Robust causal discovery from observational data under imperfect prior knowledge remains a significant and largely unresolved challenge. Existing methods typically presuppose perfect priors or can only handle specific, pre-identified error types. And their performance degrades substantially when confronted with flawed constraints of unknown location and type. This decline arises because most of them rely on inflexible and biased thresholding strategies that may conflict with the data distribution. To overcome these limitations, we propose to harmonizes knowledge and data through prior alignment and conflict resolution. First, we assess the credibility of imperfect structural constraints through a surrogate model, which then guides a sparse penalization term measuring the loss between the learned and constrained adjacency matrices. We theoretically prove that, under ideal assumption, the knowledge-driven objective aligns with the data-driven objective. Furthermore, to resolve conflicts when this assumption is violated, we introduce a multi-task learning framework optimized via multi-gradient descent, jointly minimizing both objectives. Our proposed method is robust to both linear and nonlinear settings. Extensive experiments, conducted under diverse noise conditions and structural equation model types, demonstrate the effectiveness and efficiency of our method under imperfect structural constraints.

Causal structure learning (CSL) plays a pivotal role in causality and is often formulated as an optimization problem within score-and-search methods. Under the assumption of an infinite dataset and a predefined distribution, several well-established and consistent score functions have been shown to be both optimal and reliable for identifying ground-truth causal graphs. However, in practice, these idealized assumptions are often infeasible, which can result in CSL algorithms learning suboptimal structures. In this paper, we introduce L-SFE, a framework designed to automatically discover effective score functions by exploring the "score function space". L-SFE addresses this task from a bi-level optimization perspective. First, it leverages a Large Language Model (LLM) to interpret the characteristics of score functions and generate the corresponding code implementations. Next, L-SFE employs evolutionary algorithms along with carefully designed operators, to search for solutions with higher fitness. Additionally, we take the BIC as example and prove the consistency of the generated score functions. Experimental evaluations, conducted on discrete, continuous, and real datasets, demonstrate the high stability, generality and effectiveness of L-SFE.

Learning graphical causal models from observational data can effectively elucidate the underlying causal mechanism behind the variables. In the context of limited datasets, modelers often incorporate prior knowledge, which is assumed to be correct, as a penalty in single-objective optimization. However, this approach struggles to adapt complex and uncertain priors effectively. This paper introduces UpCM, which tackles the issue from a multi-objective optimization perspective. Instead of focusing exclusively on the DAG as the optimization goal, UpCM methodically evaluate the effect of uncertain priors on specific structures, merging data-driven and knowledge-driven objectives. Utilizing the MOEA/D framework, it achieve a balanced tradeoff between these objectives. Furthermore, since uncertain priors may introduce erroneous constraints, resulting in PDAGs lacking consistent extensions, the minimal non-consistent extension is explored. This extension, which separately incorporates positive and negative constraints, aims to approximate the true causality of the PDAGs. Experimental results demonstrate that UpCM achieves significant structural accuracy improvements compared to baseline methods. It reduces the SHD by 7.94%, 13.23%, and 12.8% relative to PC stable, GES, and MAHC, respectively, when incorporating uncertain priors. In downstream inference tasks, UpCM outperforms domain-expert knowledge graphs, owing to its ability to learn explainable causal relationships that balance data-driven evidence with prior knowledge

Developing efficient motion policies for multiagents is a challenge in a decentralized dynamic situation, where each agent plans its own paths without knowing the policies of the other agents involved. This paper presents an efficient learning-based motion planning method for multiagent systems. It adopts the framework of multiagent deep deterministic policy gradient (MADDPG) to directly map partially observed information to motion commands for multiple agents. To improve the efficiency of MADDPG in sample utilization, so as to train more brilliant agents that can adapt to more complex environments, a strategy named mixed experience (ME) is introduced to MADDPG, and this has led to our proposed ME-MADDPG algorithm. The novel ME strategy can be embodied into three specific mechanisms: (1) an artificial potential field-based sample generator to produce high-quality samples in the early training stage; (2) a dynamic mixed sampling strategy to mix the training data from different sources with a variable proportion; (3) a delayed learning skill to stabilize the training of the multiple agents. A series of experiments have been conducted to verify the performance of the proposed ME-MADDPG algorithm, and it has been demonstrated that, compared with MADDPG, the proposed algorithm can significantly improve the convergence speed and convergence effect in the training process, and it has also shown better efficiency and better adaptability in complex dynamic environments while it is used for multiagent motion planning applications.

