In a multi-agent system (MAS), action semantics indicates the different influences of agents' actions toward other entities, and can be used to divide agents into groups in a physically heterogeneous MAS. Previous multi-agent reinforcement learning (MARL) algorithms apply global parameter-sharing across different types of heterogeneous agents without careful discrimination of different action semantics. This common implementation decreases the cooperation and coordination between agents in complex situations. However, fully independent agent parameters dramatically increase the computational cost and training difficulty. In order to benefit from the usage of different action semantics while also maintaining a proper parameter-sharing structure, we introduce the Unified Action Space (UAS) to fulfill the requirement. The UAS is the union set of all agent actions with different semantics. All agents first calculate their unified representation in the UAS, and then generate their heterogeneous action policies using different available-action-masks. To further improve the training of extra UAS parameters, we introduce a Cross-Group Inverse (CGI) loss to predict other groups' agent policies with the trajectory information. As a universal method for solving the physically heterogeneous MARL problem, we implement the UAS adding to both value-based and policy-based MARL algorithms, and propose two practical algorithms: U-QMIX and U-MAPPO. Experimental results in the SMAC environment prove the effectiveness of both U-QMIX and U-MAPPO compared with several state-of-the-art MARL methods.

Causality plays a pivotal role in various fields of study. Based on the framework of causal graphical models, previous works have proposed identifying whether a variable is a cause or non-cause of a target in every Markov equivalent graph solely by learning a local structure. However, the presence of prior knowledge, often represented as a partially known causal graph, is common in many causal modeling applications. Leveraging this prior knowledge allows for the further identification of causal relationships. In this paper, we first propose a method for learning the local structure using all types of causal background knowledge, including direct causal information, non-ancestral information and ancestral information. Then we introduce criteria for identifying causal relationships based solely on the local structure in the presence of prior knowledge. We also apply out method to fair machine learning, and experiments involving local structure learning, causal relationship identification, and fair machine learning demonstrate that our method is both effective and efficient.

Gaussian Processes (GPs) provide a powerful framework for making predictions and understanding uncertainty for classification with kernels and Bayesian non-parametric learning. Building such models typically requires strong prior knowledge to define preselect kernels, which could be ineffective for online applications of classification that sequentially process data because features of data may shift during the process. To alleviate the requirement of prior knowledge used in GPs and learn new features from data that arrive successively, this paper presents a novel method to automatically discover models of classification on complex data with little prior knowledge. Our method adapts a recently proposed technique for GP-based time-series structure discovery, which integrates GPs and Sequential Monte Carlo (SMC). We extend the technique to handle extra latent variables in GP classification, such that our method can effectively and adaptively learn a-priori unknown structures of classification from continuous input. In addition, our method adapts new batch of data with updated structures of models. Our experiments show that our method is able to automatically incorporate various features of kernels on synthesized data and real-world data for classification. In the experiments of real-world data, our method outperforms various classification methods on both online and offline setting achieving a 10\% accuracy improvement on one benchmark.

Bayesian optimization (BO) methods choose sample points by optimizing an acquisition function derived from a statistical model of the objective. These acquisition functions are chosen to balance sampling regions with predicted good objective values against exploring regions where the objective is uncertain. Standard acquisition functions are myopic, considering only the impact of the next sample, but non-myopic acquisition functions may be more effective. In principle, one could model the sampling by a Markov decision process, and optimally choose the next sample by maximizing an expected reward computed by dynamic programming; however, this is infeasibly expensive. More practical approaches, such as rollout, consider a parametric family of sampling policies. In this paper, we show how to efficiently estimate rollout acquisition functions and their gradients, enabling stochastic gradient-based optimization of sampling policies.

Hyperspectral unmixing is the process of determining the presence of individual materials and their respective abundances from an observed pixel spectrum. Unmixing is a fundamental process in hyperspectral image analysis, and is growing in importance as increasingly large spectral libraries are created and used. Unmixing is typically done with ordinary least squares (OLS) regression. However, unmixing with large spectral libraries where the materials present in a pixel are not a priori known, solving for the coefficients in OLS requires inverting a non-invertible matrix from a large spectral library. A number of regression methods are available that can produce a numerical solution using regularization, but with considerably varied effectiveness. Also, simple methods that are unpopular in the statistics literature (i.e. step-wise regression) are used with some level of effectiveness in hyperspectral analysis. In this paper, we provide a thorough performance evaluation of the methods considered, evaluating methods based on how often they select the correct materials in the models. Investigated methods include ordinary least squares regression, non-negative least squares regression, ridge regression, lasso regression, step-wise regression and Bayesian model averaging. We evaluated these unmixing approaches using multiple criteria: incorporation of non-negative abundances, model size, accurate mineral detection and root mean squared error (RMSE). We provide a taxonomy of the regression methods, showing that most methods can be understood as Bayesian methods with specific priors. We conclude that methods that can be derived with priors that correspond to the phenomenology of hyperspectral imagery outperform those with priors that are optimal for prediction performance under the assumptions of ordinary least squares linear regression.

