We consider the problem of finding an $\epsilon$-stationary point of a nonconvex function with a Lipschitz continuous Hessian and propose a quadratic regularized Newton method incorporating a new class of regularizers constructed from the current and previous gradients. The method leverages a recently developed linear conjugate gradient approach with a negative curvature monitor to solve the regularized Newton equation. Notably, our algorithm is adaptive, requiring no prior knowledge of the Lipschitz constant of the Hessian, and achieves a global complexity of $O(\epsilon^{-\frac{3}{2}}) + \tilde O(1)$ in terms of the second-order oracle calls, and $\tilde O(\epsilon^{-\frac{7}{4}})$ for Hessian-vector products, respectively. Moreover, when the iterates converge to a point where the Hessian is positive definite, the method exhibits quadratic local convergence. Preliminary numerical results illustrate the competitiveness of our algorithm.

Joint optimization of poses and features has been extensively studied and demonstrated to yield more accurate results in feature-based SLAM problems. However, research on jointly optimizing poses and non-feature-based maps remains limited. Occupancy maps are widely used non-feature-based environment representations because they effectively classify spaces into obstacles, free areas, and unknown regions, providing robots with spatial information for various tasks. In this paper, we propose Occupancy-SLAM, a novel optimization-based SLAM method that enables the joint optimization of robot trajectory and the occupancy map through a parameterized map representation. The key novelty lies in optimizing both robot poses and occupancy values at different cell vertices simultaneously, a significant departure from existing methods where the robot poses need to be optimized first before the map can be estimated. Evaluations using simulations and practical 2D laser datasets demonstrate that the proposed approach can robustly obtain more accurate robot trajectories and occupancy maps than state-of-the-art techniques with comparable computational time. Preliminary results in the 3D case further confirm the potential of the proposed method in practical 3D applications, achieving more accurate results than existing methods.

Operations Research (OR) is vital for decision-making in many industries. While recent OR methods have seen significant improvements in automation and efficiency through integrating Large Language Models (LLMs), they still struggle to produce meaningful explanations. This lack of clarity raises concerns about transparency and trustworthiness in OR applications. To address these challenges, we propose a comprehensive framework, Explainable Operations Research (EOR), emphasizing actionable and understandable explanations accompanying optimization. The core of EOR is the concept of Decision Information, which emerges from what-if analysis and focuses on evaluating the impact of complex constraints (or parameters) changes on decision-making. Specifically, we utilize bipartite graphs to quantify the changes in the OR model and adopt LLMs to improve the explanation capabilities. Additionally, we introduce the first industrial benchmark to rigorously evaluate the effectiveness of explanations and analyses in OR, establishing a new standard for transparency and clarity in the field.

The optimal solution to an optimization problem depends on the problem's objective function, constraints, and size. While deep neural networks (DNNs) have proven effective in solving optimization problems, changes in the problem's size, objectives, or constraints often require adjustments to the DNN architecture to maintain effectiveness, or even retraining a new DNN from scratch. Given the dynamic nature of wireless networks, which involve multiple and diverse objectives that can have conflicting requirements and constraints, we propose a multi-task learning (MTL) framework to enable a single DNN to jointly solve a range of diverse optimization problems. In this framework, optimization problems with varying dimensionality values, objectives, and constraints are treated as distinct tasks. To jointly address these tasks, we propose a conditional computation-based MTL approach with routing. The multi-task DNN consists of two components, the base DNN (bDNN), which is the single DNN used to extract the solutions for all considered optimization problems, and the routing DNN (rDNN), which manages which nodes and layers of the bDNN to be used during the forward propagation of each task. The output of the rDNN is a binary vector which is multiplied with all bDNN's weights during the forward propagation, creating a unique computational path through the bDNN for each task. This setup allows the tasks to either share parameters or use independent ones, with the decision controlled by the rDNN. The proposed framework supports both supervised and unsupervised learning scenarios. Numerical results demonstrate the efficiency of the proposed MTL approach in solving diverse optimization problems. In contrast, benchmark DNNs lacking the rDNN mechanism were unable to achieve similar levels of performance, highlighting the effectiveness of the proposed architecture.

Weight averaging has become a standard technique for enhancing model performance. However, methods such as Stochastic Weight Averaging (SWA) and Latest Weight Averaging (LAWA) often require manually designed procedures to sample from the training trajectory, and the results depend heavily on hyperparameter tuning. To minimize human effort, this paper proposes a simple yet efficient algorithm called Selective Weight Averaging (SeWA), which adaptively selects checkpoints during the final stages of training for averaging. Based on SeWA, we show that only a few points are needed to achieve better generalization and faster convergence. Theoretically, solving the discrete subset selection problem is inherently challenging. To address this, we transform it into a continuous probabilistic optimization framework and employ the Gumbel-Softmax estimator to learn the non-differentiable mask for each checkpoint. Further, we theoretically derive the SeWA's stability-based generalization bounds, which are sharper than that of SGD under both convex and non-convex assumptions. Finally, solid extended experiments in various domains, including behavior cloning, image classification, and text classification, further validate the effectiveness of our approach.

