We introduce Local Reinforcement-Based Selection of Auxiliary Objectives (LRSAO), a novel approach that selects auxiliary objectives using reinforcement learning (RL) to support the optimization process of an evolutionary algorithm (EA) as in EA+RL framework and furthermore incorporates the ability to unlearn previously used objectives. By modifying the reward mechanism to penalize moves that do no increase the fitness value and relying on the local auxiliary objectives, LRSAO dynamically adapts its selection strategy to optimize performance according to the landscape and unlearn previous objectives when necessary. We analyze and evaluate LRSAO on the black-box complexity version of the non-monotonic Jump function, with gap parameter $\ell$, where each auxiliary objective is beneficial at specific stages of optimization. The Jump function is hard to optimize for evolutionary-based algorithms and the best-known complexity for reinforcement-based selection on Jump was $O(n^2 \log(n) / \ell)$. Our approach improves over this result to achieve a complexity of $\Theta(n^2 / \ell^2 + n \log(n))$ resulting in a significant improvement, which demonstrates the efficiency and adaptability of LRSAO, highlighting its potential to outperform traditional methods in complex optimization scenarios.

We introduce a semidefinite relaxation for optimal control of linear systems with time scaling. These problems are inherently nonconvex, since the system dynamics involves bilinear products between the discretization time step and the system state and controls. The proposed relaxation is closely related to the standard second-order semidefinite relaxation for quadratic constraints, but we carefully select a subset of the possible bilinear terms and apply a change of variables to achieve empirically tight relaxations while keeping the computational load light. We further extend our method to handle piecewise-affine (PWA) systems by formulating the PWA optimal-control problem as a shortest-path problem in a graph of convex sets (GCS). In this GCS, different paths represent different mode sequences for the PWA system, and the convex sets model the relaxed dynamics within each mode. By combining a tight convex relaxation of the GCS problem with our semidefinite relaxation with time scaling, we can solve PWA optimal-control problems through a single semidefinite program.

Pap smear image segmentation is crucial for cervical cancer diagnosis. However, traditional segmentation models often struggle with complex cellular structures and variations in pap smear images. This study proposes a hybrid Dense-UNet201 optimization approach that integrates a pretrained DenseNet201 as the encoder for the U-Net architecture and optimizes it using the spider monkey optimization (SMO) algorithm. The Dense-UNet201 model excelled at feature extraction. The SMO was modified to handle categorical and discrete parameters. The SIPaKMeD dataset was used in this study and evaluated using key performance metrics, including loss, accuracy, Intersection over Union (IoU), and Dice coefficient. The experimental results showed that Dense-UNet201 outperformed U-Net, Res-UNet50, and Efficient-UNetB0. SMO Dense-UNet201 achieved a segmentation accuracy of 96.16%, an IoU of 91.63%, and a Dice coefficient score of 95.63%. These findings underscore the effectiveness of image preprocessing, pretrained models, and metaheuristic optimization in improving medical image analysis and provide new insights into cervical cell segmentation methods.

Decentralized Federated Learning (DFL) eliminates the reliance on the server-client architecture inherent in traditional federated learning, attracting significant research interest in recent years. Simultaneously, the objective functions in machine learning tasks are often nonconvex and frequently incorporate additional, potentially nonsmooth regularization terms to satisfy practical requirements, thereby forming nonconvex composite optimization problems. Employing DFL methods to solve such general optimization problems leads to the formulation of Decentralized Nonconvex Composite Federated Learning (DNCFL), a topic that remains largely underexplored. In this paper, we propose a novel DNCFL algorithm, termed \bf{DEPOSITUM}. Built upon proximal stochastic gradient tracking, DEPOSITUM mitigates the impact of data heterogeneity by enabling clients to approximate the global gradient. The introduction of momentums in the proximal gradient descent step, replacing tracking variables, reduces the variance introduced by stochastic gradients. Additionally, DEPOSITUM supports local updates of client variables, significantly reducing communication costs. Theoretical analysis demonstrates that DEPOSITUM achieves an expected $ε$-stationary point with an iteration complexity of $\mathcal{O}(1/ε^2)$. The proximal gradient, consensus errors, and gradient estimation errors decrease at a sublinear rate of $\mathcal{O}(1/T)$. With appropriate parameter selection, the algorithm achieves network-independent linear speedup without requiring mega-batch sampling. Finally, we apply DEPOSITUM to the training of neural networks on real-world datasets, systematically examining the influence of various hyperparameters on its performance. Comparisons with other federated composite optimization algorithms validate the effectiveness of the proposed method.

Feature selection is essential for efficient data mining and sometimes encounters the positive-unlabeled (PU) learning scenario, where only a few positive labels are available, while most data remains unlabeled. In certain real-world PU learning tasks, data subjected to adequate feature selection often form clusters with concentrated positive labels. Conventional feature selection methods that treat unlabeled data as negative may fail to capture the statistical characteristics of positive data in such scenarios, leading to suboptimal performance. To address this, we propose a novel feature selection method based on the cluster assumption in PU learning, called FSCPU. FSCPU formulates the feature selection problem as a binary optimization task, with an objective function explicitly designed to incorporate the cluster assumption in the PU learning setting. Experiments on synthetic datasets demonstrate the effectiveness of FSCPU across various data conditions. Moreover, comparisons with 10 conventional algorithms on three open datasets show that FSCPU achieves competitive performance in downstream classification tasks, even when the cluster assumption does not strictly hold.

