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MODIFIED ADAPTIVE TREE-STRUCTURED PARZEN ESTIMATOR FOR HYPERPARAMETER optimization

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arXiv 2025年

作者： Sieradzki, Szymon Mańdziuk, Jacek Faculty of Mathematics and Information Science Warsaw University of Technology Koszykowa 75 Warsaw Poland Faculty of Computer Science AGH University of Krakow A. Mickiewicza 30 Krakow Poland

In this paper we review hyperparameter optimization methods for machine learning models, with a particular focus on the Adaptive Tree-Structured Parzen Estimator (ATPE) algorithm. We propose several modifications to ATPE and assess their efficacy on a diverse set of standard benchmark functions. Experimental results demonstrate that the proposed modifications significantly improve the effectiveness of ATPE hyperparameter optimization on selected benchmarks, a finding that holds practical relevance for their application in real-world machine learning / optimization tasks. © 2025, CC BY-NC-SA.

关键词： optimization algorithms

A Novel Unified Parametric Assumption for Nonconvex optimization

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arXiv 2025年

作者： Riabinin, Artem Khaled, Ahmed Richtárik, Peter Thuwal Saudi Arabia Princeton University Princeton United States

Nonconvex optimization is central to modern machine learning, but the general framework of nonconvex optimization yields weak convergence guarantees that are too pessimistic compared to practice. On the other hand, while convexity enables efficient optimization, it is of limited applicability to many practical problems. To bridge this gap and better understand the practical success of optimization algorithms in nonconvex settings, we introduce a novel unified parametric assumption. Our assumption is general enough to encompass a broad class of nonconvex functions while also being specific enough to enable the derivation of a unified convergence theorem for gradient-based methods. Notably, by tuning the parameters of our assumption, we demonstrate its versatility in recovering several existing function classes as special cases and in identifying functions amenable to efficient optimization. We derive our convergence theorem for both deterministic and stochastic optimization, and conduct experiments to verify that our assumption can hold practically over optimization trajectories. © 2025, CC BY.

关键词： optimization algorithms

Perturbation-Aware Distributionally Robust optimization for Inverse Problems

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arXiv 2025年

作者： van Maarschalkerwaart, Floor Mukherjee, Subhadip Landman, Malena Sabaté Brune, Christoph Carioni, Marcello Department of Applied Mathematics University of Twente Enschede Netherlands Kharagpur India Mathematical Institute University of Oxford United Kingdom

This paper builds on classical distributionally robust optimization techniques to construct a comprehensive framework that can be used for solving inverse problems. Given an estimated distribution of inputs in X and outputs in Y , an ambiguity set is constructed by collecting all the perturbations that belong to a prescribed set K and are inside an entropy-regularized Wasserstein ball. By finding the worst-case reconstruction within K one can produce reconstructions that are robust with respect to various types of perturbations: X-robustness, Y |X-robustness and, more general, targeted robustness depending on noise type, imperfect forward operators and noise anisotropies. After defining the general robust optimization problem, we derive its (weak) dual formulation and we use it to design an efficient algorithm. Finally, we demonstrate the effectiveness of our general framework to solve matrix inversion and deconvolution problems defining K as the set of multivariate Gaussian perturbations in Y |X. Copyright © 2025, The Authors. All rights reserved.

关键词： optimization algorithms

Ensuring Truthfulness in Distributed Aggregative optimization

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arXiv 2025年

作者： Chen, Ziqin Egerstedt, Magnus Wang, Yongqiang The Department of Electrical and Computer Engineering Clemson University ClemsonSC29634 United States The Department of Electrical Engineering and Computer Science University of California Irvine IrvineCA92697 United States

Distributed aggregative optimization methods are gaining increased traction due to their ability to address cooperative control and optimization problems, where the objective function of each agent depends not only on its own decision variable but also on the aggregation of other agents' decision variables. Nevertheless, existing distributed aggregative optimization methods implicitly assume all agents to be truthful in information sharing, which can be unrealistic in real-world scenarios, where agents may act selfishly or strategically. In fact, an opportunistic agent may deceptively share false information in its own favor to minimize its own loss, which, however, will compromise the network-level global performance. To solve this issue, we propose a new distributed aggregative optimization algorithm that can ensure truthfulness of agents and convergence performance. To the best of our knowledge, this is the first algorithm that ensures truthfulness in a fully distributed setting, where no "centralized" aggregator exists to collect private information/decision variables from participating agents. We systematically characterize the convergence rate of our algorithm under nonconvex/convex/strongly convex objective functions, which generalizes existing distributed aggregative optimization results that only focus on convex objective functions. We also rigorously quantify the tradeoff between convergence performance and the level of enabled truthfulness under different convexity conditions. Numerical simulations using distributed charging of electric vehicles confirm the efficacy of our algorithm. Copyright © 2025, The Authors. All rights reserved.

关键词： optimization algorithms

Distributed Variational Quantum Algorithm with Many-qubit for optimization Challenges

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arXiv 2025年

作者： Kim, Seongmin Suh, In-Saeng National Center for Computational Sciences Oak Ridge National Laboratory Oak RidgeTN37830 United States

optimization problems are critical across various domains, yet existing quantum algorithms, despite their great potential, struggle with scalability and accuracy due to excessive reliance on entanglement. To address these limitations, we propose variational quantum optimization algorithm (VQOA), which leverages many-qubit (MQ) operations in an ansatz solely employing quantum superposition, completely avoiding entanglement. This ansatz significantly reduces circuit complexity, enhances noise robustness, mitigates Barren Plateau issues, and enables efficient partitioning for highly complex large-scale optimization. Furthermore, we introduce distributed VQOA (DVQOA), which integrates high-performance computing with quantum computing to achieve superior performance across MQ systems and classical nodes. These features enable a significant acceleration of material optimization tasks (e.g., metamaterial design), achieving more than 50× speedup compared to state-of-the-art optimization algorithms. Additionally, DVQOA efficiently solves quantum chemistry problems and N-ary (N ≥ 2) optimization problems involving higher-order interactions. These advantages establish DVQOA as a highly promising and versatile solver for real-world problems, demonstrating the practical utility of the quantum-classical approach. © 2025, CC BY.

