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Causal Bayesian optimization with Unknown Graphs

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arXiv 2025年

作者： Durand, Jean Annadani, Yashas Bauer, Stefan Parbhoo, Sonali Imperial College London United Kingdom Germany

Causal Bayesian optimization (CBO) is a methodology designed to optimize an outcome variable by leveraging known causal relationships through targeted interventions. Traditional CBO methods require a fully and accurately specified causal graph, which is a limitation in many real-world scenarios where such graphs are unknown. To address this, we propose a new method for the CBO framework that operates without prior knowledge of the causal graph. Consistent with causal bandit theory, we demonstrate through theoretical analysis and that focusing on the direct causal parents of the target variable is sufficient for optimization, and provide empirical validation in the context of CBO. Furthermore we introduce a new method that learns a Bayesian posterior over the direct parents of the target variable. This allows us to optimize the outcome variable while simultaneously learning the causal structure. Our contributions include a derivation of the closed-form posterior distribution for the linear case. In the nonlinear case where the posterior is not tractable, we present a Gaussian Process (GP) approximation that still enables CBO by inferring the parents of the outcome variable. The proposed method performs competitively with existing benchmarks and scales well to larger graphs, making it a practical tool for real-world applications where causal information is incomplete. © 2025, CC BY-SA.

关键词： optimization algorithms

An exponentially stable discrete-time primal-dual algorithm for distributed constrained optimization

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arXiv 2025年

作者： Ren, Xiaoxing Bin, Michelangelo Notarnicola, Ivano Parisini, Thomas Department of Electrical and Electronic Engineering Imperial College London London United Kingdom Department of Electrical Electronic and Information Engineering University of Bologna Italy Department of Electronic Systems Aalborg University Denmark Department of Engineering and Architecture University of Trieste Trieste Italy

This paper studies a distributed algorithm for constrained consensus optimization that is obtained by fusing the Arrow-Hurwicz-Uzawa primal-dual gradient method for centralized constrained optimization and the Wang-Elia method for distributed unconstrained optimization. It is shown that the optimal primal-dual point is a semiglobally exponentially stable equilibrium for the algorithm, which implies linear convergence. The analysis is based on the separation between a slow centralized optimization dynamics describing the evolution of the average estimate toward the optimum, and a fast dynamics describing the evolution of the consensus error over the network. These two dynamics are mutually coupled, and the stability analysis builds on control theoretic tools such as time-scale separation, Lyapunov theory, and the small-gain principle. Our analysis approach highlights that the consensus dynamics can be seen as a fast, parasite one, and that stability of the distributed algorithm is obtained as a robustness consequence of the semiglobal exponential stability properties of the centralized method. This perspective can be used to enable other significant extensions, such as time-varying networks or delayed communication, that can be seen as "perturbations" of the centralized *** Codes 65K05, 93A14, 93A16, 90C25, 90C30, 90C35, 93D05, 93D23 © 2025, CC BY-NC-ND.

关键词： optimization algorithms

Application of Quantum Approximate optimization Algorithm in Solving the Total Domination Problem

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arXiv 2024年

作者： Pan, Haoqian Wang, Shiyue Lu, Changhong Shanghai Key Laboratory of PMMP East China Normal University Shanghai200241 China

Recent advancements in quantum computing have led to significant research into applying quantum algorithms to combinatorial optimization problems. Among these challenges, the Total Domination Problem (TDP) is particularly noteworthy, representing a classic and critical example in the field. Since the last century, research efforts have focused on establishing its NP-completeness and developing algorithms for its resolution, which have been fundamental to combinatorial mathematics. Despite this rich history, the application of quantum algorithms to the TDP remains largely unexplored. In this study, we present a pioneering application of the Quantum Approximate optimization Algorithm (QAOA) to tackle the TDP, evaluating its efficacy across a diverse array of parameters. Our experimental findings indicate that QAOA is effective in addressing the TDP;under most parameter combinations, it successfully computes the correct total dominating set (TDS). However, the algorithm’s performance in identifying the optimal TDS is contingent upon the specific parameter choices, revealing a significant bias in the distribution of effective parameter points. This research contributes valuable insights into the potential of quantum algorithms for addressing the TDP and lays the groundwork for future investigations in this area. Copyright © 2024, The Authors. All rights reserved.

关键词： optimization algorithms

Alternating direction method of multipliers for polynomial optimization

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arXiv 2025年

作者： Cerone, V. Fosson, S.M. Pirrera, S. Regruto, D. Dipartimento di Automatica e Informatica Politecnico di Torino corso Duca degli Abruzzi 24 Torino10129 Italy

Multivariate polynomial optimization is a prevalent model for a number of engineering problems. From a mathematical viewpoint, polynomial optimization is challenging because it is non-convex. The Lasserre’s theory, based on semidefinite relaxations, provides an effective tool to overcome this issue and to achieve the global optimum. However, this approach can be computationally complex for medium and large scale problems. For this motivation, in this work, we investigate a local minimization approach, based on the alternating direction method of multipliers, which is low-complex, straightforward to implement, and prone to decentralization. The core of the work is the development of the algorithm tailored to polynomial optimization, along with the proof of its convergence. Through a numerical example we show a practical implementation and test the effectiveness of the proposed algorithm with respect to state-of-the-art methodologies. © 2025, CC BY-NC-ND.

