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Explicit Convergence Rate of The Proximal Point Algorithm under R-Continuity

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arXiv 2024年

作者： Le, Ba Khiet Théra, Michel Optimization Research Group Faculty of Mathematics and Statistics Ton Duc Thang University Ho Chi Minh City Viet Nam Mathematics and Computer Science Department University of Limoges 123 Avenue Albert Thomas Limoges87060 CEDEX France School of Engineering IT and Physical Sciences Federation University BallaratVIC3350 Australia

The paper provides a thorough comparison between R-continuity and other fundamental tools in optimization such as metric regularity, metric subregularity and calmness. We show that R-continuity has some advantages in the convergence rate analysis of algorithms solving optimization problems. We also present some properties of R-continuity and study the explicit convergence rate of the Proximal Point Algorithm (PPA) under the R-continuity. © 2024, CC BY.

关键词： optimization algorithms

A Review of Energy Management Strategies for Range Extended Electric Vehicles

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A Review of Energy Management Strategies for Range Extended ...

第三十一届中国汽车工程学会年会暨展览会（SAECCE 2024）

作者： Li Qian Zhang Caizhi Zhang Jintai Liu Bin College of Mechanical and Vehicle Engineering State Key Laboratory of Mechanical Transmissions for Advanced EquipmentChongqing Automotive Collaborative Innovation CenterChongqing University Powertrain Development Division Chongqing Changan Automobile Co.Ltd

With the increasing global attention to sustainable development and environmental protection,electric vehicles have gradually gained widespread attention as a clean and low-carbon transportation ***,limited range remains one of the main obstacles to the promotion and widespread adoption of electric *** address this issue,range extended electric vehicles(REEVs) have *** extend the vehicle's range by incorporating a range-extending system composed of an engine and a generator outside the battery *** management strategies play a crucial role in achieving efficient energy utilization for *** paper aims to review the research progress of energy management strategies for REEVs,including traditional energy management strategies,optimization algorithms,and hybrid energy management *** comprehensive analysis and summary of relevant literature,the future development directions and challenges in the research of energy management strategies for REEVs are proposed.

关键词： range extender electric vehicle energy management strategies optimization algorithms

An angle rounding parameter initialization technique for ma-QAOA

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arXiv 2024年

作者： Wilkie, Anthony Ostrowski, James Herrman, Rebekah Industrial and Systems Engineering University of Tennessee at Knoxville KnoxvilleTN United States

The multi-angle quantum approximate optimization algorithm (ma-QAOA) is a recently introduced algorithm that gives at least the same approximation ratio as the quantum approximate optimization algorithm (QAOA) and, in most cases, gives a significantly higher approximation ratio than QAOA. One drawback to ma-QAOA is that it uses significantly more classical parameters than QAOA, so the classical optimization component more complex. In this paper, we motivate a new parameter initialization strategy in which angles are initially randomly set to multiples of π/8 between -π and π and this vector is used to seed one round of BFGS. We find that this parameter initialization strategy gives average approximation ratios of 0.900, 0.982, and 0.997 for p = 1, 2, 3 layers of ma-QAOA. This is comparable to the average approximation ratios of ma-QAOA where the optimal parameters are found using BFGS with 1 random starting seed, which are 0.900, 0.982, and 0.996. We also test another parameter initialization strategy in which angles corresponding to maximal degree vertices in the graph are set to 0 while all other are randomly initialized to random multiples of π/8. Using this strategy, the average approximation ratios are 0.897, 0.984, and 0.997. © 2024, CC BY.

