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A Lower Bound and a Near-Optimal Algorithm for Bilevel Empirical Risk Minimization

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arXiv 2023年

作者： Dagréou, Mathieu Moreau, Thomas Vaiter, Samuel Ablin, Pierre Université Paris-Saclay Inria CEA Palaiseau France Université de Côte d’Azur CNRS LJAD Nice France Apple Paris France

Bilevel optimization problems, which are problems where two optimization problems are nested, have more and more applications in machine learning. In many practical cases, the upper and the lower objectives correspond to empirical risk minimization problems and therefore have a sum structure. In this context, we propose a bilevel extension of the celebrated SARAH algorithm. We demonstrate that the algorithm requires O((n + m)1/2 Ε−1) oracle calls to achieve Ε-stationarity with n + m the total number of samples, which improves over all previous bilevel algorithms. Moreover, we provide a lower bound on the number of oracle calls required to get an approximate stationary point of the objective function of the bilevel problem. This lower bound is attained by our algorithm, making it optimal in terms of sample complexity. © 2023, CC BY.

关键词： optimization algorithms

Mfwoa: Multifactorial Whale Optimisation Algorithm

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SSRN

SSRN 2024年

作者： Ye, Lei Xiang, Benhua Ding, Hangqi Wu, Yue Gong, Maoguo Test center National University of Defense Technology Xi’an710100 China School of Computer Science and Technology Xidian University Xi’an710071 China School of Electronic Engineering Xidian University Xi’an710071 China Key Laboratory of Collaborative Intelligence Systems Ministry of Education Xi’an710071 China College of Mathematics Science Inner Mongolia Normal University Hohhot010028 China

Multi-task optimisation is a new research topic in the area of evolutionary computing, and it has received extensive attention from researchers since it was proposed. It can exploit the potential synergistic facilitation between tasks to solve multiple optimisation problems simultaneously and efficiently. Whale optimisation algorithm (WOA) is an emerging swarm intelligence algorithm, which has the advantages of rapid convergence and strong global exploration ability. Therefore, this article is the first attempt to use WOA as a search mechanism to implement multi-task optimisation, and proposes the multifactorial whale optimisation algorithm (MFWOA). Among them, the inter-task knowledge transfer strategy which plays a key role is designed in detail. This strategy is implemented in two ways. The first way is to exchange the search experience by adding distance terms from other tasks. Another way is to generate a new random individual or optimal individual through crossover and mutation operators, and then use them to guide position updates. By combining the two ways, it can explore a wider area. In addition, to better balance the useful information transfer between tasks and within tasks, a random mating probability parameter self-adaptive strategy is designed. Finally, we provide an exhaustive analysis of the overall optimisation ability of the proposed algorithm. The experimental findings demonstrate that the algorithm achieves effective and efficient knowledge transfer and can achieve better convergence speed and accuracy, showing that the algorithm is a promising emerging multi-task optimisation algorithm. © 2024, The Authors. All rights reserved.

关键词： optimization algorithms

Submodular Framework for Structured-Sparse Optimal Transport

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arXiv 2024年

作者： Manupriya, Piyushi Jawanpuria, Pratik Gurumoorthy, Karthik S. Jagarlapudi, SakethaNath Mishra, Bamdev Department of Computer Science and Engineering IIT Hyderabad India Microsoft India Walmart Global Tech India

Unbalanced optimal transport (UOT) has recently gained much attention due to its flexible framework for handling un-normalized measures and its robustness properties. In this work, we explore learning (structured) sparse transport plans in the UOT setting, i.e., transport plans have an upper bound on the number of non-sparse entries in each column (structured sparse pattern) or in the whole plan (general sparse pattern). We propose novel sparsity-constrained UOT formulations building on the recently explored maximum mean discrepancy based UOT. We show that the proposed optimization problem is equivalent to the maximization of a weakly submodular function over a uniform matroid or a partition matroid. We develop efficient gradient-based discrete greedy algorithms and provide the corresponding theoretical guarantees. Empirically, we observe that our proposed greedy algorithms select a diverse support set and we illustrate the efficacy of the proposed approach in various applications. © 2024, CC BY.

