Federated learning (FL) has emerged as a promising paradigm for distributed machine learning, enabling collaborative training of a global model across multiple local devices without requiring them to share raw data. Despite its advancements, FL is limited by factors such as: (i) privacy risks arising from the unprotected transmission of local model updates to the fusion center (FC) and (ii) decreased learning utility caused by heterogeneity in model quantization resolution across participating devices. Prior work typically addresses only one of these challenges because maintaining learning utility under both privacy risks and quantization heterogeneity is a non-trivial task. In this paper, our aim is therefore to improve the learning utility of a privacy-preserving FL that allows clusters of devices with different quantization resolutions to participate in each FL round. Specifically, we introduce a novel stochastic quantizer (SQ) that is designed to simultaneously achieve differential privacy (DP) and minimum quantization error. Notably, the proposed SQ guarantees bounded distortion, unlike other DP approaches. To address quantization heterogeneity, we introduce a cluster size optimization technique combined with a linear fusion approach to enhance model aggregation accuracy. Numerical simulations validate the benefits of our approach in terms of privacy protection and learning utility compared to the conventional LaplaceSQ-FL algorithm.

Visualization techniques are a critical means of shedding light on the behavior of metaheuristic numerical optimization algorithms. Conventional methods such as convergence analysis, trajectory visualizations, and fitness landscape analysis provide valuable insights into aspects like convergence speed, diversity, and solution quality. However, these approaches often fail to capture the structural dynamics of the search process, particularly in high-dimensional or complex spaces. Existing methods rarely address the location of the solution candidates in the search space, which can reveal crucial information about the exploratory and exploitative strategies of an algorithm. We propose ClustOpt, a novel representation and visualization methodology for metaheuristic numerical population-based optimization algorithms, that focuses on clustering solution candidates explored by optimization algorithms.

Survival analysis is an important problem in healthcare because it models the relationship between an individual's covariates and the onset time of an event of interest (e.g., death). It is important for survival models to be well-calibrated (i.e., for their predicted probabilities to be close to ground-truth probabilities) because badly calibrated systems can result in erroneous clinical decisions. Existing survival models are typically calibrated at the population level only, and thus run the risk of being poorly calibrated for one or more minority subpopulations. We propose a model called GRADUATE that achieves multicalibration by ensuring that all subpopulations are well-calibrated too. GRADUATE frames multicalibration as a constrained optimization problem, and optimizes both calibration and discrimination in-training to achieve a good balance between them. We mathematically prove that the optimization method used yields a solution that is both near-optimal and feasible with high probability. Empirical comparisons against state-of-the-art baselines on real-world clinical datasets demonstrate GRADUATE's efficacy. In a detailed analysis, we elucidate the shortcomings of the baselines vis-a-vis GRADUATE's strengths.

This paper leverages the recently introduced concept of algorithm footprints to investigate the interplay between algorithm configurations and problem characteristics. Performance footprints are calculated for six modular variants of the CMA-ES algorithm (modCMA), evaluated on 24 benchmark problems from the BBOB suite, across two-dimensional settings: 5-dimensional and 30-dimensional. These footprints provide insights into why different configurations of the same algorithm exhibit varying performance and identify the problem features influencing these outcomes. Our analysis uncovers shared behavioral patterns across configurations due to common interactions with problem properties, as well as distinct behaviors on the same problem driven by differing problem features. The results demonstrate the effectiveness of algorithm footprints in enhancing interpretability and guiding configuration choices.

This paper considers the problem of cost-aware downlink sum-rate maximization via joint optimal radio access technologies (RATs) assignment and power allocation in next-generation heterogeneous wireless networks (HetNets). We consider a future HetNet comprised of multi-RATs and serving multi-connectivity edge devices (EDs), and we formulate the problem as mixed-integer non-linear programming (MINP) problem. Due to the high complexity and combinatorial nature of this problem and the difficulty to solve it using conventional methods, we propose a hierarchical multi-agent deep reinforcement learning (DRL)-based framework, called DeepRAT, to solve it efficiently and learn system dynamics. In particular, the DeepRAT framework decomposes the problem into two main stages; the RATs-EDs assignment stage, which implements a single-agent Deep Q Network (DQN) algorithm, and the power allocation stage, which utilizes a multi-agent Deep Deterministic Policy Gradient (DDPG) algorithm. Using simulations, we demonstrate how the various DRL agents efficiently interact to learn system dynamics and derive the global optimal policy. Furthermore, our simulation results show that the proposed DeepRAT algorithm outperforms existing state-of-the-art heuristic approaches in terms of network utility. Finally, we quantitatively show the ability of the DeepRAT model to quickly and dynamically adapt to abrupt changes in network dynamics, such as EDs mobility.