Fine-tuning plays a crucial role in adapting models to downstream tasks with minimal training efforts. However, the rapidly increasing size of foundation models poses a daunting challenge for accommodating foundation model fine-tuning in most commercial devices, which often have limited memory bandwidth. Techniques like model sharding and tensor parallelism address this issue by distributing computation across multiple devices to meet memory requirements. Nevertheless, these methods do not fully leverage their foundation nature in facilitating the fine-tuning process, resulting in high computational costs and imbalanced workloads. We introduce a novel Distributed Dynamic Fine-Tuning (D2FT) framework that strategically orchestrates operations across attention modules based on our observation that not all attention modules are necessary for forward and backward propagation in fine-tuning foundation models. Through three innovative selection strategies, D2FT significantly reduces the computational workload required for fine-tuning foundation models. Furthermore, D2FT addresses workload imbalances in distributed computing environments by optimizing these selection strategies via multiple knapsack optimization. Our experimental results demonstrate that the proposed D2FT framework reduces the training computational costs by 40% and training communication costs by 50% with only 1% to 2% accuracy drops on the CIFAR-10, CIFAR-100, and Stanford Cars datasets. Moreover, the results show that D2FT can be effectively extended to recent LoRA, a state-of-the-art parameter-efficient fine-tuning technique. By reducing 40% computational cost or 50% communication cost, D2FT LoRA top-1 accuracy only drops 4% to 6% on Stanford Cars dataset.

In recent years, fairness in machine learning has emerged as a critical concern to ensure that developed and deployed predictive models do not have disadvantageous predictions for marginalized groups. It is essential to mitigate discrimination against individuals based on protected attributes such as gender and race. In this work, we consider applying subgroup justice concepts to gradient-boosting machines designed for supervised learning problems. Our approach expanded gradient-boosting methodologies to explore a broader range of objective functions, which combines conventional losses such as the ones from classification and regression and a min-max fairness term. We study relevant theoretical properties of the solution of the min-max optimization problem. The optimization process explored the primal-dual problems at each boosting round. This generic framework can be adapted to diverse fairness concepts. The proposed min-max primal-dual gradient boosting algorithm was theoretically shown to converge under mild conditions and empirically shown to be a powerful and flexible approach to address binary and subgroup fairness.

Multi-objective optimization involving Quadratic Unconstrained Binary Optimization (QUBO) problems arises in various domains. A fundamental challenge in this context is the effective balancing of multiple objectives, each potentially operating on very different scales. This imbalance introduces complications such as the selection of appropriate weights when scalarizing multiple objectives into a single objective function. In this paper, we propose a novel technique for scaling QUBO objectives that uses an exact computation of the variance of each individual QUBO objective. By scaling each objective to have unit variance, we align all objectives onto a common scale, thereby allowing for more balanced solutions to be found when scalarizing the objectives with equal weights, as well as potentially assisting in the search or choice of weights during scalarization. Finally, we demonstrate its advantages through empirical evaluations on various multi-objective optimization problems. Our results are noteworthy since manually selecting scalarization weights is cumbersome, and reliable, efficient solutions are scarce.

Accurate prediction and stabilization of blast furnace temperatures are crucial for optimizing the efficiency and productivity of steel production. Traditional methods often struggle with the complex and non-linear nature of the temperature fluctuations within blast furnaces. This paper proposes a novel approach that combines hybrid quantum machine learning with pulverized coal injection control to address these challenges. By integrating classical machine learning techniques with quantum computing algorithms, we aim to enhance predictive accuracy and achieve more stable temperature control. For this we utilized a unique prediction-based optimization method. Our method leverages quantum-enhanced feature space exploration and the robustness of classical regression models to forecast temperature variations and optimize pulverized coal injection values. Our results demonstrate a significant improvement in prediction accuracy over 25 percent and our solution improved temperature stability to +-7.6 degrees of target range from the earlier variance of +-50 degrees, highlighting the potential of hybrid quantum machine learning models in industrial steel production applications.

We develop two classes of variance-reduced fast operator splitting methods to approximate solutions of both finite-sum and stochastic generalized equations. Our approach integrates recent advances in accelerated fixed-point methods, co-hypomonotonicity, and variance reduction. First, we introduce a class of variance-reduced estimators and establish their variance-reduction bounds. This class covers both unbiased and biased instances and comprises common estimators as special cases, including SVRG, SAGA, SARAH, and Hybrid-SGD. Next, we design a novel accelerated variance-reduced forward-backward splitting (FBS) algorithm using these estimators to solve finite-sum and stochastic generalized equations. Our method achieves both $\mathcal{O}(1/k^2)$ and $o(1/k^2)$ convergence rates on the expected squared norm $\mathbb{E}[ \| G_{\lambda}x^k\|^2]$ of the FBS residual $G_{\lambda}$, where $k$ is the iteration counter. Additionally, we establish, for the first time, almost sure convergence rates and almost sure convergence of iterates to a solution in stochastic accelerated methods. Unlike existing stochastic fixed-point algorithms, our methods accommodate co-hypomonotone operators, which potentially include nonmonotone problems arising from recent applications. We further specify our method to derive an appropriate variant for each stochastic estimator -- SVRG, SAGA, SARAH, and Hybrid-SGD -- demonstrating that they achieve the best-known complexity for each without relying on enhancement techniques. Alternatively, we propose an accelerated variance-reduced backward-forward splitting (BFS) method, which attains similar convergence rates and oracle complexity as our FBS method. Finally, we validate our results through several numerical experiments and compare their performance.