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Parallelization of Gillespie algorithm based on binary words

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arXiv 2024年

作者： Lacoste, David Castellana, Michele Institut Curie PSL Research University CNRS UMR168 11 rue Pierre et Marie Curie Paris 75005 France Gulliver Laboratory UMR CNRS 7083 PSL Research University ESPCI 10 Rue Vauquelin Paris F-75231 France

We present an improvement of the Gillespie Exact Stochastic Simulation Algorithm, which leverages a bitwise representation of variables to perform independent simulations in parallel. We show that the subsequent gain in computational yield is significant, and it may allow to perform simulations of non-well mixed chemical systems. We illustrate this idea with simulations of Frank model, originally introduced to explain the emergence of homochirality in prebiotic systems. © 2024, CC BY.

关键词： optimization algorithms

Anderson Acceleration in Nonsmooth Problems: Local Convergence via Active Manifold Identification

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arXiv 2024年

作者： Li, Kexin Bai, Luwei Wang, Xiao Wang, Hao School of Information Science and Technology ShanghaiTech University Shanghai China Department of AI Computing Peng Cheng Laboratory Shenzhen China

Anderson acceleration is an effective technique for enhancing the efficiency of fixed-point iterations;however, analyzing its convergence in nonsmooth settings presents significant challenges. In this paper, we investigate a class of nonsmooth optimization algorithms characterized by the active manifold identification property. This class includes a diverse array of methods such as the proximal point method, proximal gradient method, proximal linear method, proximal coordinate descent method, Douglas-Rachford splitting (or the alternating direction method of multipliers), and the iteratively reweighted 1 method, among others. Under the assumption that the optimization problem possesses an active manifold at a stationary point, we establish a local R-linear convergence rate for the Anderson-accelerated algorithm. Our extensive numerical experiments further highlight the robust performance of the proposed Anderson-accelerated methods. Copyright © 2024, The Authors. All rights reserved.

关键词： optimization algorithms

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

Black-Box Uniform Stability for Non-Euclidean Empirical Risk Minimization

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arXiv 2024年

作者： Vary, Simon Martínez-Rubio, David Rebeschini, Patrick Department of Statistics University of Oxford United Kingdom Signal Theory and Communications Department Carlos III University of Madrid Spain

We study first-order algorithms that are uniformly stable for empirical risk minimization (ERM) problems that are convex and smooth with respect to p-norms, p ≥ 1. We propose a black-box reduction method that, by employing properties of uniformly convex regularizers, turns an optimization algorithm for Hölder smooth convex losses into a uniformly stable learning algorithm with optimal statistical risk bounds on the excess risk, up to a constant factor depending on p. Achieving a black-box reduction for uniform stability was posed as an open question by Attia and Koren [AK22], which had solved the Euclidean case p = 2. We explore applications that leverage non-Euclidean geometry in addressing binary classification *** Codes 68Q32, 90C25 © 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

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