Submodular functions, as well as the sub-class of decomposable submodular functions, and their optimization appear in a wide range of applications in machine learning, recommendation systems, and welfare maximization. However, optimization of decomposable submodular functions with millions of component functions is computationally prohibitive. Furthermore, the component functions may be private (they might represent user preference function, for example) and cannot be widely shared. To address these issues, we propose a {\em federated optimization} setting for decomposable submodular optimization. In this setting, clients have their own preference functions, and a weighted sum of these preferences needs to be maximized. We implement the popular {\em continuous greedy} algorithm in this setting where clients take parallel small local steps towards the local solution and then the local changes are aggregated at a central server. To address the large number of clients, the aggregation is performed only on a subsampled set. Further, the aggregation is performed only intermittently between stretches of parallel local steps, which reduces communication cost significantly. We show that our federated algorithm is guaranteed to provide a good approximate solution, even in the presence of above cost-cutting measures. Finally, we show how the federated setting can be incorporated in solving fundamental discrete submodular optimization problems such as Maximum Coverage and Facility Location.

Motivated by COVID-19 vaccine allocation, where vulnerable subpopulations are simultaneously more impacted in terms of health and more disadvantaged in terms of access to the vaccine, we formalize and study the problem of resource allocation when there are inherent access differences that correlate with advantage and disadvantage. We identify reducing resource disparity as a key goal in this context and show its role as a proxy to more nuanced downstream impacts. We develop a concrete access model that helps quantify how a given allocation translates to resource flow for the advantaged vs. the disadvantaged, based on the access gap between them. We then provide a methodology for access-aware allocation. Intuitively, the resulting allocation leverages more vaccines in locations with higher vulnerable populations to mitigate the access gap and reduce overall disparity. Surprisingly, knowledge of the access gap is often not needed to perform access-aware allocation. To support this formalism, we provide empirical evidence for our access model and show that access-aware allocation can significantly reduce resource disparity and thus improve downstream outcomes. We demonstrate this at various scales, including at county, state, national, and global levels.

Machine teaching often involves the creation of an optimal (typically minimal) dataset to help a model (referred to as the `student') achieve specific goals given by a teacher. While abundant in the continuous domain, the studies on the effectiveness of machine teaching in the discrete domain are relatively limited. This paper focuses on machine teaching in the discrete domain, specifically on manipulating student models' predictions based on the goals of teachers via changing the training data efficiently. We formulate this task as a combinatorial optimization problem and solve it by proposing an iterative searching algorithm. Our algorithm demonstrates significant numerical merit in the scenarios where a teacher attempts at correcting erroneous predictions to improve the student's models, or maliciously manipulating the model to misclassify some specific samples to the target class aligned with his personal profits. Experimental results show that our proposed algorithm can have superior performance in effectively and efficiently manipulating the predictions of the model, surpassing conventional baselines.

Traditional benchmarking methods are often used to evaluate algorithms in isolation, with a single algorithm configuration (hyper-parameter setting) or with a limited set of a few variations against a limited set of state-of-the-art algorithms, leading to limited insights into their comparative performance and practical applicability. This study addresses these challenges by employing modular optimization approaches and explainable AI techniques in order to derive insights into the algorithmic behaviour of a large set of algorithm components (modules) and their hyper-parameters. Modular optimization frameworks allow for the comparison of various modifications on a core algorithm, facilitating a deeper understanding of each component's influence on the algorithm's performance in different scenarios. There is already a wide variety of modular algorithm frameworks available, but their application for explicit explainability of the various algorithmic components and settings has been relatively unexplored. This paper aims to bridge this gap by providing a comprehensive framework for explainable benchmarking in iterative optimization heuristics and by providing a software library (IOH-Xplainer) to facilitate researchers to use the proposed framework.

Despite the basic premise that next-generation wireless networks (e.g., 6G) will be artificial intelligence (AI)-native, to date, most existing efforts remain either qualitative or incremental extensions to existing "AI for wireless" paradigms. Indeed, creating AI-native wireless networks faces significant technical challenges due to the limitations of data-driven, training-intensive AI. These limitations include the black-box nature of the AI models, their curve-fitting nature, which can limit their ability to reason and adapt, their reliance on large amounts of training data, and the energy inefficiency of large neural networks. In response to these limitations, this article presents a comprehensive, forward-looking vision that addresses these shortcomings by introducing a novel framework for building AI-native wireless networks; grounded in the emerging field of causal reasoning. Causal reasoning, founded on causal discovery, causal representation learning, and causal inference, can help build explainable, reasoning-aware, and sustainable wireless networks. Towards fulfilling this vision, we first highlight several wireless networking challenges that can be addressed by causal discovery and representation, including ultra-reliable beamforming for terahertz (THz) systems, near-accurate physical twin modeling for digital twins, training data augmentation, and semantic communication. We showcase how incorporating causal discovery can assist in achieving dynamic adaptability, resilience, and cognition in addressing these challenges. Furthermore, we outline potential frameworks that leverage causal inference to achieve the overarching objectives of future-generation networks, including intent management, dynamic adaptability, human-level cognition, reasoning, and the critical element of time sensitivity.

