Federated learning (FL) and split learning (SL) are two effective distributed learning paradigms in wireless networks, enabling collaborative model training across mobile devices without sharing raw data. While FL supports low-latency parallel training, it may converge to less accurate model. In contrast, SL achieves higher accuracy through sequential training but suffers from increased delay. To leverage the advantages of both, hybrid split and federated learning (HSFL) allows some devices to operate in FL mode and others in SL mode. This paper aims to accelerate HSFL by addressing three key questions: 1) How does learning mode selection affect overall learning performance? 2) How does it interact with batch size? 3) How can these hyperparameters be jointly optimized alongside communication and computational resources to reduce overall learning delay? We first analyze convergence, revealing the interplay between learning mode and batch size. Next, we formulate a delay minimization problem and propose a two-stage solution: a block coordinate descent method for a relaxed problem to obtain a locally optimal solution, followed by a rounding algorithm to recover integer batch sizes with near-optimal performance. Experimental results demonstrate that our approach significantly accelerates convergence to the target accuracy compared to existing methods.

Most prompt-optimization methods refine a single static template, making them ineffective in complex and dynamic user scenarios. Existing query-dependent approaches rely on unstable textual feedback or black-box reward models, providing weak and uninterpretable optimization signals. More fundamentally, prompt quality itself lacks a unified, systematic definition, resulting in fragmented and unreliable evaluation signals. Our approach first establishes a performance-oriented, systematic, and comprehensive prompt evaluation framework. Furthermore, we develop and finetune an execution-free evaluator that predicts multi-dimensional quality scores directly from text. The evaluator then instructs a metric-aware optimizer that diagnoses failure modes and rewrites prompts in an interpretable, query-dependent manner. Our evaluator achieves the strongest accuracy in predicting prompt performance, and the evaluation-instructed optimization consistently surpass both static-template and query-dependent baselines across eight datasets and on three backbone models. Overall, we propose a unified, metric-grounded perspective on prompt quality, and demonstrated that our evaluation-instructed optimization pipeline delivers stable, interpretable, and model-agnostic improvements across diverse tasks.

Abstract--We study distributed convex optimization with two ubiquitous forms of coupling: consensus constraints and gl obal affine equalities. Without smooth ness or strong convexity, we establish non-ergodic sublinear ra tes of order O (1/ k) for both the objective optimality and the consensus violation. Leveraging duality, we then show that the eco nomic dispatch problem admits a dual consensus formulation, and t hat applying the same algorithm to the dual economic dispatch yi elds non-ergodic O (1/ k) decay for the error of the summation of the cost over the network and the equality-constraint resid ual under convexity and Slater's condition. Numerical results on the IEEE 118-bus system demonstrate faster reduction of bot h objective error and feasibility error relative to the state -of-the-art baselines, while the dual variables reach network-wide con sensus. This paper studies large-scale convex optimization proble ms formulated over networks, which frequently arise in engineering applications.

This paper presents the Safe Sequential Quadratically Constrained Quadratic Programming (SS-QCQP) algorithm, a first-order method for smooth inequality-constrained nonconvex optimization that guarantees feasibility at every iteration. The method is derived from a continuous-time dynamical system whose vector field is obtained by solving a convex QCQP that enforces monotonic descent of the objective and forward invariance of the feasible set. The resulting continuous-time dynamics achieve an $O(1/t)$ convergence rate to first-order stationary points under standard constraint qualification conditions. We then propose a safeguarded Euler discretization with adaptive step-size selection that preserves this convergence rate while maintaining both descent and feasibility in discrete time. To enhance scalability, we develop an active-set variant (SS-QCQP-AS) that selectively enforces constraints near the boundary, substantially reducing computational cost without compromising theoretical guarantees. Numerical experiments on a multi-agent nonlinear optimal control problem demonstrate that SS-QCQP and SS-QCQP-AS maintain feasibility, exhibit the predicted convergence behavior, and deliver solution quality comparable to second-order solvers such as SQP and IPOPT.

The processing of high-dimensional streaming data commonly utilizes online streaming feature selection (OSFS) techniques. However, practical implementations often face challenges with data incompleteness due to equipment failures and technical constraints. Online Sparse Streaming Feature Selection (OS2FS) tackles this issue through latent factor analysis-based missing data imputation. Despite this advancement, existing OS2FS approaches exhibit substantial limitations in feature evaluation, resulting in performance deterioration. To address these shortcomings, this paper introduces a novel Online Differential Evolution for Sparse Feature Selection (ODESFS) in data streams, incorporating two key innovations: (1) missing value imputation using a latent factor analysis model, and (2) feature importance evaluation through differential evolution. Comprehensive experiments conducted on six real-world datasets demonstrate that ODESFS consistently outperforms state-of-the-art OSFS and OS2FS methods by selecting optimal feature subsets and achieving superior accuracy.