关键词： optimization algorithms

NON-MYOPIC MULTIFIDELITY BAYESIAN optimization

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arXiv 2022年

作者： Di Fiore, Francesco Mainini, Laura Politecnico di Torino Italy Massachusetts Institute of Technology Politecnico di Torino United States

Bayesian optimization is a popular framework for the optimization of black box functions. Multifidelity methods allows to accelerate Bayesian optimization by exploiting low-fidelity representations of expensive objective functions. Popular multifidelity Bayesian strategies rely on sampling policies that account for the immediate reward obtained evaluating the objective function at a specific input, precluding greater informative gains that might be obtained looking ahead more steps. This paper proposes a non-myopic multifidelity Bayesian framework to grasp the long-term reward from future steps of the optimization. Our computational strategy comes with a two-step lookahead multifidelity acquisition function that maximizes the cumulative reward obtained measuring the improvement in the solution over two steps ahead. We demonstrate that the proposed algorithm outperforms a standard multifidelity Bayesian framework on popular benchmark optimization problems. Copyright © 2022, The Authors. All rights reserved.

关键词： optimization algorithms

Investigating layer-selective transfer learning of QAOA parameters for Max-Cut problem

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arXiv 2024年

作者： Venturelli, Francesco Aldo Das, Sreetama Caruso, Filippo Department of Engineering University Pompeu Fabra Tànger 122-140 Barcelona08018 Spain Sesto FiorentinoI-50019 Italy Department of Physics and Astronomy University of Florence Via Sansone 1 Sesto FiorentinoI-50019 Italy University of Florence Via Nello Carrara 1 Sesto FiorentinoI-50019 Italy

Quantum approximate optimization algorithm (QAOA) is a variational quantum algorithm (VQA) ideal for noisy intermediate-scale quantum (NISQ) processors, and is highly successful for solving combinatorial optimization problems (COPs). It has been observed that the optimal variational parameters obtained from one instance of a COP can be transferred to another instance, producing sufficiently satisfactory solutions for the latter. In this context, a suitable method for further improving the solution is to fine-tune a subset of the transferred parameters. We numerically explore the role of optimizing individual QAOA layers in improving the approximate solution of the Max-Cut problem after parameter transfer. We also investigate the trade-off between a good approximation and the required optimization time when optimizing transferred QAOA parameters. These studies show that optimizing a subset of layers can be more effective at a lower time-cost compared to optimizing all layers. © 2024, CC BY.

关键词： optimization algorithms

Centralized Selection with Preferences in the Presence of Biases

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arXiv 2024年

作者： Celis, L. Elisa Kumar, Amit Vishnoi, Nisheeth K. Xu, Andrew Yale University United States IIT Delhi India

This paper considers the scenario in which there are multiple institutions, each with a limited capacity for candidates, and candidates, each with preferences over the institutions. A central entity evaluates the utility of each candidate to the institutions, and the goal is to select candidates for each institution in a way that maximizes utility while also considering the candidates’ preferences. The paper focuses on the setting in which candidates are divided into multiple groups and the observed utilities of candidates in some groups are biased–systematically lower than their true utilities. The first result is that, in these biased settings, prior algorithms can lead to selections with sub-optimal true utility and significant discrepancies in the fraction of candidates from each group that get their preferred choices. Subsequently, an algorithm is presented along with proof that it produces selections that achieve near-optimal group fairness with respect to preferences while also nearly maximizing the true utility under distributional assumptions. Further, extensive empirical validation of these results in real-world and synthetic settings, in which the distributional assumptions may not hold, are presented. © 2024, CC BY.

关键词： optimization algorithms

Evolutionary Algorithm with Detection Region Method for Constrained Multi-Objective Problems with Binary Constraints

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arXiv 2024年

作者： Huang, Weixiong Wang, Rui Zhang, Tao Qi, Sheng Wang, Ling College of Systems Engineering National University of Defense Technology Changsha410073 China Xiangjiang Laboratory Changsha410205 China Department of Automation Tsinghua University Beijing100084 China