As one of the essential deep learning models, a restricted Boltzmann machine (RBM) is a commonly used generative training model. By adaptively growing the size of the hidden units, infinite RBM (IRBM) is obtained, which possesses an excellent property of automatically choosing the hidden layer size depending on a specific task. An IRBM presents a competitive generative capability with the traditional RBM. First, a generative model called Gaussian IRBM (GIRBM) is proposed to deal with practical scenarios from the perspective of data discretization. Subsequently, a discriminative IRBM (DIRBM) and a discriminative GIRBM (DGIRBM) are established to solve classification problems by attaching extra-label units next to the input layer. They are motivated by the fact that a discriminative variant of an RBM can complete an individual framework for classification with better performance than some standard classifiers. Remarkably, the proposed models retain both generative and discriminative properties synchronously, that is, they can reconstruct data effectively and be established in considerable self-contained classifiers. The experimental results on image classification (both large and small), text identification, and facial recognition (both clean and noisy) reflect that a DIRBM and a DGIRBM are superior to some state-of-the-art RBM models in terms of the reconstruction error and the classification accuracy. Intuitively, they require models to avoid utilizing more hidden units than needed when confronted with various sizes of data, prioritizing smaller networks. In addition, the proposed models behave more robustly than other classic classifiers when dealing with noisy facial recognition.

Parameter learning is an important aspect of learning in Bayesian networks. Although the maximum likelihood algorithm is often effective, it suffers from overfitting when there is insufficient data. To address this, prior distributions of model parameters are often imposed. When training a Bayesian network, the parameters of the network are optimized to fit the data. However, imposing prior distributions can reduce the fitness between parameters and data. Therefore, a trade-off is needed between fitting and overfitting. In this study, a new algorithm, named MiniMax Fitness (MMF) is developed to address this problem. The method includes three main steps. First, the maximum a posterior estimation that combines data and prior distribution is derived. Then, the hyper-parameters of the prior distribution are optimized to minimize the fitness between posterior estimation and data. Finally, the order of posterior estimation is checked and adjusted to match the order of the statistical counts from the data. In addition, we introduce an improved constrained maximum entropy method, named Prior Free Constrained Maximum Entropy (PF-CME), to facilitate parameter learning when domain knowledge is provided. Experiments show that the proposed methods outperforms most of existing parameter learning methods.

Multiple unmanned aerial vehicle (UAV) team often needs to perform some certain tasks cooperatively. In the process of UAVs performing these tasks, the bandwidth of the communication network will affect the task assignment results, then the problem of task allocation for multi-UAV teams under the condition of limited communication bandwidth is considered. For a target, UAVs need to perform reconnaissance, attack and assessment tasks in coordination. The Consensus-Based Bundle Algorithm(CBBA) requires each task is assigned to no more than one UAV, so this paper extends CBBA by duplicating cooperative tasks to modify the task list and adding a judgment mechanism to ensure the uniqueness of the duplicate tasks' allocation in order to achieve the purpose of allocating multiple UAVs to the same task. At the same time, this paper utilizes a bid warping link to improve the algorithm performance and applies CBBA in asynchronous environment to reduce communication burden. Simulation results show that this improved algorithm is feasible and more efficient to improve the task allocation result for multi-UAVs teams with fewer messages transmission and a larger global reward.

Ordering-based search methods have advantages over graph-based search methods for structure learning of Bayesian networks in terms of both efficiency and accuracy. With the aim of further increasing the accuracy of ordering-based search methods, we propose to increase the search space, which can facilitate escaping from local optima. We present our search operators with majorizations, which are easy to implement. Experiments demonstrate that the proposed algorithm achieves significant accuracy improvement and exhibits high efficiency at the same time on both synthetic and real data sets. With regard to further improve the algorithm efficiency on learning large scale networks, we discuss a solution at the end of the paper.

To improve the coverage of multi-UAVs cooperative search, various communication constraints have to be considered: communication distance, communication delay and communication network structure. A kind of network building method based on tree concept of data structure is presented, and a communication strategy based on information fusion is proposed. These method and strategy could effectively improve the efficiency of multi-UAVs cooperative search. Different situations are designed to verify the rationality and validity of the proposed network building method and communication strategy for improving coverage rate of multi-UAVs cooperative search.

One of the essential problems on Bayesian networks (BNs) is parameter learning. When purely data-driven methods fail to work, incorporating supplemental information, like expert judgments, can improve the learning of BN parameters. In practice, expert judgments are provided and transformed into qualitative parameter constraints. Moreover, prior distributions of BN parameters are also useful information. In this paper we propose a Bayesian approach to learn parameters from small datasets by integrating both parameter constraints and prior distributions. First, the feasible parameter region is derived from constraints. Then, using the prior distribution, a posterior distribution over the feasible region is developed based on the Bayes theorem. Finally, the parameter estimations are taken as the mean values of the posterior distribution. Learning experiments on standard BNs reveal that the proposed method outperforms most of the existing methods.

To improve the accuracy of structure learning for Dynamic Bayesian Network (DBN), this paper proposes Mutual Information-Binary Particle Swarm Optimization (MI-BPSO) algorithm. The MI-BPSO algorithm firstly uses MI and conditional independence test to prune the search space and speed up the convergence of the searching phase, then calls BPSO algorithm to search the constrained space and get the intra-network and inter-network of DBN. Experimental results show that this algorithm performs as well as K2 while it doesn't need a given variable ordering, and performs better than MWST-GES, MWST-HC and I-BN-PSO.