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.