This paper presents a leaderless cooperative guidance strategy for simultaneous time-constrained interception of a stationary target when the interceptors exchange information over switched dynamic graphs. We specifically focus on scenarios when the interceptors lack radial acceleration capabilities, relying solely on their lateral acceleration components. This consideration aligns with their inherent kinematic turn constraints. The proposed strategy explicitly addresses the complexities of coupled 3D engagements, thereby mitigating performance degradation that typically arises when the pitch and yaw channels are decoupled into two separate, mutually orthogonal planar engagements. Moreover, our formulation incorporates modeling uncertainties associated with the time-to-go estimation into the derivation of cooperative guidance commands to ensure robustness against inaccuracies in dynamic engagement scenarios. To optimize control efficiency, we analytically derive the lateral acceleration components in the orthogonal pitch and yaw channels by solving an instantaneous optimization problem, subject to an affine constraint. We show that the proposed cooperative guidance commands guarantee consensus in time-to-go values within a predefined time, which can be prescribed as a design parameter, regardless of the interceptors' initial configurations. We provide simulations to attest to the efficacy of the proposed method.

Stochastic control problems in high dimensions are notoriously difficult to solve due to the curse of dimensionality. An alternative to traditional dynamic programming is Pontryagin's Maximum Principle (PMP), which recasts the problem as a system of Forward-Backward Stochastic Differential Equations (FBSDEs). In this paper, we introduce a formal framework for solving such problems with deep learning by defining a \textbf{Neural Hamiltonian Operator (NHO)}. This operator parameterizes the coupled FBSDE dynamics via neural networks that represent the feedback control and an ansatz for the value function's spatial gradient. We show how the optimal NHO can be found by training the underlying networks to enforce the consistency conditions dictated by the PMP. By adopting this operator-theoretic view, we situate the deep FBSDE method within the rigorous language of statistical inference, framing it as a problem of learning an unknown operator from simulated data. This perspective allows us to prove the universal approximation capabilities of NHOs under general martingale drivers and provides a clear lens for analyzing the significant optimization challenges inherent to this class of models.

In this paper, we propose SubLoRA, a rank determination method for Low-Rank Adaptation (LoRA) based on submodular function maximization. In contrast to prior approaches, such as AdaLoRA, that rely on first-order (linearized) approximations of the loss function, SubLoRA utilizes second-order information to capture the potentially complex loss landscape by incorporating the Hessian matrix. We show that the linearization becomes inaccurate and ill-conditioned when the LoRA parameters have been well optimized, motivating the need for a more reliable and nuanced second-order formulation. To this end, we reformulate the rank determination problem as a combinatorial optimization problem with a quadratic objective. However, solving this problem exactly is NP-hard in general. To overcome the computational challenge, we introduce a submodular function maximization framework and devise a greedy algorithm with approximation guarantees. We derive a sufficient and necessary condition under which the rank-determination objective becomes submodular, and construct a closed-form projection of the Hessian matrix that satisfies this condition while maintaining computational efficiency. Our method combines solid theoretical foundations, second-order accuracy, and practical computational efficiency. We further extend SubLoRA to a joint optimization setting, alternating between LoRA parameter updates and rank determination under a rank budget constraint. Extensive experiments on fine-tuning physics-informed neural networks (PINNs) for solving partial differential equations (PDEs) demonstrate the effectiveness of our approach. Results show that SubLoRA outperforms existing methods in both rank determination and joint training performance.

We present an analysis of landscape features for predicting the performance of multi-objective combinatorial optimization algorithms. We consider features from the recently proposed compressed Pareto Local Optimal Solutions Networks (C-PLOS-net) model of combinatorial landscapes. The benchmark instances are a set of rmnk-landscapes with 2 and 3 objectives and various levels of ruggedness and objective correlation. We consider the performance of three algorithms -- Pareto Local Search (PLS), Global Simple EMO Optimizer (GSEMO), and Non-dominated Sorting Genetic Algorithm (NSGA-II) - using the resolution and hypervolume metrics. Our tailored analysis reveals feature combinations that influence algorithm performance specific to certain landscapes. This study provides deeper insights into feature importance, tailored to specific rmnk-landscapes and algorithms.

Fine-tuning pre-trained large language models (LLMs) in a distributed manner poses significant challenges on resource-constrained edge networks. To address this challenge, we propose SflLLM, a novel framework that integrates split federated learning with parameter-efficient fine-tuning techniques. By leveraging model splitting and low-rank adaptation (LoRA), SflLLM reduces the computational burden on edge devices. Furthermore, the introduction of a federated server facilitates parallel training and enhances data privacy. To accommodate heterogeneous communication conditions and diverse computational capabilities of edge devices, as well as the impact of LoRA rank selection on model convergence and training cost, we formulate a joint optimization problem of both communication and computation resource. The formulated problem jointly optimizes subchannel allocation, power control, model splitting point selection, and LoRA rank configuration, aimed at minimizing total training delay. An iterative optimization algorithm is proposed to solve this problem efficiently. Specifically, a greedy heuristic is employed for subchannel allocation, the power control subproblem is reformulated as a convex optimization problem using auxiliary variables, and an exhaustive search is adopted for optimal split position and rank selection. Simulation results demonstrate that the proposed SflLLM framework achieves comparable model accuracy while significantly reducing client-side computational requirements. Furthermore, the proposed resource allocation scheme and adaptive LoRA rank selection strategy notably reduce the training latency compared to conventional approaches.