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arXiv 2024年

作者： Volk, Amanda A. Reyes, Kristofer G. Ethier, Jeffrey G. Baldwin, Luke A. National Research Council Research Associate Air Force Research Laboratory Wright-Patterson Air Force Base OH45433 United States Department of Materials Design and Innovation University at Buffalo BuffaloNY14260 United States Materials and Manufacturing Directorate Air Force Research Laboratory Wright-Patterson Air Force Base OH45433 United States

Asynchronous Bayesian optimization is a recently implemented technique that allows for parallel operation of experimental systems and disjointed workflows. Contrasting with serial Bayesian optimization which individually selects experiments one at a time after conducting a measurement for each experiment, asynchronous policies sequentially assign multiple experiments before measurements can be taken and evaluate new measurements continuously as they are made available. This technique allows for faster data generation and therefore faster optimization of an experimental space. This work extends the capabilities of asynchronous optimization methods beyond prior studies by evaluating four additional policies that incorporate pessimistic predictions in the training data set. Combined with a conventional policy that uses model predictions, the five total policies were evaluated in a simulated environment and benchmarked with serial sampling. Under some conditions and parameter space dimensionalities, the pessimistic prediction asynchronous policy reached optimum experimental conditions in significantly fewer experiments than equivalent serial policies and proved to be less susceptible to convergence onto local optima at higher dimensions. Without accounting for the faster sampling rate, the pessimistic asynchronous algorithm presented in this work could result in more efficient algorithm driven optimization of high-cost experimental spaces. Accounting for sampling rate, the presented asynchronous algorithm could allow for faster optimization in experimental spaces where multiple experiments can be run before results are collected. Copyright © 2024, The Authors. All rights reserved.

关键词： optimization algorithms

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Randomized Submanifold Subgradient Method for optimization over Stiefel Manifolds

arXiv

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arXiv 2024年

作者： Cheung, Andy Yat-Ming Wang, Jinxin Yue, Man-Chung So, Anthony Man-Cho Department of Applied Mathematics The Hong Kong Polytechnic University Hong Kong Department of Systems Engineering and Engineering Management The Chinese University of Hong Kong Hong Kong Department of Industrial and Manufacturing Systems Engineering Musketeers Foundation Institute of Data Science The University of Hong Kong Hong Kong

optimization over Stiefel manifolds has found wide applications in many scientific and engineering domains. Despite considerable research effort, high-dimensional optimization problems over Stiefel manifolds remain challenging, and the situation is exacerbated by nonsmooth objective functions. The purpose of this paper is to propose and study a novel coordinate-type algorithm for weakly convex (possibly nonsmooth) optimization problems over high-dimensional Stiefel manifolds, named randomized submanifold subgradient method (RSSM). Similar to coordinate-type algorithms in the Euclidean setting, RSSM exhibits low per-iteration cost and is suitable for high-dimensional problems. We prove that RSSM converges to the set of stationary points and attains Ε-stationary points with respect to a natural stationarity measure in O(Ε−4) iterations in both expectation and the almost-sure senses. To the best of our knowledge, these are the first convergence guarantees for coordinate-type algorithms to optimize nonconvex nonsmooth functions over Stiefel manifolds. An important technical tool in our convergence analysis is a new Riemannian subgradient inequality for weakly convex functions on proximally smooth matrix manifolds, which could be of independent interest. Copyright © 2024, The Authors. All rights reserved.

关键词： optimization algorithms

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Stochastic optimization Schemes for Performative Prediction with Nonconvex Loss

arXiv

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arXiv 2024年

作者： Li, Qiang Wai, Hoi-To Department of Systems Engineering and Engineering Management The Chinese University of Hong Kong Shatin Hong Kong

This paper studies a risk minimization problem with decision dependent data distribution. The problem pertains to the performative prediction setting in which a trained model can affect the outcome estimated by the model. Such dependency creates a feedback loop that influences the stability of optimization algorithms such as stochastic gradient descent (SGD). We present the first study on performative prediction with smooth but possibly non-convex loss. We analyze a greedy deployment scheme with SGD (SGD-GD). Note that in the literature, SGD-GD is often studied with strongly convex loss. We first propose the definition of stationary performative stable (SPS) solutions through relaxing the popular performative stable condition. We then prove that SGD-GD converges to a biased SPS solution in expectation. We consider two conditions of sensitivity on the distribution shifts: (i) the sensitivity is characterized by Wasserstein-1 distance and the loss is Lipschitz w.r.t. data samples, or (ii) the sensitivity is characterized by total variation (TV) divergence and the loss is bounded. In both conditions, the bias levels are proportional to the stochastic gradient’s variance and sensitivity level. Our analysis is extended to a lazy deployment scheme where models are deployed once per several SGD updates, and we show that it converges to an SPS solution with reduced bias. Numerical experiments corroborate our theories. © 2024, CC BY.

