Federated learning (FL) has emerged as a method to preserve privacy in collaborative distributed learning. In FL, clients train AI models directly on their devices rather than sharing data with a centralized server, which can pose privacy risks. However, it has been shown that despite FL's partial protection of local data privacy, information about clients' data can still be inferred from shared model updates during training. In recent years, several privacy-preserving approaches have been developed to mitigate this privacy leakage in FL, though they often provide privacy at the cost of model performance or system efficiency. Balancing these trade-offs presents a significant challenge in implementing FL schemes. In this manuscript, we introduce a privacy-preserving FL framework that combines differential privacy and system immersion tools from control theory. The core idea is to treat the optimization algorithms used in standard FL schemes (e.g., gradient-based algorithms) as a dynamical system that we seek to immerse into a higher-dimensional system (referred to as the target optimization algorithm). The target algorithm's dynamics are designed such that, first, the model parameters of the original algorithm are immersed in its parameters; second, it operates on distorted parameters; and third, it converges to an encoded version of the true model parameters from the original algorithm. These encoded parameters can then be decoded at the server to retrieve the original model parameters. We demonstrate that the proposed privacy-preserving scheme can be tailored to offer any desired level of differential privacy for both local and global model parameters, while maintaining the same accuracy and convergence rate as standard FL algorithms.

Many critical treatment assignment problems are inherently dynamic in nature. For example, consider the allocation of job-training programs to newly unemployed individuals. Such programs are often funded through a fixed yearly budget determined in advance by the legislature, while job-seekers arrive at job centers sequentially throughout the year. Policymakers must decide whether to allocate training to each individual, recognizing that each decision affects the remaining budget and the availability of training for future applicants who may benefit even more. In essence, policymakers face a dynamic optimization problem, balancing immediate needs against long-term budgetary constraints.

Bayesian optimization (BO) methods based on information theory have obtained state-of-the-art results in several tasks. These techniques heavily rely on the Kullback-Leibler (KL) divergence to compute the acquisition function. In this work, we introduce a novel information-based class of acquisition functions for BO called Alpha Entropy Search (AES). AES is based on the {\alpha}-divergence, that generalizes the KL divergence. Iteratively, AES selects the next evaluation point as the one whose associated target value has the highest level of the dependency with respect to the location and associated value of the global maximum of the optimization problem. Dependency is measured in terms of the {\alpha}-divergence, as an alternative to the KL divergence. Intuitively, this favors the evaluation of the objective function at the most informative points about the global maximum. The {\alpha}-divergence has a free parameter {\alpha}, which determines the behavior of the divergence, trading-off evaluating differences between distributions at a single mode, and evaluating differences globally. Therefore, different values of {\alpha} result in different acquisition functions. AES acquisition lacks a closed-form expression. However, we propose an efficient and accurate approximation using a truncated Gaussian distribution. In practice, the value of {\alpha} can be chosen by the practitioner, but here we suggest to use a combination of acquisition functions obtained by simultaneously considering a range of values of {\alpha}. We provide an implementation of AES in BOTorch and we evaluate its performance in both synthetic, benchmark and real-world experiments involving the tuning of the hyper-parameters of a deep neural network. These experiments show that the performance of AES is competitive with respect to other information-based acquisition functions such as JES, MES or PES.

Federated Learning (FL) is a distributed learning approach that trains neural networks across multiple devices while keeping their local data private. However, FL often faces challenges due to data heterogeneity, leading to inconsistent local optima among clients. These inconsistencies can cause unfavorable convergence behavior and generalization performance degradation. Existing studies mainly describe this issue through \textit{convergence analysis}, focusing on how well a model fits training data, or through \textit{algorithmic stability}, which examines the generalization gap. However, neither approach precisely captures the generalization performance of FL algorithms, especially for neural networks. In this paper, we introduce the first generalization dynamics analysis framework in federated optimization, highlighting the trade-offs between model stability and optimization. Through this framework, we show how the generalization of FL algorithms is affected by the interplay of algorithmic stability and optimization. This framework applies to standard federated optimization and its advanced versions, like server momentum. We find that fast convergence from large local steps or accelerated momentum enlarges stability but obtains better generalization performance. Our insights into these trade-offs can guide the practice of future algorithms for better generalization.

As multi-modal large language models (MLLMs) are increasingly applied to complex reasoning tasks, the diversity and quality of reasoning paths become crucial factors affecting their performance. Although current methods aim to enhance reasoning quality through path expansion, they often neglect the diversity of reasoning paths and effective information sharing, leading to local optima and inefficiency. To address these challenges, we propose Evolution of Thought (EoT), a multi-objective framework designed to improve reasoning by fostering both high-quality and diverse reasoning paths. Specifically, we introduce the Non-dominated Sorting Genetic Algorithm II for multi-objective optimization, utilizing crossover and mutation operators to promote greater diversity in reasoning solutions. Additionally, we propose a Condensation-Aggregation mechanism to cluster and eliminate redundant paths, facilitate improved information sharing among parent nodes, and ultimately enhance both the efficiency and quality of the reasoning process. Validation experiments on various vision-language and language reasoning tasks demonstrate that EoT achieves superior reasoning performance and efficiency compared to other competitive baselines. Our study provides a novel perspective on the design of heuristic reasoning frameworks for MLLMs.