关键词： optimization algorithms

An overview of the operation architectures and energy management system for multiple microgrid clusters

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iEnergy 2022年第3期1卷 306-314页

作者： Yajuan Guan Baoze Wei Josep M.Guerrero Juan C.Vasquez Yonghao Gui Center for Research on Microgrids(CROM) AAU EnergyAalborg University9220 AalborgDenmark The Electrification and Energy Infras-tructures Division Oak Ridge National LaboratoryUnited States

The emerging novel energy infrastructures,such as energy communities,smart building-based microgrids,electric vehicles enabled mobile energy storage units raise the requirements for a more interconnective and interoperable energy *** leads to a transition from simple and isolated microgrids to relatively large-scale and complex interconnected microgrid systems named multi-microgrid *** order to efficiently,optimally,and flexibly control multi-microgrid clusters,cross-disciplinary technologies such as power electronics,control theory,optimization algorithms,information and communication technologies,cyber-physical,and big-data analysis are *** paper introduces an overview of the relevant aspects for multi-microgrids,including the out-standing features,architectures,typical applications,existing control mechanisms,as well as the challenges.

关键词： Renewable energy resource multi-microgrid cluster power electronics control theory optimization algorithms information and communication technologies big-data analysis.

Super Gradient Descent: Global optimization requires Global Gradient

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arXiv 2024年

作者： Achour, Seifeddine

Global minimization is a fundamental challenge in optimization, especially in machine learning, where finding the global minimum of a function directly impacts model performance and convergence. This article introduces a novel optimization method that we called Super Gradient Descent, designed specifically for one-dimensional functions, guaranteeing convergence to the global minimum for any k-Lipschitz function defined on a closed interval [a, b]. Our approach addresses the limitations of traditional optimization algorithms, which often get trapped in local minima. In particular, we introduce the concept of global gradient which offers a robust solution for precise and well-guided global optimization. By focusing on the global minimization problem, this work bridges a critical gap in optimization theory, offering new insights and practical advancements in different optimization problems in particular Machine Learning problems like line search. © 2024, CC BY-NC-ND.

关键词： optimization algorithms

Structured Preconditioners in Adaptive optimization: A Unified Analysis

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arXiv 2025年

作者： Xie, Shuo Wang, Tianhao Reddi, Sashank Kumar, Sanjiv Li, Zhiyuan Toyota Technological Institute Chicago United States Google Research United States

We present a novel unified analysis for a broad class of adaptive optimization algorithms with structured (e.g., layerwise, diagonal, and kronecker-factored) preconditioners for both online regret minimization and offline convex optimization. Our analysis not only provides matching rate to several important structured preconditioned algorithms including diagonal AdaGrad, full-matrix AdaGrad, and AdaGrad-Norm, but also gives an improved convergence rate for a one-sided variant of Shampoo over that of original Shampoo. Interestingly, more structured preconditioners (e.g., diagonal Adagrad, AdaGrad-Norm which use less space and compute) are often presented as computationally efficient approximations to full-matrix Adagrad, aiming for improved optimization performance through better approximations. Our unified analysis challenges this prevailing view and reveals, perhaps surprisingly, that more structured preconditioners, despite using less space and computation per step, can outperform their less structured counterparts. To demonstrate this, we show that one-sided Shampoo, which is relatively much cheaper than full-matrix AdaGrad could outperform it both theoretically and experimentally. © 2025, CC BY.

关键词： optimization algorithms

FEATURE-BASED EVOLUTIONARY DIVERSITY optimization OF DISCRIMINATING INSTANCES FOR CHANCE-CONSTRAINED optimization PROBLEMS

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arXiv 2025年

作者： Ahouei, Saba Sadeghi Antipov, Denis Neumann, Aneta Neumann, Frank Optimisation and Logistics School of Computer and Mathematical Sciences The University of Adelaide Adelaide Australia LIP6 Sorbonne University Paris France

Algorithm selection is crucial in the field of optimization, as no single algorithm performs perfectly across all types of optimization problems. Finding the best algorithm among a given set of algorithms for a given problem requires a detailed analysis of the problem’s features. To do so, it is important to have a diverse set of benchmarking instances highlighting the difference in algorithms’ performance. In this paper, we evolve diverse benchmarking instances for chance-constrained optimization problems that contain stochastic components characterized by their expected values and variances. These instances clearly differentiate the performance of two given algorithms, meaning they are easy to solve by one algorithm and hard to solve by the other. We introduce a (µ+1) EA for feature-based diversity optimization to evolve such differentiating instances. We study the chance-constrained maximum coverage problem with stochastic weights on the vertices as an example of chance-constrained optimization problems. The experimental results demonstrate that our method successfully generates diverse instances based on different features while effectively distinguishing the performance between a pair of algorithms. Copyright © 2025, The Authors. All rights reserved.

关键词： optimization algorithms

Concentration Inequalities for the Stochastic optimization of Unbounded Objectives with Application to Denoising Score Matching

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arXiv 2025年

作者： Birrell, Jeremiah Department of Mathematics Texas State University San MarcosTX78666 United States

We derive novel concentration inequalities that bound the statistical error for a large class of stochastic optimization problems, focusing on the case of unbounded objective functions. Our derivations utilize the following tools: 1) A new form of McDiarmid’s inequality that is based on sample-dependent one-component-difference bounds and which leads to a novel uniform law of large numbers result for unbounded functions. 2) A Rademacher complexity bound for families of functions that satisfy an appropriate local-Lipschitz property. As an application of these results, we derive statistical error bounds for denoising score matching (DSM), an application that inherently requires one to consider unbounded objective functions, even when the data distribution has bounded support. In addition, our results establish the benefit of sample-reuse in algorithms that employ easily-sampled auxiliary random variables in addition to the training data, e.g., as in DSM, which uses auxiliary Gaussian random variables. Copyright © 2025, The Authors. All rights reserved.

关键词： optimization algorithms