Solving constrained multi-objective optimization problems (CMOPs) is a challenging task. While many practical algorithms have been developed to tackle CMOPs, real-world scenarios often present cases where the constraint functions are unknown or unquantifiable, resulting in only binary outcomes (feasible or infeasible). This limitation reduces the effectiveness of constraint violation guidance, which can negatively impact the performance of existing algorithms that rely on this approach. Such challenges are particularly detrimental for algorithms employing the ϵ-based method, as they hinder effective relaxation of the feasible region. To address these challenges, this paper proposes a novel algorithm called DRMCMO based on the detection region method. In DRMCMO, detection regions dynamic monitor feasible solutions to enhance convergence, helping the population escape local optima. Additionally, these regions collaborate with the neighbor pairing strategy to improve population diversity within narrow feasible areas. We have modified three existing test suites to serve as benchmark test problems for CMOPs with binary constraints(CMOP/BC) and conducted comprehensive comparative experiments with state-ofthe- art algorithms on these test suites and real-world problems. The results demonstrate the strong competitiveness of DRMCMO against state-of-the-art algorithms. Given the limited research on CMOP/BC, our study offers a new perspective for advancing this field. Impact Statement-CMOPs are common in real-world optimization scenarios, with those involving binary constraints presenting significant challenges for existing algorithms. This work introduces DRMCMO, a novel algorithm designed to address CMOPs with binary constraints. The detection region method empowers traditional algorithms to solve these challenges effectively, and its high portability indicates that it may serve as a valuable tool for optimization researchers and practitioners in the future. Comprehensive ex

关键词： optimization algorithms

Approximating Metric Magnitude of Point Sets

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arXiv 2024年

作者： Andreeva, Rayna Ward, James Skraba, Primoz Gao, Jie Sarkar, Rik School of Informatics University of Edinburgh United Kingdom Queen Mary University of London United Kingdom Rutgers University United States

Metric magnitude is a measure of the "size" of point clouds with many desirable geometric properties. It has been adapted to various mathematical contexts and recent work suggests that it can enhance machine learning and optimization algorithms. But its usability is limited due to the computational cost when the dataset is large or when the computation must be carried out repeatedly (e.g. in model training). In this paper, we study the magnitude computation problem, and show efficient ways of approximating it. We show that it can be cast as a convex optimization problem, but not as a submodular optimization. The paper describes two new algorithms - an iterative approximation algorithm that converges fast and is accurate, and a subset selection method that makes the computation even faster. It has been previously proposed that magnitude of model sequences generated during stochastic gradient descent is correlated to generalization gap. Extension of this result using our more scalable algorithms shows that longer sequences in fact bear higher correlations. We also describe new applications of magnitude in machine learning - as an effective regularizer for neural network training, and as a novel clustering criterion. Copyright © 2024, The Authors. All rights reserved.

关键词： optimization algorithms

GD doesn’t make the cut: Three ways that non-differentiability affects neural network training

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arXiv 2024年

作者： Kumar, Siddharth Krishna Upwork inc. San Francisco United States

This paper critically examines the fundamental distinctions between gradient methods applied to non-differentiable functions (NGDMs) and classical gradient descents (GDs) for differentiable functions, revealing significant gaps in current deep learning optimization theory. We demonstrate that NGDMs exhibit markedly different convergence properties compared to GDs, strongly challenging the applicability of extensive neural network convergence literature based on L − smoothness to non-smooth neural networks. Our analysis reveals paradoxical behavior of NDGM solutions for L1-regularized problems, where increasing regularization counterintuitively leads to larger L1 norms of optimal solutions. This finding calls into question widely adopted L1 penalization techniques for network pruning. We further challenge the common assumption that optimization algorithms like RMSProp behave similarly in differentiable and non-differentiable contexts. Expanding on the Edge of Stability phenomenon, we demonstrate its occurrence in a broader class of functions, including Lipschitz continuous convex differentiable functions. This finding raises important questions about its relevance and interpretation in non-convex, nondifferentiable neural networks, particularly those using ReLU activations. Our work identifies critical misunderstandings of NDGMs in influential literature, stemming from an overreliance on strong smoothness assumptions. These findings necessitate a reevaluation of optimization dynamics in deep learning, emphasizing the crucial need for more nuanced theoretical foundations in analyzing these complex systems. © 2024, CC BY.

关键词： optimization algorithms