Simply by rearranging the regions of an image, we can create a new image of any subject matter. The definition of regions is user definable, ranging from regularly and irregularly-shaped blocks, concentric rings, or even individual pixels. Our method extends and improves recent work in the generation of optical illusions by simultaneously learning not only the content of the images, but also the parameterized transformations required to transform the desired images into each other. By learning the image transforms, we allow any source image to be pre-specified; any existing image (e.g. the Mona Lisa) can be transformed to a novel subject. We formulate this process as a constrained optimization problem and address it through interleaving the steps of image diffusion with an energy minimization step. Unlike previous methods, increasing the number of regions actually makes the problem easier and improves results. We demonstrate our approach in both pixel and latent spaces. Creative extensions, such as using infinite copies of the source image and employing multiple source images, are also given.

Adversarial learning is critical for enhancing model robustness, aiming to defend against adversarial attacks that jeopardize machine learning systems. Traditional methods often lack efficient mechanisms to explore diverse adversarial perturbations, leading to limited model resilience. Inspired by game-theoretic principles, where adversarial dynamics are analyzed through frameworks like Nash equilibrium, exploration mechanisms in such setups allow for the discovery of diverse strategies, enhancing system robustness. However, existing adversarial learning methods often fail to incorporate structured exploration effectively, reducing their ability to improve model defense comprehensively. To address these challenges, we propose a novel Exploration-enhanced Adversarial Learning Algorithm (ExAL), leveraging the Exponentially Weighted Momentum Particle Swarm Optimizer (EMPSO) to generate optimized adversarial perturbations. ExAL integrates exploration-driven mechanisms to discover perturbations that maximize impact on the model's decision boundary while preserving structural coherence in the data. We evaluate the performance of ExAL on the MNIST Handwritten Digits and Blended Malware datasets. Experimental results demonstrate that ExAL significantly enhances model resilience to adversarial attacks by improving robustness through adversarial learning.

Black-box optimization, a rapidly growing field, faces challenges due to limited knowledge of the objective function's internal mechanisms. One promising approach to address this is the Stochastic Order Oracle Concept. This concept, similar to other Order Oracle Concepts, relies solely on relative comparisons of function values without requiring access to the exact values. This paper presents a novel, improved estimation of the covariance matrix for the asymptotic convergence of the Stochastic Order Oracle Concept. Our work surpasses existing research in this domain by offering a more accurate estimation of asymptotic convergence rate. Finally, numerical experiments validate our theoretical findings, providing strong empirical support for our proposed approach.

Non-maximum suppression (NMS) is an indispensable post-processing step in object detection. With the continuous optimization of network models, NMS has become the ``last mile'' to enhance the efficiency of object detection. This paper systematically analyzes NMS from a graph theory perspective for the first time, revealing its intrinsic structure. Consequently, we propose two optimization methods, namely QSI-NMS and BOE-NMS. The former is a fast recursive divide-and-conquer algorithm with negligible mAP loss, and its extended version (eQSI-NMS) achieves optimal complexity of $\mathcal{O}(n\log n)$. The latter, concentrating on the locality of NMS, achieves an optimization at a constant level without an mAP loss penalty. Moreover, to facilitate rapid evaluation of NMS methods for researchers, we introduce NMS-Bench, the first benchmark designed to comprehensively assess various NMS methods. Taking the YOLOv8-N model on MS COCO 2017 as the benchmark setup, our method QSI-NMS provides $6.2\times$ speed of original NMS on the benchmark, with a $0.1\%$ decrease in mAP. The optimal eQSI-NMS, with only a $0.3\%$ mAP decrease, achieves $10.7\times$ speed. Meanwhile, BOE-NMS exhibits $5.1\times$ speed with no compromise in mAP.

In this paper, we study second-order algorithms for solving nonconvex-strongly concave minimax problems, which have attracted much attention in recent years in many fields, especially in machine learning. We propose a gradient norm regularized trust region (GRTR) algorithm to solve nonconvex-strongly concave minimax problems, where the objective function of the trust region subproblem in each iteration uses a regularized version of the Hessian matrix, and the regularization coefficient and the radius of the ball constraint are proportional to the square root of the gradient norm. The iteration complexity of the proposed GRTR algorithm to obtain an $\mathcal{O}(\epsilon,\sqrt{\epsilon})$-second-order stationary point is proved to be upper bounded by $\tilde{\mathcal{O}}(\rho^{0.5}\kappa^{1.5}\epsilon^{-3/2})$, where $\rho$ and $\kappa$ are the Lipschitz constant of the Jacobian matrix and the condition number of the objective function respectively, which matches the best known iteration complexity of second-order methods for solving nonconvex-strongly concave minimax problems. We further propose a Levenberg-Marquardt algorithm with a gradient norm regularization coefficient and use the negative curvature direction to correct the iteration direction (LMNegCur), which does not need to solve the trust region subproblem at each iteration. We also prove that the LMNegCur algorithm achieves an $\mathcal{O}(\epsilon,\sqrt{\epsilon})$-second-order stationary point within $\tilde{\mathcal{O}}(\rho^{0.5}\kappa^{1.5}\epsilon^{-3/2})$ number of iterations. Numerical results show the efficiency of both proposed algorithms.