关键词： optimization algorithms

Community Membership Hiding via Gradient-based optimization

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arXiv 2025年

作者： Silvestri, Matteo Gabrielli, Edoardo Silvestri, Fabrizio Tolomei, Gabriele Department of Computer Science Sapienza University of Rome Rome Italy Department of Computer Control and Management Engineering Sapienza University of Rome Rome Italy

We tackle the problem of community membership hiding, which involves strategically altering a network’s structure to obscure a target node’s membership in a specific community identified by a detection algorithm. We reformulate the original discrete counterfactual graph objective as a differentiable constrained optimization task. To solve this, we propose ∇- CMH, a gradient-based method that modifies the network’s structure within the feasible bounds for an individual target node, effectively concealing its membership. Experimental results across multiple datasets and community detection algorithms show that our approach surpasses existing baselines, offering a better balance between accuracy and computational efficiency. © 2025, CC BY.

关键词： optimization algorithms

Enhancing power system stability by coordinating a wind turbine voltage regulator and lead-lag power system stabilizer using GOOSE optimization

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SCIENTIFIC REPORTS 2025年第1期15卷 1-22页

作者： Ibrahim, Nader M. A. El-Fergany, Attia A. Hemade, Bassam A. Suez Univ Fac Technol & Educ Dept Elect POB 43221 Suez Egypt Zagazig Univ Elect Power & Machines Dept Zagazig 44519 Egypt

Integrating wind energy into power systems can negatively impact stability by reducing oscillation damping. Wind Turbine Voltage Regulators (WT VRs) are designed to manage reactive power and maintain voltage stability;however, they often do not coordinate effectively with Power System Stabilizers (PSS) from synchronous generators (SG). This study utilizes the GOOSE optimization Algorithm (GOA) to optimize and coordinate the gains of the WT proportional-integral virtual regulator (WT PI-VR) and the SG proportional-integral-type lead-lag PSS (PI-type LL-PSS), to enhance power system stability and performance. The GOA performance compared with the Osprey optimization Algorithm (OOA) and Particle Swarm Optimizer (PSO). The PI-type LL-PSS performance is compared with proportional-integral-derivative PID-PSS configurations, highlighting its robustness. Testing scenarios include step changes, voltage sags, and three-phase short-circuit faults, using metrics like integral time absolute error, settling time, and standard deviation for robustness evaluation. Statistical analysis shows several benefits from the proposed methodology: (i) A 48.85% stability improvement in coordinating WT PI-VR with PID-PSS using GOA versus OOA, (ii) A 24.40% performance boost with GOA over OOA using PI-type LL-PSS, (iii) A 14.4% enhancement when coordinating WT PI-VR with PI-type LL-PSS compared to PID-PSS, and (iv) A 34.23% performance increase using GOA instead of PSO for coordinating WT PI-VR with PI-type LL-PSS.

关键词： Controller coordination Doubly fed induction generators optimization algorithms Small-signal stability Wind turbine integration

Projected proximal gradient trust-region algorithm for nonsmooth optimization

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arXiv 2025年

作者： Dao, Minh N. Phan, Hung M. Roberts, Lindon School of Science RMIT University MelbourneVIC3000 Australia Department of Mathematics and Statistics Kennedy College of Sciences University of Massachusetts Lowell LowellMA01854 United States School of Mathematics and Statistics University of Sydney CamperdownNSW2006 Australia

We consider trust-region methods for solving optimization problems where the objective is the sum of a smooth, nonconvex function and a nonsmooth, convex regularizer. We extend the global convergence theory of such methods to include worst-case complexity bounds in the case of unbounded model Hessian growth, and introduce a new, simple nonsmooth trust-region subproblem solver based on combining several iterations of proximal gradient descent with a single projection into the trust region, which meets the sufficient descent requirements for algorithm convergence and has promising numerical results. Copyright © 2025, The Authors. All rights reserved.

关键词： optimization algorithms

A consensus-based optimization method for nonsmooth nonconvex programs with approximated gradient descent scheme

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arXiv 2025年

作者： Wei, Jiazhen Wu, Fan Bian, Wei School of Mathematics Harbin Institute of Technology Harbin China

In this paper, we are interested in finding the global minimizer of a nonsmooth nonconvex unconstrained optimization problem. By combining the discrete consensus-based optimization (CBO) algorithm and the gradient descent method, we develop a novel CBO algorithm with an extra gradient descent scheme evaluated by the forward-difference technique on the function values, where only the objective function values are used in the proposed algorithm. First, we prove that the proposed algorithm can exhibit global consensus in an exponential rate in two senses and possess a unique global consensus point. Second, we evaluate the error estimate between the objective function value on the global consensus point and its global minimum. In particular, as the parameter β tends to ∞, the error converges to zero and the convergence rate is O (logββ) . Third, under some suitable assumptions on the objective function, we provide the number of iterations required for the mean square error in expectation to reach the desired accuracy. It is worth underlining that the theoretical analysis in this paper does not use the mean-field limit. Finally, we illustrate the improved efficiency and promising performance of our novel CBO method through some experiments on several nonconvex benchmark problems and the application to train deep neural networks. Copyright © 2025, The Authors. All rights reserved.

关键词： optimization algorithms