, even better than many offline methods using explicit models.

A Markov network characterizes the conditional independence structure, or Markov property, among a set of random variables. Existing work focuses on specific families of distributions (e.g., exponential families) and/or certain structures of graphs, and most of them can only handle variables of a single data type (continuous or discrete). In this work, we characterize the conditional independence structure in general distributions for all data types (i.e., continuous, discrete, and mixed-type) with a Generalized Precision Matrix (GPM). Besides, we also allow general functional relations among variables, thus giving rise to a Markov network structure learning algorithm in one of the most general settings. To deal with the computational challenge of the problem, especially for large graphs, we unify all cases under the same umbrella of a regularized score matching framework. We validate the theoretical results and demonstrate the scalability empirically in various settings.

Diffusions are a successful technique to sample from high-dimensional distributions can be either explicitly given or learnt from a collection of samples. They implement a diffusion process whose endpoint is a sample from the target distribution and whose drift is typically represented as a neural network. Stochastic localization is a successful technique to prove mixing of Markov Chains and other functional inequalities in high dimension. An algorithmic version of stochastic localization was introduced in [EAMS2022], to obtain an algorithm that samples from certain statistical mechanics models. This notes have three objectives: (i) Generalize the construction [EAMS2022] to other stochastic localization processes; (ii) Clarify the connection between diffusions and stochastic localization. In particular we show that standard denoising diffusions are stochastic localizations but other examples that are naturally suggested by the proposed viewpoint; (iii) Describe some insights that follow from this viewpoint.

Typical generative diffusion models rely on a Gaussian diffusion process for training the backward transformations, which can then be used to generate samples from Gaussian noise. However, real world data often takes place in discrete-state spaces, including many scientific applications. Here, we develop a theoretical formulation for arbitrary discrete-state Markov processes in the forward diffusion process using exact (as opposed to variational) analysis. We relate the theory to the existing continuous-state Gaussian diffusion as well as other approaches to discrete diffusion, and identify the corresponding reverse-time stochastic process and score function in the continuous-time setting, and the reverse-time mapping in the discrete-time setting. As an example of this framework, we introduce ``Blackout Diffusion'', which learns to produce samples from an empty image instead of from noise. Numerical experiments on the CIFAR-10, Binarized MNIST, and CelebA datasets confirm the feasibility of our approach. Generalizing from specific (Gaussian) forward processes to discrete-state processes without a variational approximation sheds light on how to interpret diffusion models, which we discuss.

To solve this problem, there are two main classes of computational methods that provide different approaches to approximate π. The first one is Markov chain Monte Carlo (MCMC) methods (Metropolis et al., 1953; Hastings, 1970; Robert and Casella, 1999). For many years, MCMC has been the standard approach for Bayesian analysis because of its theoretical soundness. The method constructs a Markov chain to produce simulation consistent samples from the target distribution π. A general MCMC approach is the Metropolis-Hastings algorithm that generates a Markov chain by first generating a proposed state from a proposal distribution, then using an acceptance rule to decide whether to accept the proposal or stay at the current state (Robert and Casella, 1999).

We introduce Dynamic Contextual Markov Decision Processes (DCMDPs), a novel reinforcement learning framework for history-dependent environments that generalizes the contextual MDP framework to handle non-Markov environments, where contexts change over time. We consider special cases of the model, with a focus on logistic DCMDPs, which break the exponential dependence on history length by leveraging aggregation functions to determine context transitions. This special structure allows us to derive an upper-confidence-bound style algorithm for which we establish regret bounds. Motivated by our theoretical results, we introduce a practical model-based algorithm for logistic DCMDPs that plans in a latent space and uses optimism over history-dependent features. We demonstrate the efficacy of our approach on a recommendation task (using MovieLens data) where user behavior dynamics evolve in response to recommendations.

A brain-computer interface (BCI) is a technology that enables direct communication between the brain and an external device or computer system. It allows individuals to interact with the device using only their thoughts, and holds immense potential for a wide range of applications in medicine, rehabilitation, and human augmentation. An electroencephalogram (EEG) and event-related potential (ERP)- based speller system is a type of BCI that allows users to spell words without using a physical keyboard, but instead by recording and interpreting brain signals under different stimulus presentation paradigms. Conventional non-adaptive paradigms treat each word selection independently, leading to a lengthy learning process. To improve the sampling efficiency, we cast the problem as a sequence of best-arm identification tasks in multi-armed bandits. Leveraging pre-trained large language models (LLMs), we utilize the prior knowledge learned from previous tasks to inform and facilitate subsequent tasks. To do so in a coherent way, we propose a sequential top-two Thompson sampling (STTS) algorithm under the fixed-confidence setting and the fixed-budget setting. We study the theoretical property of the proposed algorithm, and demonstrate its substantial empirical improvement through both synthetic data analysis as well as a P300 BCI speller simulator example.

Wind power is becoming an increasingly important source of renewable energy worldwide. However, wind farm power control faces significant challenges due to the high system complexity inherent in these farms. A novel communication-based multi-agent deep reinforcement learning large-scale wind farm multivariate control is proposed to handle this challenge and maximize power output. A wind farm multivariate power model is proposed to study the influence of wind turbines (WTs) wake on power. The multivariate model includes axial induction factor, yaw angle, and tilt angle controllable variables. The hierarchical communication multi-agent proximal policy optimization (HCMAPPO) algorithm is proposed to coordinate the multivariate large-scale wind farm continuous controls. The large-scale wind farm is divided into multiple wind turbine aggregators (WTAs), and neighboring WTAs can exchange information through hierarchical communication to maximize the wind farm power output. Simulation results demonstrate that the proposed multivariate HCMAPPO can significantly increase wind farm power output compared to the traditional PID control, coordinated model-based predictive control, and multi-agent deep deterministic policy gradient algorithm. Particularly, the HCMAPPO algorithm can be trained with the environment based on the thirteen-turbine wind farm and effectively applied to larger wind farms. At the same time, there is no significant increase in the fatigue damage of the wind turbine blade from the wake control as the wind farm scale increases. The multivariate HCMAPPO control can realize the collective large-scale wind farm maximum power output.

Multi-agent reinforcement learning (MARL) is a widely used Artificial Intelligence (AI) technique. However, current studies and applications need to address its scalability, non-stationarity, and trustworthiness. This paper aims to review methods and applications and point out research trends and visionary prospects for the next decade. First, this paper summarizes the basic methods and application scenarios of MARL. Second, this paper outlines the corresponding research methods and their limitations on safety, robustness, generalization, and ethical constraints that need to be addressed in the practical applications of MARL. In particular, we believe that trustworthy MARL will become a hot research topic in the next decade. In addition, we suggest that considering human interaction is essential for the practical application of MARL in various societies. Therefore, this paper also analyzes the challenges while MARL is applied to human-machine interaction.

We present a novel approach for black-box VI that bypasses the difficulties of stochastic gradient ascent, including the task of selecting step-sizes. Our approach involves using a sequence of sample average approximation (SAA) problems. SAA approximates the solution of stochastic optimization problems by transforming them into deterministic ones. We use quasi-Newton methods and line search to solve each deterministic optimization problem and present a heuristic policy to automate hyperparameter selection. Our experiments show that our method simplifies the VI problem and achieves faster performance than existing methods.