Recent breakthroughs in artificial intelligence (AI), wireless communications, and sensing technologies have accelerated the evolution of edge intelligence. However, conventional systems still grapple with issues such as low communication efficiency, redundant data acquisition, and poor model generalization. To overcome these challenges, we propose an innovative framework that enhances edge intelligence through AI-in-the-loop joint sensing and communication (JSAC). This framework features an AI-driven closed-loop control architecture that jointly optimizes system resources, thereby delivering superior system-level performance. A key contribution of our work is establishing an explicit relationship between validation loss and the system's tunable parameters. This insight enables dynamic reduction of the generalization error through AI-driven closed-loop control. Specifically, for sensing control, we introduce an adaptive data collection strategy based on gradient importance sampling, allowing edge devices to autonomously decide when to terminate data acquisition and how to allocate sample weights based on real-time model feedback. For communication control, drawing inspiration from stochastic gradient Langevin dynamics (SGLD), our joint optimization of transmission power and batch size converts channel and data noise into gradient perturbations that help mitigate overfitting. Experimental evaluations demonstrate that our framework reduces communication energy consumption by up to 77 percent and sensing costs measured by the number of collected samples by up to 52 percent while significantly improving model generalization -- with up to 58 percent reductions of the final validation loss. It validates that the proposed scheme can harvest the mutual benefit of AI and JSAC systems by incorporating the model itself into the control loop of the system.

Recent advances in diffusion models show promising potential for learning-based optimization by leveraging their multimodal sampling capability to escape local optima. However, existing diffusion-based optimization approaches, often reliant on supervised training, lacks a mechanism to ensure strict constraint satisfaction which is often required in real-world applications. One resulting observation is the distributional misalignment, i.e. the generated solution distribution often exhibits small overlap with the feasible domain. In this paper, we propose DiOpt, a novel diffusion paradigm that systematically learns near-optimal feasible solution distributions through iterative self-training. Our framework introduces several key innovations: a target distribution specifically designed to maximize overlap with the constrained solution manifold; a bootstrapped self-training mechanism that adaptively weights candidate solutions based on the severity of constraint violations and optimality gaps; and a dynamic memory buffer that accelerates convergence by retaining high-quality solutions over training iterations. To our knowledge, DiOpt represents the first successful integration of self-supervised diffusion with hard constraint satisfaction. Evaluations on diverse tasks, including power grid control, motion retargeting, wireless allocation demonstrate its superiority in terms of both optimality and constraint satisfaction.

Primary care providers are essential to the healthcare ecosystem because they are the first point of contact for many patients (Pearson and Raeke, 2000; Wu et al., 2022). Patients rely on primary care providers for routine checkups and referrals to specialists. Moreover, care continuity can instill trust and improve medication uptake rates and patient health (Wu et al., 2022). Unfortunately, high provider turnover rates frequently lead to patients without an assigned provider (Reddy et al., 2015). Provider turnover disrupts patient care and leads to worse care (Reddy et al., 2015). In principle, healthcare administrators reassign unmatched patients to other providers; however, in practice, the process takes months due to provider scarcity and the logistical burden of rematching and coordinating patient matches (Hedden et al., 2021). While many patients find their new provider quickly, others have to wait years to find a new provider due to large numbers of patients, high turnover rates, and provider scarcity (Hedden et al., 2021; Shanafelt et al., 2012). Algorithms that automatically match patients and providers can reduce logistical hassle but require balancing patient autonomy and system-wide utility. For example, while automatically assigning each patient to a provider would decrease wait times, it also reduces patient autonomy because patients cannot select their provider (Entwistle et al., 2010; Gaynor et al., 2016). 1

This article presents applied research on line balancing within the modern garment industry, focusing on the significant impact of intelligent hanger systems and hanger lines on the stitching process, by Lean Methodology for garment modernization. It explores the application of line balancing in the modern garment industry, focusing on the significant impact of intelligent hanger systems and hanger lines on the stitching process. It aligns with Lean Methodology principles for garment modernization. Without the implementation of line balancing technology, the garment manufacturing process using hanger systems cannot improve output rates. The case study demonstrates that implementing intelligent line balancing in a straightforward practical setup facilitates lean practices combined with a digitalization system and automaton. This approach illustrates how to enhance output and reduce accumulated work in progress.

In this paper, we investigate the performance of Thompson Sampling (TS) for online learning with censored feedback, focusing primarily on the classic repeated newsvendor model--a foundational framework in inventory management--and demonstrating how our techniques can be naturally extended to a broader class of problems. We model demand using a Weibull distribution and initialize TS with a Gamma prior to dynamically adjust order quantities. Our analysis establishes optimal (up to logarithmic factors) frequentist regret bounds for TS without imposing restrictive prior assumptions. More importantly, it yields novel and highly interpretable insights on how TS addresses the exploration-exploitation trade-off in the repeated newsvendor setting. Specifically, our results show that when past order quantities are sufficiently large to overcome censoring, TS accurately estimates the unknown demand parameters, leading to near-optimal ordering decisions. Conversely, when past orders are relatively small, TS automatically increases future order quantities to gather additional demand information. Extensive numerical simulations further demonstrate that TS outperforms more conservative and widely-used approaches such as online convex optimization, upper confidence bounds, and myopic Bayesian dynamic programming. This study also lays the foundation for exploring general online learning problems with censored feedback.