Task decomposition has shown promise in complex cooperative multi-agent reinforcement learning (MARL) tasks, which enables efficient hierarchical learning for long-horizon tasks in dynamic and uncertain environments. However, learning dynamic task decomposition from scratch generally requires a large number of training samples, especially exploring the large joint action space under partial observability. In this paper, we present the Conditional Diffusion Model for Dynamic Task Decomposition (CD3T), a novel two-level hierarchical MARL framework designed to automatically infer subtask and coordination patterns. The high-level policy learns subtask representation to generate a subtask selection strategy based on subtask effects. To capture the effects of subtasks on the environment, CD3T predicts the next observation and reward using a conditional diffusion model. At the low level, agents collaboratively learn and share specialized skills within their assigned subtasks. Moreover, the learned subtask representation is also used as additional semantic information in a multi-head attention mixing network to enhance value decomposition and provide an efficient reasoning bridge between individual and joint value functions. Experimental results on various benchmarks demonstrate that CD3T achieves better performance than existing baselines.

Multiagent reinforcement learning (MARL) has been widely investigated, ranging from theoretical analysis to real-life applications. However, the utilization of existing non-transparent neural network architectures has resulted in opaque decision-making processes, making it difficult for humans to understand and trust the models being used. Fundamentally, all data is a topological structure, which provides reliable transparency for MARL tasks due to its powerful relational expression capability, scalability, and explicit structural relationships. In this article, we propose a novel approach of graph cooperation modeling (GCM), explicitly capturing and comprehending the complex dynamics of collaborative relationships among agents with the graph structure. GCM learns a metric function to discern beneficial interactions among agents, integrating it into the agent aggregation strategy of a graph neural network (GNN) capable of modeling arbitrary-order interactions. Furthermore, GCM utilizes identity semantics together with global state and individual value functions to estimate the credit of each agent, enhancing each agent's distinct focus on task-related regions. Extensive experiments on a range of challenging MARL benchmarks demonstrate that GCM not only delivers up to 28.75% relative performance gains on super-hard maps but also offers clear interpretability that provides insights into the underlying cooperative patterns.

Diffusion transformers (DiTs) struggle to generate images at resolutions higher than their training resolutions. The primary obstacle is that the explicit positional encodings (PE), such as RoPE, need extrapolating to unseen positions which degrades performance when the inference resolution differs from training. In this paper, We propose a Length-Extrapolatable Diffusion Transformer (LEDiT) to overcome this limitation. LEDiT needs no explicit PEs, thereby avoiding PE extrapolation. The key innovation of LEDiT lies in the use of causal attention. We demonstrate that causal attention can implicitly encode global positional information and show that such information facilitates extrapolation. We further introduce a locality enhancement module, which captures fine-grained local information to complement the global coarse-grained position information encoded by causal attention. Experimental results on both conditional and text-to-image generation tasks demonstrate that LEDiT supports up to 4× resolution scaling (e.g., from 256$\times$256 to 512$\times$512), achieving better image quality compared to the state-of-the-art length extrapolation methods. We believe that LEDiT marks a departure from the standard RoPE-based methods and offers a promising insight into length extrapolation. Project page: https://shenzhang2145.github.io/ledit/

This paper is concerned with the selection and computation of pairwise stable networks when agents have differentiable and concave utility functions. We show that a pairwise stable network can be obtained by finding a Nash equilibrium of a noncooperative game played by the nodes and links in the network. Based on this observation, we introduce a logarithmic tracing procedure and a path-following algorithm for network formation games. We apply the algorithm to several models in the literature and make comparisons with two existing algorithms: a path-following algorithm based on the linear tracing procedure (LinTP) and a decompose and exhaustive search method (DaE). Numerical results indicate that the proposed method is more than four times as efficient as LinTP. Although DaE demonstrates exceptional efficiency for small-scale problems, our method outperforms it significantly for large-scale problems, where DaE may fail to find a solution. We also show that the decomposition technique of DaE can be used to further accelerate our algorithm for a special class of problems. History: Accepted by Antonio Frangioni, Area Editor for Design & Analysis of Algorithms–Continuous. Funding: This work was supported in part by the National Natural Science Foundation of China [Grants 12201289, 12122107, and 72394363/72394360], the Natural Science Foundation of Jiangsu Province [Grant BK20220754], the Guangdong Basic and Applied Basic Research Foundation [Grant 2021A1515110207], the Young Elite Scientists Sponsorship Program by CAST [Grant 2023QNRC001], and the Open Research Fund from the Guangdong Provincial Key Laboratory of Big Data Computing [Grant B10120210117-OF05]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2024.0546 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2024.0546 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

In real applications, it is often that the collected multiview data contain missing views. Most existing incomplete multiview clustering (IMVC) methods cannot fully utilize the underlying information of missing data or sufficiently explore the consistent and complementary characteristics. In this article, we propose a novel Low-rAnk Tensor regularized viEws Recovery (LATER) method for IMVC, which jointly reconstructs and utilizes the missing views and learns multilevel graphs for comprehensive similarity discovery in a unified model. The missing views are recovered from a common latent representation, and the recovered views conversely improve the learning of shared patterns. Based on the shared subspace representations and recovered complete multiview data, the multilevel graphs are learned by self-representation to fully exploit the consistent and complementary information among views. Besides, a tensor nuclear norm regularizer is introduced to pursue the global low-rank property and explore the interview correlations. An alternating direction minimization algorithm is presented to optimize the proposed model. Moreover, a new initialization method is proposed to promote the effectiveness of our method for latent representation learning and missing data recovery. Extensive experiments demonstrate that our method outperforms the state-of-the-art approaches.

