Modern optimization faces a fundamental challenge: local gradient-based methods provide no global information about the objective function $L$ landscape, often leading to suboptimal convergence and sensitivity to initialization. We introduce a novel optimization framework that leverages resurgence theory from complex analysis to extract global structural information from divergent asymptotic series. Our key insight is that the factorially divergent perturbative expansions of parameter space partition functions encode precise information about all critical objective function value in the landscape through their Borel transform singularities. The algorithm works by computing the statistical mechanical partition function $Z(g) = \int e^{-L(θ)/g} dθ$ for small coupling $g\ll 1$, extracting its asymptotic series coefficients, and identifying Borel plane singularities that correspond one-to-one with critical objective function values. These target values provide global guidance to local optimizers, enabling principled learning rate adaptation and escape from suboptimal regions. Unlike heuristic adaptive methods, targets are theoretically grounded in the geometry of the optimization landscape.

This work explores the integration of Quantum Machine Learning (QML) and Quantum-Inspired (QI) techniques for optimizing end-to-end (E2E) network services in telecommunication systems, particularly focusing on 5G networks and beyond. The application of QML and QI algorithms is investigated, comparing their performance with classical Machine Learning (ML) approaches. The present study employs a hybrid framework combining quantum and classical computing leveraging the strengths of QML and QI, without the penalty of quantum hardware availability. This is particularized for the optimization of the Quality of Experience (QoE) over cellular networks. The framework comprises an estimator for obtaining the expected QoE based on user metrics, service settings, and cell configuration, and an optimizer that uses the estimation to choose the best cell and service configuration. Although the approach is applicable to any QoE-based network management, its implementation is particularized for the optimization of network configurations for Cloud Gaming services. Then, it is evaluated via performance metrics such as accuracy and model loading and inference times for the estimator, and time to solution and solution score for the optimizer. The results indicate that QML models achieve similar or superior accuracy to classical ML models for estimation, while decreasing inference and loading times. Furthermore, potential for better performance is observed for higher-dimensional data, highlighting promising results for higher complexity problems. Thus, the results demonstrate the promising potential of QML in advancing network optimization, although challenges related to data availability and integration complexities between quantum and classical ML are identified as future research lines.

Efficient adversarial attack methods are critical for assessing the robustness of computer vision models. In this paper, we reconstruct the optimization objective for generating adversarial examples as "maximizing the difference between the non-true labels' probability upper bound and the true label's probability," and propose a gradient-based attack method termed Sequential Difference Maximization (SDM). SDM establishes a three-layer optimization framework of "cycle-stage-step." The processes between cycles and between iterative steps are respectively identical, while optimization stages differ in terms of loss functions: in the initial stage, the negative probability of the true label is used as the loss function to compress the solution space; in subsequent stages, we introduce the Directional Probability Difference Ratio (DPDR) loss function to gradually increase the non-true labels' probability upper bound by compressing the irrelevant labels' probabilities. Experiments demonstrate that compared with previous SOTA methods, SDM not only exhibits stronger attack performance but also achieves higher attack cost-effectiveness. Additionally, SDM can be combined with adversarial training methods to enhance their defensive effects. The code is available at https://github.com/X-L-Liu/SDM.

At the intersection of the cutting-edge technologies and privacy concerns, Federated Learning (FL) with its distributed architecture, stands at the forefront in a bid to facilitate collaborative model training across multiple clients while preserving data privacy. However, the applicability of FL systems is hindered by fairness concerns arising from numerous sources of heterogeneity that can result in biases and undermine a system's effectiveness, with skewed predictions, reduced accuracy, and inefficient model convergence. This survey thus explores the diverse sources of bias, including but not limited to, data, client, and model biases, and thoroughly discusses the strengths and limitations inherited within the array of the state-of-the-art techniques utilized in the literature to mitigate such disparities in the FL training process. We delineate a comprehensive overview of the several notions, theoretical underpinnings, and technical aspects associated with fairness and their adoption in FL-based multidisciplinary environments. Furthermore, we examine salient evaluation metrics leveraged to measure fairness quantitatively. Finally, we envisage exciting open research directions that have the potential to drive future advancements in achieving fairer FL frameworks, in turn, offering a strong foundation for future research in this pivotal area.

In this paper, we propose an evolutionary Multi-objective Optimization for Replica-Exchange-based Physics-informed Operator learning Network, which is a novel operator learning network to efficiently solve parametric partial differential equations. In forward and inverse settings, this operator learning network only admits minimum requirement of noisy observational data. While physics-informed neural networks and operator learning approaches such as Deep Operator Networks and Fourier Neural Operators offer promising alternatives to traditional numerical solvers, they struggle with balancing operator and physics losses, maintaining robustness under noisy or sparse data, and providing uncertainty quantification. The proposed framework addresses these limitations by integrating: (i) evolutionary multi-objective optimization to adaptively balance operator and physics-based losses in the Pareto front; (ii) replica exchange stochastic gradient Langevin dynamics to improve global parameter-space exploration and accelerate convergence; and (iii) built-in Bayesian uncertainty quantification from stochastic sampling. The proposed operator learning method is tested numerically on several different problems including one-dimensional Burgers equation and the time-fractional mixed diffusion-wave equation. The results indicate that our framework consistently outperforms the general operator learning methods in accuracy, noise robustness, and the ability to quantify uncertainty.