关键词： optimization algorithms

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Simple Policy optimization

arXiv

引用

arXiv 2024年

作者： Xie, Zhengpeng Zhang, Qiang Yang, Fan Hutter, Marco Xu, Renjing The Hong Kong University of Science and Technology Guangzhou China ETH Zurich Switzerland

Model-free reinforcement learning algorithms have seen remarkable progress, but key challenges remain. Trust Region Policy optimization (TRPO) is known for ensuring monotonic policy improvement through conservative updates within a trust region, backed by strong theoretical guarantees. However, its reliance on complex second-order optimization limits its practical efficiency. Proximal Policy optimization (PPO) addresses this by simplifying TRPO’s approach using ratio clipping, improving efficiency but sacrificing some theoretical robustness. This raises a natural question: Can we combine the strengths of both methods? In this paper, we introduce Simple Policy optimization (SPO), a novel unconstrained first-order algorithm. By slightly modifying the policy loss used in PPO, SPO can achieve the best of both worlds. Our new objective improves upon ratio clipping, offering stronger theoretical properties and better constraining the probability ratio within the trust region. Empirical results demonstrate that SPO outperforms PPO with a simple implementation, particularly for training large, complex network architectures end-to-end. Copyright © 2024, The Authors. All rights reserved.

关键词： optimization algorithms

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Analyzing the speed of convergence in nonsmooth optimization via the Goldstein subdifferential with application to descent methods

arXiv

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arXiv 2024年

作者： Gebken, Bennet Department of Mathematics Technical University of Munich Boltzmannstr. 3 b. München Garching85748 Germany

The Goldstein Ε-subdifferential is a relaxed version of the Clarke subdifferential which has recently appeared in several algorithms for nonsmooth optimization. With it comes the notion of (Ε, δ)-critical points, which are points in which the element with the smallest norm in the Ε-subdifferential has norm at most δ. To obtain points that are critical in the classical sense, Ε and δ must vanish. In this article, we analyze at which speed the distance of (Ε, δ)-critical points to the minimum vanishes with respect to Ε and δ. Afterwards, we apply our results to gradient sampling methods and perform numerical experiments. Throughout the article, we put a special emphasis on supporting the theoretical results with simple examples that visualize *** Codes 90C30, 90C56, 49J52 Copyright © 2024, The Authors. All rights reserved.

关键词： optimization algorithms

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A Landscape-Aware Differential Evolution for Multimodal optimization Problems

arXiv

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arXiv 2024年

作者： Lin, Guo-Yun Chen, Zong-Gan Liu, Chuanbin Jiang, Yuncheng Kwong, Sam Zhang, Jun Zhan, Zhi-Hui School of Computer Science South China Normal University Guangzhou510631 China The Center for Scientific Research and Development in Higher Education Institutes Ministry of Education China The Department of Computing and Decision Science Lingnan University Hong Kong The College of Artificial Intelligence Nankai University Tianjin300350 China The Hanyang University ERICA 15588 Korea Republic of

How to simultaneously locate multiple global peaks and achieve certain accuracy on the found peaks are two key challenges in solving multimodal optimization problems (MMOPs). In this paper, a landscape-aware differential evolution (LADE) algorithm is proposed for MMOPs, which utilizes landscape knowledge to maintain sufficient diversity and provide efficient search guidance. In detail, the landscape knowledge is efficiently utilized in the following three aspects. First, a landscape-aware peak exploration helps each individual evolve adaptively to locate a peak and simulates the regions of the found peaks according to search history to avoid an individual locating a found peak. Second, a landscape-aware peak distinction distinguishes whether an individual locates a new global peak, a new local peak, or a found peak. Accuracy refinement can thus only be conducted on the global peaks to enhance the search efficiency. Third, a landscape-aware reinitialization specifies the initial position of an individual adaptively according to the distribution of the found peaks, which helps explore more peaks. The experiments are conducted on 20 widely-used benchmark MMOPs. Experimental results show that LADE obtains generally better or competitive performance compared with seven well-performed algorithms proposed recently and four winner algorithms in the IEEE CEC competitions for multimodal optimization. Copyright © 2024, The Authors. All rights reserved.

