This paper addresses query scheduling for goal-oriented semantic communication in pull-based status update systems. We consider a system where multiple sensing agents (SAs) observe a source characterized by various attributes and provide updates to multiple actuation agents (AAs), which act upon the received information to fulfill their heterogeneous goals at the endpoint. A hub serves as an intermediary, querying the SAs for updates on observed attributes and maintaining a knowledge base, which is then broadcast to the AAs. The AAs leverage the knowledge to perform their actions effectively. To quantify the semantic value of updates, we introduce a grade of effectiveness (GoE) metric. Furthermore, we integrate cumulative perspective theory (CPT) into the long-term effectiveness analysis to account for risk awareness and loss aversion in the system. Leveraging this framework, we compute effect-aware scheduling policies aimed at maximizing the expected discounted sum of CPT-based total GoE provided by the transmitted updates while complying with a given query cost constraint. To achieve this, we propose a model-based solution based on dynamic programming and model-free solutions employing state-of-the-art deep reinforcement learning (DRL) algorithms. Our findings demonstrate that effect-aware scheduling significantly enhances the effectiveness of communicated updates compared to benchmark scheduling methods, particularly in settings with stringent cost constraints where optimal query scheduling is vital for system performance and overall effectiveness.

Polynomial inequality proving is fundamental to many mathematical disciplines and finds wide applications in diverse fields. Current traditional algebraic methods are based on searching for a polynomial positive definite representation over a set of basis. However, these methods are limited by truncation degree. To address this issue, this paper proposes an approach based on reinforcement learning to find a {Krivine-basis} representation for proving polynomial inequalities. Specifically, we formulate the inequality proving problem as a linear programming (LP) problem and encode it as a basis selection problem using reinforcement learning (RL), achieving a non-negative {Krivine basis}. Moreover, a fast multivariate polynomial multiplication method based on Fast Fourier Transform (FFT) is employed to enhance the efficiency of action space search. Furthermore, we have implemented a tool called {APPIRL} (Automated Proof of Polynomial Inequalities via Reinforcement Learning). Experimental evaluation on benchmark problems demonstrates the feasibility and effectiveness of our approach. In addition, {APPIRL} has been successfully applied to solve the maximum stable set problem.

Reduced Rank Regression (RRR) is a widely used method for multi-response regression. However, RRR assumes a linear relationship between features and responses. While linear models are useful and often provide a good approximation, many real-world problems involve more complex relationships that cannot be adequately captured by simple linear interactions. One way to model such relationships is via multilinear transformations. This paper introduces Higher Order Reduced Rank Regression (HORRR), an extension of RRR that leverages multi-linear transformations, and as such is capable of capturing nonlinear interactions in multi-response regression. HORRR employs tensor representations for the coefficients and a Tucker decomposition to impose multilinear rank constraints as regularization akin to the rank constraints in RRR. Encoding these constraints as a manifold allows us to use Riemannian optimization to solve this HORRR problems. We theoretically and empirically analyze the use of Riemannian optimization for solving HORRR problems.

Generating overtaking trajectories in autonomous racing is a challenging task, as the trajectory must satisfy the vehicle's dynamics and ensure safety and real-time performance running on resource-constrained hardware. This work proposes the Fast and Safe Data-Driven Planner to address this challenge. Sparse Gaussian predictions are introduced to improve both the computational efficiency and accuracy of opponent predictions. Furthermore, the proposed approach employs a bi-level quadratic programming framework to generate an overtaking trajectory leveraging the opponent predictions. The first level uses polynomial fitting to generate a rough trajectory, from which reference states and control inputs are derived for the second level. The second level formulates a model predictive control optimization problem in the Frenet frame, generating a trajectory that satisfies both kinematic feasibility and safety. Experimental results on the F1TENTH platform show that our method outperforms the State-of-the-Art, achieving an 8.93% higher overtaking success rate, allowing the maximum opponent speed, ensuring a smoother ego trajectory, and reducing 74.04% computational time compared to the Predictive Spliner method. The code is available at: https://github.com/ZJU-DDRX/FSDP.

This paper deals with the identification of the stochastic Ornstein-Uhlenbeck (OU) process error model, which is characterized by an inverse time constant, and the unknown variances of the process and observation noises. Although the availability of the explicit expression of the log-likelihood function allows one to obtain the maximum likelihood estimator (MLE), this entails evaluating the nontrivial gradient and also often struggles with local optima. To address these limitations, we put forth a sample-efficient global optimization approach based on the Bayesian optimization (BO) framework, which relies on a Gaussian process (GP) surrogate model for the objective function that effectively balances exploration and exploitation to select the query points. Specifically, each evaluation of the objective is implemented efficiently through the Kalman filter (KF) recursion. Comprehensive experiments on various parameter settings and sampling intervals corroborate that BO-based estimator consistently outperforms MLE implemented by the steady-state KF approximation and the expectation-maximization algorithm (whose derivation is a side contribution) in terms of root mean-square error (RMSE) and statistical consistency, confirming the effectiveness and robustness of the BO for identification of the stochastic OU process. Notably, the RMSE values produced by the BO-based estimator are smaller than the classical Cram\'{e}r-Rao lower bound, especially for the inverse time constant, estimating which has been a long-standing challenge. This seemingly counterintuitive result can be explained by the data-driven prior for the learning parameters indirectly injected by BO through the GP prior over the objective function.