With the rapid evolution of large language models, retrieval enhanced generation technology has been widely used due to its ability to integrate external knowledge to improve output accuracy. However, the performance of the system is highly dependent on the quality of the retrieval module. If the retrieval results have low relevance to user needs or contain noisy information, it will directly lead to distortion of the generated content. In response to the performance bottleneck of existing models in processing tabular features, this paper proposes an XGBoost machine learning regression model based on feature engineering and particle swarm optimization. Correlation analysis shows that answer_quality is positively correlated with doc_delevance by 0.66, indicating that document relevance has a significant positive effect on answer quality, and improving document relevance may enhance answer quality; The strong negative correlations between semantic similarity, redundancy, and diversity were -0.89 and -0.88, respectively, indicating a tradeoff between semantic similarity, redundancy, and diversity. In other words, as the former two increased, diversity significantly decreased. The experimental results comparing decision trees, AdaBoost, etc. show that the VMD PSO BiLSTM model is superior in all evaluation indicators, with significantly lower MSE, RMSE, MAE, and MAPE compared to the comparison model. The R2 value is higher, indicating that its prediction accuracy, stability, and data interpretation ability are more outstanding. This achievement provides an effective path for optimizing the retrieval quality and improving the generation effect of RAG system, and has important value in promoting the implementation and application of related technologies.

Smart grid technological advances present a recent class of complex interdisciplinary modeling and increasingly difficult simulation problems to solve using traditional computational methods. To simulate a smart grid requires a systemic approach to integrated modeling of power systems, energy markets, demand-side management, and much other resources and assets that are becoming part of the current paradigm of the power grid. This paper presents a backbone model of a smart grid to test alternative scenarios for the grid. This tool simulates disparate systems to validate assumptions before the human scale model. Thanks to a distributed optimization of subsystems, the production and consumption scheduling is achieved while maintaining flexibility and scalability.

Federated learning (FL) enables collaborative model training across multiple parties without sharing raw data, with semi-asynchronous FL (SAFL) emerging as a balanced approach between synchronous and asynchronous FL. However, SAFL faces significant challenges in optimizing both gradient-based (e.g., FedSGD) and model-based (e.g., FedAvg) aggregation strategies, which exhibit distinct trade-offs in accuracy, convergence speed, and stability. While gradient aggregation achieves faster convergence and higher accuracy, it suffers from pronounced fluctuations, whereas model aggregation offers greater stability but slower convergence and suboptimal accuracy. This paper presents FedQS, the first framework to theoretically analyze and address these disparities in SAFL. FedQS introduces a divide-and-conquer strategy to handle client heterogeneity by classifying clients into four distinct types and adaptively optimizing their local training based on data distribution characteristics and available computational resources. Extensive experiments on computer vision, natural language processing, and real-world tasks demonstrate that FedQS achieves the highest accuracy, attains the lowest loss, and ranks among the fastest in convergence speed, outperforming state-of-the-art baselines. Our work bridges the gap between aggregation strategies in SAFL, offering a unified solution for stable, accurate, and efficient federated learning. The code and datasets are available at https://github.com/bkjod/FedQS_.

Recently, there has been significant progress in learning-based diffusion samplers, which aim to sample from a given unnormalized density. Many of these approaches formulate the sampling task as a stochastic optimal control (SOC) problem using a canonical uninformative reference process, which limits their ability to efficiently guide trajectories toward the target distribution. In this work, we propose the Non-Equilibrium Annealed Adjoint Sampler (NAAS), a novel SOC-based diffusion framework that employs annealed reference dynamics as a non-stationary base SDE. This annealing structure provides a natural progression toward the target distribution and generates informative reference trajectories, thereby enhancing the stability and efficiency of learning the control. Owing to our SOC formulation, our framework can incorporate a variety of SOC solvers, thereby offering high flexibility in algorithmic design. As one instantiation, we employ a lean adjoint system inspired by adjoint matching, enabling efficient and scalable training. We demonstrate the effectiveness of NAAS across a range of tasks, including sampling from classical energy landscapes and molecular Boltzmann distributions.

Searching large and complex design spaces for a global optimum can be infeasible and unnecessary. A practical alternative is to iteratively refine the neighborhood of an initial design using local optimization methods such as gradient descent. We propose local entropy search (LES), a Bayesian optimization paradigm that explicitly targets the solutions reachable by the descent sequences of iterative optimizers. The algorithm propagates the posterior belief over the objective through the optimizer, resulting in a probability distribution over descent sequences. It then selects the next evaluation by maximizing mutual information with that distribution, using a combination of analytic entropy calculations and Monte-Carlo sampling of descent sequences. Empirical results on high-complexity synthetic objectives and benchmark problems show that LES achieves strong sample efficiency compared to existing local and global Bayesian optimization methods.