关键词： optimization algorithms

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Zeroth-order Random Subspace Algorithm for Non-smooth Convex optimization

arXiv

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arXiv 2024年

作者： Nozawa, Ryota Poirion, Pierre-Louis Takeda, Akiko Department of Mathematical Informatics The University of Tokyo Tokyo Japan Center for Advanced Intelligence Project RIKEN Tokyo Japan

Zeroth-order optimization, which does not use derivative information, is one of the significant research areas in the field of mathematical optimization and machine learning. Although various studies have explored zeroth-order algorithms, one of the theoretical limitations is that oracle complexity depends on the dimension, i.e., on the number of variables, of the optimization problem. In this paper, to reduce the dependency of the dimension in oracle complexity, we propose a zeroth-order random subspace algorithm by combining a gradient-free algorithm (specifically, Gaussian randomized smoothing with central differences) with random projection. We derive the worst-case oracle complexity of our proposed method in non-smooth and convex settings;it is equivalent to standard results for full-dimensional non-smooth convex algorithms. Furthermore, we prove that ours also has a local convergence rate independent of the original dimension under additional assumptions. In addition to the theoretical results, numerical experiments show that when an objective function has a specific structure, the proposed method can become experimentally more efficient due to random *** Codes 90C56 (Primary) 49J52, 60B20, 90C06, 90C25 (Secondary) © 2024, CC BY.

关键词： optimization algorithms

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Universal subgradient and proximal bundle methods for convex and strongly convex hybrid composite optimization

arXiv

引用

arXiv 2024年

作者： Guigues, Vincent Liang, Jiaming Monteiro, Renato D.C. School of Applied Mathematics FGV/EMAp Rio de Janeiro22250-900 Brazil Goergen Institute for Data Science Department of Computer Science University of Rochester RochesterNY14620 United States School of Industrial and Systems Engineering Georgia Institute of Technology AtlantaGA30332 United States

This paper develops two parameter-free methods for solving convex and strongly convex hybrid composite optimization problems, namely, a composite subgradient type method and a proximal bundle type method. Both functional and stationary complexity bounds for the two methods are established in terms of the unknown strong convexity parameter. To the best of our knowledge, the two proposed methods are the first universal methods for solving hybrid strongly convex composite optimization problems that do not rely on any restart scheme nor require the knowledge of the optimal value. © 2024, CC BY.

关键词： optimization algorithms

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TOPOLOGY optimization TAKING INTO ACCOUNT GEOMETRICAL CONSTRAINT OF NO-CLOSED HOLE FOR ADDITIVE MANUFACTURING BASED ON FICTITIOUS PHYSICAL MODEL CONCEPT 47

TOPOLOGY OPTIMIZATION TAKING INTO ACCOUNT GEOMETRICAL CONSTR...

引用

ASME International Design Engineering Technical Conferences / 41st Annual Computers and Information in Engineering Conference (IDETC-CIE) / 47th Design Automation Conference (DAC)

作者： Yamada, Takayuki Noguchi, Yuki Univ Tokyo Sch Engn Inst Engn Innovat Dept Strateg Studies Tokyo 1138656 Japan

ISBN: (纸本)9780791885390

This paper proposes a topology optimization method that considers the geometrical constraint of a non-closed hole for additive manufacturing based on the fictitious physical model concept. First, the basic topology optimization concept and level set-based method are introduced. Second, the concept of a fictitious physical model for geometrical constraint in the topology optimization framework is discussed. Then, the model for the geometrical constraint of a non-closed hole for additive manufacturing is proposed. Numerical examples are provided to validate the proposed model. In addition, topology optimization considering this geometrical constraint is formulated, and topology optimization algorithms are constructed using the finite element method. Finally, optimization examples are provided to validate the proposed topology optimization method.

关键词： optimization Topology Additive manufacturing optimization algorithms Finite element methods

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Nonlinear Distributionally Robust optimization

arXiv

引用

arXiv 2023年

作者： Sheriff, Mohammed Rayyan Esfahani, Peyman Mohajerin Delft Center for Systems and Control Delft University of Technology Delft Netherlands

This article focuses on a class of distributionally robust optimization (DRO) problems where, unlike the growing body of the literature, the objective function is potentially nonlinear in the distribution. Existing methods to optimize nonlinear functions in probability space use the Frechet derivatives, which present both theoretical and computational challenges. Motivated by this, we propose an alternative notion for the derivative and corresponding smoothness based on Gateaux (G)-derivative for generic risk measures. These concepts are explained via three running risk measure examples of variance, entropic risk, and risk on finite support sets. We then propose a G-derivative based Frank-Wolfe (FW) algorithm for generic nonlinear optimization problems in probability spaces and establish its convergence under the proposed notion of smoothness in a completely norm-independent manner. We use the set-up of the FW algorithm to devise a methodology to compute a saddle point of the nonlinear DRO problem. Finally, we validate our theoretical results on two cases of the entropic and variance risk measures in the context of portfolio selection problems. In particular, we analyze their regularity conditions and "sufficient statistic", compute the respective FW-oracle in various settings, and confirm the theoretical outcomes through numerical validation. © 2023, CC BY.

关键词： optimization algorithms

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