The kidney paired donation (KPD) program provides an innovative solution to overcome incompatibility challenges in kidney transplants by matching incompatible donor-patient pairs and facilitating kidney exchanges. To address unequal access to transplant opportunities, there are two widely used fairness criteria: group fairness and individual fairness. However, these criteria do not consider protected patient features, which refer to characteristics legally or ethically recognized as needing protection from discrimination, such as race and gender. Motivated by the calibration principle in machine learning, we introduce a new fairness criterion: the matching outcome should be conditionally independent of the protected feature, given the sensitization level. We integrate this fairness criterion as a constraint within the KPD optimization framework and propose a computationally efficient solution. Theoretically, we analyze the associated price of fairness using random graph models. Empirically, we compare our fairness criterion with group fairness and individual fairness through both simulations and a real-data example.

Generative Flow Networks (GFlowNets) have recently emerged as a suitable framework for generating diverse and high-quality molecular structures by learning from rewards treated as unnormalized distributions. Previous works in this framework often restrict exploration by using predefined molecular fragments as building blocks, limiting the chemical space that can be accessed. In this work, we introduce Atomic GFlowNets (A-GFNs), a foundational generative model leveraging individual atoms as building blocks to explore drug-like chemical space more comprehensively. We propose an unsupervised pre-training approach using drug-like molecule datasets, which teaches A-GFNs about inexpensive yet informative molecular descriptors such as drug-likeliness, topological polar surface area, and synthetic accessibility scores. These properties serve as proxy rewards, guiding A-GFNs towards regions of chemical space that exhibit desirable pharmacological properties. We further implement a goal-conditioned finetuning process, which adapts A-GFNs to optimize for specific target properties. In this work, we pretrain A-GFN on a subset of ZINC dataset, and by employing robust evaluation metrics we show the effectiveness of our approach when compared to other relevant baseline methods for a wide range of drug design tasks.

Node embedding is a key technique for representing graph nodes as vectors while preserving structural and relational properties, which enables machine learning tasks like feature extraction, clustering, and classification. While classical methods such as DeepWalk, node2vec, and graph convolutional networks learn node embeddings by capturing structural and relational patterns in graphs, they often require significant computational resources and struggle with scalability on large graphs. Quantum computing provides a promising alternative for graph-based learning by leveraging quantum effects and introducing novel optimization approaches. Variational quantum circuits and quantum kernel methods have been explored for embedding tasks, but their scalability remains limited due to the constraints of noisy intermediate-scale quantum (NISQ) hardware. In this paper, we investigate quantum annealing (QA) as an alternative approach that mitigates key challenges associated with quantum gate-based models. We propose several formulations of the node embedding problem as a quadratic unconstrained binary optimization (QUBO) instance, making it compatible with current quantum annealers such as those developed by D-Wave. We implement our algorithms on a D-Wave quantum annealer and evaluate their performance on graphs with up to 100 nodes and embedding dimensions of up to 5. Our findings indicate that QA is a viable approach for graph-based learning, providing a scalable and efficient alternative to previous quantum embedding techniques.

This paper proposes an accelerated consensus-based distributed iterative algorithm for resource allocation and scheduling. The proposed gradient-tracking algorithm introduces an auxiliary variable to add momentum towards the optimal state. We prove that this solution is all-time feasible, implying that the coupling constraint always holds along the algorithm iterative procedure; therefore, the algorithm can be terminated at any time. This is in contrast to the ADMM-based solutions that meet constraint feasibility asymptotically. Further, we show that the proposed algorithm can handle possible link nonlinearity due to logarithmically-quantized data transmission (or any sign-preserving odd sector-bound nonlinear mapping). We prove convergence over uniformly-connected dynamic networks (i.e., a hybrid setup) that may occur in mobile and time-varying multi-agent networks. Further, the latency issue over the network is addressed by proposing delay-tolerant solutions. To our best knowledge, accelerated momentum-based convergence, nonlinear linking, all-time feasibility, uniform network connectivity, and handling (possible) time delays are not altogether addressed in the literature. These contributions make our solution practical in many real-world applications.

Hierarchical Federated Learning (HFL) introduces intermediate aggregation layers, addressing the limitations of conventional Federated Learning (FL) in geographically dispersed environments with limited communication infrastructure. An application of HFL is in smart IoT systems, such as remote monitoring, disaster response, and battlefield operations, where cellular connectivity is often unreliable or unavailable. In these scenarios, UAVs serve as mobile aggregators, providing connectivity to the terrestrial IoT devices. This paper studies an HFL architecture for energy-constrained UAVs in smart IoT systems, pioneering a solution to minimize global training cost increased caused by UAV disconnection. In light of this, we formulate a joint optimization problem involving learning configuration, bandwidth allocation, and device-to-UAV association, and perform global aggregation in time before UAV drops disconnect and redeployment of UAVs. The problem explicitly accounts for the dynamic nature of IoT devices and their interruptible communications and is unveiled to be NP-hard. To address this, we decompose it into three subproblems. First, we optimize the learning configuration and bandwidth allocation using an augmented Lagrangian function to reduce training costs. Second, we propose a device fitness score, integrating data heterogeneity (via Kullback-Leibler divergence), device-to-UAV distances, and IoT device resources, and develop a twin-delayed deep deterministic policy gradient (TD3)-based algorithm for dynamic device-to-UAV assignment. Third, We introduce a low-complexity two-stage greedy strategy for finding the location of UAVs redeployment and selecting the appropriate global aggregator UAV. Experiments on real-world datasets demonstrate significant cost reductions and robust performance under communication interruptions.