While deep learning in 3D domain has achieved revolutionary performance in many tasks, the robustness of these models has not been sufficiently studied or explored. Regarding the 3D adversarial samples, most existing works focus on manipulation of local points, which may fail to invoke the global geometry properties, like robustness under linear projection that preserves the Euclidean distance, i.e., isometry. In this work, we show that existing state-of-the-art deep 3D models are extremely vulnerable to isometry transformations. Armed with the Thompson Sampling, we develop a black-box attack with success rate over 95% on ModelNet40 data set. Incorporating with the Restricted Isometry Property, we propose a novel framework of white-box attack on top of spectral norm based perturbation. In contrast to previous works, our adversarial samples are experimentally shown to be strongly transferable. Evaluated on a sequence of prevailing 3D models, our white-box attack achieves success rates from 98.88% to 100%. It maintains a successful attack rate over 95% even within an imperceptible rotation range [±2.81◦].

Wasserstein \textbf{D}istributionally \textbf{R}obust \textbf{O}ptimization (DRO) is concerned with finding decisions that perform well on data that are drawn from the worst probability distribution within a Wasserstein ball centered at a certain nominal distribution. In recent years, it has been shown that various DRO formulations of learning models admit tractable convex reformulations. However, most existing works propose to solve these convex reformulations by general-purpose solvers, which are not well-suited for tackling large-scale problems. In this paper, we focus on a family of Wasserstein distributionally robust support vector machine (DRSVM) problems and propose two novel epigraphical projection-based incremental algorithms to solve them. The updates in each iteration of these algorithms can be computed in a highly efficient manner. Moreover, we show that the DRSVM problems considered in this paper satisfy a Hölderian growth condition with explicitly determined growth exponents. Consequently, we are able to establish the convergence rates of the proposed incremental algorithms. Our numerical results indicate that the proposed methods are orders of magnitude faster than the state-of-the-art, and the performance gap grows considerably as the problem size increases.

In order to improve the performance of Water Cycle Algorithm (WCA), an alternative adaptation approach for enhancing the global searching ability is proposed. The proposed algorithm, named WCA-ALR, uses a new diversity enhancement approach to effectively improve the exploration capability of the WCA. The proposed approach consists of two major modifications: (1) an active selection method for choosing learning targets; (2) a promising position sifting and returning strategy. The benefits prove that actively selecting a learning target performs better than that of learning from a fixed one. A promising position sifting and returning strategy can also enhance the exploration ability. In order to verify the performance, numerical experiments on five basic benchmark problems are conducted. Then, a set of benchmark problems from the CEC2017 on 10 and 30 dimensions are used to prove the effectiveness of WCA-ALR. Experimental results affirm that the proposed approach can obtain better results, compared to the original WCA.

The alternating direction method of multipliers (ADMM) is a popular and efficient first-order method that has recently found numerous applications, and the proximal ADMM is an important variant of it. The main contributions of this paper are the proposition and the analysis of a class of inertial proximal ADMMs, which unify the basic ideas of the inertial proximal point method and the proximal ADMM, for linearly constrained separable convex optimization. This class of methods are of inertial nature because at each iteration the proximal ADMM is applied to a point extrapolated at the current iterate in the direction of last movement. The recently proposed inertial primal-dual algorithm [A. Chambolle and T. Pock, On the ergodic convergence rates of a first-order primal-dual algorithm, preprint, 2014, Algorithm 3] and the inertial linearized ADMM [C. Chen, S. Ma, and J. Yang, arXiv:1407.8238, eq. (3.23)] are covered as special cases. The proposed algorithmic framework is very general in the sense that the weighting matrices in the proximal terms are allowed to be only positive semidefinite, but not necessarily positive definite as required by existing methods of the same kind. By setting the two proximal terms to zero, we obtain an inertial variant of the classical ADMM, which is to the best of our knowledge new. We carry out a unified analysis for the entire class of methods under very mild assumptions. In particular, convergence, as well as asymptotic $o(1/\sqrt{k})$ and nonasymptotic $O(1/\sqrt{k})$ rates of convergence, are established for the best primal function value and feasibility residues, where $k$ denotes the iteration counter. The global iterate convergence of the generated sequence is established under an additional assumption. We also present extensive experimental results on total variation--based image reconstruction problems to illustrate the profits gained by introducing the inertial extrapolation steps.

In this paper, a new framework for confocal microscopy based on the novel theory of compressive sensing is proposed. Unlike wide field microscopy or conventional parallel beam confocal imaging systems that use charge-coupled devices (CCD) as acquisition devices in addition to complex mechanical scanning system, the proposed compressive confocal microscopy is a kind of parallel beam confocal imaging system which exploits the rich theory of compressive sensing by using a single pixel detector and a digital micromirror device (DMD) to capture linear projections of the in-focus image. With the proposed system, confocal imaging of high optical sectioning ability can be achieved at sub-Nyquist sampling rates. Theoretical analysis, simulations and experimental results are shown to demonstrate the characteristics and potential of the proposed approach.