Robot manipulation in unstructured environments requires efficient and reliable Swept Volume Collision Detection (SVCD) for safe motion planning. Traditional discrete methods potentially miss collisions between these points, whereas SVCD continuously checks for collisions along the entire trajectory. Existing SVCD methods typically face a trade-off between efficiency and accuracy, limiting practical use. In this paper, we introduce NeuralSVCD, a novel neural encoder-decoder architecture tailored to overcome this trade-off. Our approach leverages shape locality and temporal locality through distributed geometric representations and temporal optimization. This enhances computational efficiency without sacrificing accuracy. Comprehensive experiments show that NeuralSVCD consistently outperforms existing state-of-the-art SVCD methods in terms of both collision detection accuracy and computational efficiency, demonstrating its robust applicability across diverse robotic manipulation scenarios. Code and videos are available at https://neuralsvcd.github.io/.

This paper presents two types of extended diffeomorphism designs to compensate for spatial placement differences between robot workspaces. Teleoperation of multiple robots is attracting attention to expand the utilization of the robot embodiment. Real-time reproduction of robot motion would facilitate the efficient execution of similar tasks by multiple robots. A challenge in the motion reproduction is compensating for the spatial arrangement errors of target keypoints in robot workspaces. This paper proposes a methodology for smooth mappings that transform primary robot poses into follower robot poses based on the predefined key points in each workspace. Through a picking task experiment using a dual-arm UR5 robot, this study demonstrates that the proposed mapping generation method can balance lower mapping errors for precise operation and lower mapping gradients for smooth replicated movement.

Partially observable restless multi-armed bandits have found numerous applications including in recommendation systems, communication systems, public healthcare outreach systems, and in operations research. We study multi-action partially observable restless multi-armed bandits, it is a generalization of the classical restless multi-armed bandit problem -- 1) each bandit has finite states, and the current state is not observable, 2) each bandit has finite actions. In particular, we assume that more than two actions are available for each bandit. We motivate our problem with the application of public-health intervention planning. We describe the model and formulate a long term discounted optimization problem, where the state of each bandit evolves according to a Markov process, and this evolution is action dependent. The state of a bandit is not observable but one of finitely many feedback signals are observable. Each bandit yields a reward, based on the action taken on that bandit. The agent is assumed to have a budget constraint. The bandits are assumed to be independent. However, they are weakly coupled at the agent through the budget constraint. We first analyze the Lagrangian bound method for our partially observable restless bandits. The computation of optimal value functions for finite-state, finite-action POMDPs is non-trivial. Hence, the computation of Lagrangian bounds is also challenging. We describe approximations for the computation of Lagrangian bounds using point based value iteration (PBVI) and online rollout policy. We further present various properties of the value functions and provide theoretical insights on PBVI and online rollout policy. We study heuristic policies for multi-actions PORMAB. Finally, we discuss present Whittle index policies and their limitations in our model.

The optimal power flow (OPF) is a large-scale optimization problem that is central in the operation of electric power systems. Although it can be posed as a nonconvex quadratically constrained quadratic program, the complexity of modern-day power grids raises scalability and optimality challenges. In this context, this work proposes a variational quantum paradigm for solving the OPF. We encode primal variables through the state of a parameterized quantum circuit (PQC), and dual variables through the probability mass function associated with a second PQC. The Lagrangian function can thus be expressed as scaled expectations of quantum observables. An OPF solution can be found by minimizing/maximizing the Lagrangian over the parameters of the first/second PQC. We pursue saddle points of the Lagrangian in a hybrid fashion. Gradients of the Lagrangian are estimated using the two PQCs, while PQC parameters are updated classically using a primal-dual method. We propose permuting primal variables so that OPF observables are expressed in a banded form, allowing them to be measured efficiently. Numerical tests on the IEEE 57-node power system using Pennylane's simulator corroborate that the proposed doubly variational quantum framework can find high-quality OPF solutions. Although showcased for the OPF, this framework features a broader scope, including conic programs with numerous variables and constraints, problems defined over sparse graphs, and training quantum machine learning models to satisfy constraints.

Satellite Communication (SatCom) networks represent a fundamental pillar in modern global connectivity, facilitating reliable service and extensive coverage across a plethora of applications. The expanding demand for high-bandwidth services and the proliferation of mega satellite constellations highlight the limitations of traditional exclusive satellite spectrum allocation approaches. Cognitive Radio (CR) leading to Cognitive Satellite (CogSat) networks through Dynamic Spectrum Management (DSM), which enables the dynamic adaptability of radio equipment to environmental conditions for optimal performance, presents a promising solution for the emerging spectrum scarcity. In this survey, we explore the adaptation of intelligent DSM methodologies to SatCom, leveraging satellite network integrations. We discuss contributions and hurdles in regulations and standardizations in realizing intelligent DSM in SatCom, and deep dive into DSM techniques, which enable CogSat networks. Furthermore, we extensively evaluate and categorize state-of-the-art Artificial Intelligence (AI)/Machine Learning (ML) methods leveraged for DSM while exploring operational resilience and robustness of such integrations. In addition, performance evaluation metrics critical for adaptive resource management and system optimization in CogSat networks are thoroughly investigated. This survey also identifies open challenges and outlines future research directions in regulatory frameworks, network architectures, and intelligent spectrum management, paving the way for sustainable and scalable SatCom networks for enhanced global connectivity.