Causal inference in hybrid domains, characterized by a mixture of discrete and continuous variables, presents a formidable challenge. We take a step towards this direction and propose Characteristic Interventional Sum-Product Network ($\chi$SPN) that is capable of estimating interventional distributions in presence of random variables drawn from mixed distributions. $\chi$SPN uses characteristic functions in the leaves of an interventional SPN (iSPN) thereby providing a unified view for discrete and continuous random variables through the Fourier-Stieltjes transform of the probability measures. A neural network is used to estimate the parameters of the learned iSPN using the intervened data. Our experiments on 3 synthetic heterogeneous datasets suggest that $\chi$SPN can effectively capture the interventional distributions for both discrete and continuous variables while being expressive and causally adequate. We also show that $\chi$SPN generalize to multiple interventions while being trained only on a single intervention data.

Inverter-based volt-var control is studied in this paper. One key issue in DRL-based approaches is the limited measurement deployment in active distribution networks, which leads to problems of a partially observable state and unknown reward. To address those problems, this paper proposes a robust DRL approach with a conservative critic and a surrogate reward. The conservative critic utilizes the quantile regression technology to estimate conservative state-action value function based on the partially observable state, which helps to train a robust policy; the surrogate rewards of power loss and voltage violation are designed that can be calculated from the limited measurements. The proposed approach optimizes the power loss of the whole network and the voltage profile of buses with measurable voltages while indirectly improving the voltage profile of other buses. Extensive simulations verify the effectiveness of the robust DRL approach in different limited measurement conditions, even when only the active power injection of the root bus and less than 10% of bus voltages are measurable.

Learning from Label Proportion (LLP) is a weakly supervised learning scenario in which training data is organized into predefined bags of instances, disclosing only the class label proportions per bag. This paradigm is essential for user modeling and personalization, where user privacy is paramount, offering insights into user preferences without revealing individual data. LLP faces a unique difficulty: the misalignment between bag-level supervision and the objective of instance-level prediction, primarily due to the inherent ambiguity in label proportion matching. Previous studies have demonstrated deep representation learning can generate auxiliary signals to promote the supervision level in the image domain. However, applying these techniques to tabular data presents significant challenges: 1) they rely heavily on label-invariant augmentation to establish multi-view, which is not feasible with the heterogeneous nature of tabular datasets, and 2) tabular datasets often lack sufficient semantics for perfect class distinction, making them prone to suboptimality caused by the inherent ambiguity of label proportion matching. To address these challenges, we propose an augmentation-free contrastive framework TabLLP-BDC that introduces class-aware supervision (explicitly aware of class differences) at the instance level. Our solution features a two-stage Bag Difference Contrastive (BDC) learning mechanism that establishes robust class-aware instance-level supervision by disassembling the nuance between bag label proportions, without relying on augmentations. Concurrently, our model presents a pioneering multi-task pretraining pipeline tailored for tabular-based LLP, capturing intrinsic tabular feature correlations in alignment with label proportion distribution. Extensive experiments demonstrate that TabLLP-BDC achieves state-of-the-art performance for LLP in the tabular domain.

Monotonic Partially Observable Markov Decision Processes (POMDPs), where the system state progressively decreases until a restorative action is performed, can be used to model sequential repair problems effectively. This paper considers the problem of solving budget-constrained multi-component monotonic POMDPs, where a finite budget limits the maximal number of restorative actions. For a large number of components, solving such a POMDP using current methods is computationally intractable due to the exponential growth in the state space with an increasing number of components. To address this challenge, we propose a two-step approach. Since the individual components of a budget-constrained multi-component monotonic POMDP are only connected via the shared budget, we first approximate the optimal budget allocation among these components using an approximation of each component POMDP's optimal value function which is obtained through a random forest model. Subsequently, we introduce an oracle-guided meta-trained Proximal Policy Optimization (PPO) algorithm to solve each of the independent budget-constrained single-component monotonic POMDPs. The oracle policy is obtained by performing value iteration on the corresponding monotonic Markov Decision Process (MDP). This two-step method provides scalability in solving truly massive multi-component monotonic POMDPs. To demonstrate the efficacy of our approach, we consider a real-world maintenance scenario that involves inspection and repair of an administrative building by a team of agents within a maintenance budget. Finally, we perform a computational complexity analysis for a varying number of components to show the scalability of the proposed approach.

The Sleeping Beauty problem is a puzzle in probability theory that has gained much attention since Elga's discussion of it [Elga, Adam, Analysis 60 (2), p.143-147 (2000)]. Sleeping Beauty is put asleep, and a coin is tossed. If the outcome of the coin toss is Tails, Sleeping Beauty is woken up on Monday, put asleep again and woken up again on Tuesday (with no recollection of having woken up on Monday). If the outcome is Heads, Sleeping Beauty is woken up on Monday only. Each time Sleeping Beauty is woken up, she is asked what her belief is that the outcome was Heads. What should Sleeping Beauty reply? In literature arguments have been given for both 1/3 and 1/2 as the correct answer. In this short note we argue using simple Bayesian probability theory why 1/3 is the right answer, and not 1/2. Briefly, when Sleeping Beauty awakens, her being awake is nontrivial extra information that leads her to update her beliefs about Heads to 1/3. We strengthen our claim by considering an additional observer, Prince Probability, who may or may not meet Sleeping Beauty. If he meets Sleeping Beauty while she is awake, he lowers his credence in Heads to 1/3. We also briefly consider the credence in Heads of a Sleeping Beauty who knows that she is dreaming (and thus asleep).