It is known that adaptive optimization algorithms represent the key pillar behind the rise of the Machine Learning field. In the Optimization literature numerous studies have been devoted to accelerated gradient methods but only recently adaptive iterative techniques were analyzed from a theoretical point of view. In the present paper we introduce new adaptive algorithms endowed with momentum terms for stochastic non-convex optimization problems. Our purpose is to show a deep connection between accelerated methods endowed with different inertial steps and AMSGrad-type momentum methods. Our methodology is based on the framework of stochastic and possibly non-convex objective mappings, along with some assumptions that are often used in the investigation of adaptive algorithms. In addition to discussing the finite-time horizon analysis in relation to a certain final iteration and the almost sure convergence to stationary points, we shall also look at the worst-case iteration complexity. This will be followed by an estimate for the expectation of the squared Euclidean norm of the gradient. Various computational simulations for the training of neural networks are being used to support the theoretical analysis. For future research we emphasize that there are multiple possible extensions to our work, from which we mention the investigation regarding non-smooth objective functions and the theoretical analysis of a more general formulation that encompass our adaptive optimizers in a stochastic framework.

This study explores modeling and control for quadrotor acrobatics, focusing on executing flip maneuvers. Flips are an elegant way to deliver sensor probes into no-fly or hazardous zones, like volcanic vents. Successful flips require feasible trajectories and precise control, influenced by rotor dynamics, thrust allocation, and control methodologies. The research introduces a novel approach using Model Predictive Control (MPC) for real-time trajectory planning. The MPC considers dynamic constraints and environmental variables, ensuring system stability during maneuvers. The proposed methodology's effectiveness is examined through simulation studies in ROS and Gazebo, providing insights into quadrotor behavior, response time, and trajectory accuracy. Real-time flight experiments on a custom agile quadrotor using PixHawk 4 and Hardkernel Odroid validate MPC-designed controllers. Experiments confirm successful execution and adaptability to real-world scenarios. Outcomes contribute to autonomous aerial robotics, especially aerial acrobatics, enhancing mission capabilities. MPC controllers find applications in probe throws and optimal image capture views through efficient flight paths, e.g., full roll maneuvers. This research paves the way for quadrotors in demanding scenarios, showcasing groundbreaking applications. Video Link: \url{ https://www.youtube.com/watch?v=UzR0PWjy9W4}

The Conditional Markov Chain Search (CMCS) is a framework for automated design of metaheuristics for discrete combinatorial optimisation problems. Given a set of algorithmic components such as hill climbers and mutations, CMCS decides in which order to apply those components. The decisions are dictated by the CMCS configuration that can be learnt offline. CMCS does not have an acceptance criterion; any moves are accepted by the framework. As a result, it is particularly good in exploration butis not as good at exploitation. Inthis study,we explore several extensions of the framework to improve its exploitation abilities. To perform a computational study, we applied the framework to the three-index assignment problem. The results of our experiments showed that a two-stage CMCS is indeed superior to a single-stage CMCS. Keywords: Conditional Markov Chain Search (CMCS) three-index assignment problem axial index assignment problem automated algorithm design automated meta-heuristic design combinatorial optimisation.

Machine learning models traditionally assume that training and test data are independently and identically distributed. However, in real-world applications, the test distribution often differs from training. This problem, known as out-of-distribution generalization, challenges conventional models. Invariant Risk Minimization (IRM) emerges as a solution, aiming to identify features invariant across different environments to enhance out-of-distribution robustness. However, IRM's complexity, particularly its bi-level optimization, has led to the development of various approximate methods. Our study investigates these approximate IRM techniques, employing the Expected Calibration Error (ECE) as a key metric. ECE, which measures the reliability of model prediction, serves as an indicator of whether models effectively capture environment-invariant features. Through a comparative analysis of datasets with distributional shifts, we observe that Information Bottleneck-based IRM, which condenses representational information, achieves a balance in improving ECE while preserving accuracy relatively. This finding is pivotal, as it demonstrates a feasible path to maintaining robustness without compromising accuracy. Nonetheless, our experiments also caution against over-regularization, which can diminish accuracy. This underscores the necessity for a systematic approach in evaluating out-of-distribution generalization metrics, one that beyond mere accuracy to address the nuanced interplay between accuracy and calibration.

Federated learning (FL) is a novel approach to machine learning that allows multiple edge devices to collaboratively train a model without disclosing their raw data. However, several challenges hinder the practical implementation of this approach, especially when devices and the server communicate over wireless channels, as it suffers from communication and computation bottlenecks in this case. By utilizing a communication-efficient framework, we propose a novel zero-order (ZO) method with a one-point gradient estimator that harnesses the nature of the wireless communication channel without requiring the knowledge of the channel state coefficient. It is the first method that includes the wireless channel in the learning algorithm itself instead of wasting resources to analyze it and remove its impact. The two main difficulties of this work are that in FL, the objective function is usually not convex, which makes the extension of FL to ZO methods challenging, and that including the impact of wireless channels requires extra attention. However, we overcome these difficulties and comprehensively analyze the proposed zero-order federated learning (ZOFL) framework. We establish its convergence theoretically, and we prove a convergence rate of $O(\frac{1}{\sqrt[3]{K}})$ in the nonconvex setting. We further demonstrate the potential of our algorithm with experimental results, taking into account independent and identically distributed (IID) and non-IID device data distributions.