关键词： optimization algorithms

EIT image regularization by a new Multi-Objective Simulated Annealing Algorithm

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EIT image regularization by a new Multi-Objective Simulated ...

Annual International Conference of the IEEE Engineering in Medicine and Biology Society

作者： Thiago Castro Martins Marcos Sales Guerra Tsuzuki Escola Politécnica da Universidade de S?o Paulo Brazil. Computational Geometry Laboratory

ISBN: (纸本)9781424492695

Multi-Objective optimization can be used to produce regularized Electrical Impedance Tomography (EIT) images where the weight of the regularization term is not known a priori. This paper proposes a novel Multi-Objective optimization algorithm based on Simulated Annealing tailored for EIT image reconstruction. Images are reconstructed from experimental data and compared with images from other Multi and Single Objective optimization methods. A significant performance enhancement from traditional techniques can be inferred from the results.

关键词： EIT regularization term results EIT images optimization algorithms enhancing performance simulated annealing optimization methods

In-situ re-calibration of implanted pressure sensors

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In-situ re-calibration of implanted pressure sensors

IEEE Sensors

作者： Dixon Leung Simon Malpas Daniel McCormick David Budgett Auckland Bioengineering Institute University of Auckland Auckland

ISBN: (纸本)9781509010134

Feasibility of the novel utilization of a pressure switch mechanism for re-calibrating drifted implanted pressure sensors in-situ is demonstrated. We have designed and characterized the pressure response of a system, which can quantify the offset of a sensor after it has been implanted. The benchtop device is constructed of a 25 pm thick titanium diaphragm with 10 mm working diameter. An optimization algorithm detected a characteristic change in the pressure response produced by the activation of a pressure switch. The repeatability of detection across three sensors is within ±0.23 mmHg over 8 pressurization cycles.

关键词： pressure sensor calibration implantable intracranial pressure hydrocephalus long term drift Pressure Sensor Device Component Implants and Prostheses pressure respond Intracranial Pressure Hydrocephalus Calibration Sensors optimization algorithms

Binary sequence design for transmit diversity MIMO radar

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Binary sequence design for transmit diversity MIMO radar

IET International Radar Conference 2015

作者： Haiqing Wang Xiaohua Zhu Jindong Zhang College of Electronic Engineering and Optical Technology Nanjing University of Science and Technology Jiangsu China 210094 College of Electronic and Information Engineering Nanjing University of Aeronautics and Astronautics Jiangsu China 210094

ISBN: (纸本)9781510822023

Orthogonal binary sequences play an important role in Multiple-input multiple-output (MIMO) radar. However, mainly due to mathematical difficulties, the synthesis problem of multiple binary sequences with low auto and cross correlation sidelobes is still an open problem. In this paper, mismatched filter, which basically aims at reducing the sidelobe levels at the pulse compression output, is exploited and multiple binary sequences and mismatched filters are optimized by joint synthesis algorithms (JSA), based on an alternating direction method. JSA for minimizing the integrated sidelobe level (ISL) and peak sidelobe level (PSL) metrics are proposed, and the corresponding computation complexities are analyzed. Simulation results show the effectiveness of our proposed algorithms.

关键词： Binary sequence design MIMO radar optimization algorithm MIMO radar optimization algorithms binary sequences side lobe level JOB SAFETY ANALYSIS sidelobe diversity reception

The Fragility of Optimized Bandit algorithms

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arXiv 2021年

作者： Fan, Lin Glynn, Peter W. Kellogg School of Management Northwestern University EvanstonIL60208 United States Department of Management Science and Engineering Stanford University StanfordCA94305 United States

Much of the literature on optimal design of bandit algorithms is based on minimization of expected regret. It is well known that algorithms that are optimal over certain exponential families can achieve expected regret that grows logarithmically in the number of trials, at a rate specified by the Lai-Robbins lower bound. In this paper, we show that when one uses such optimized algorithms, the resulting regret distribution necessarily has a very heavy tail, specifically, that of a truncated Cauchy distribution. Furthermore, for p > 1, the p’th moment of the regret distribution grows much faster than poly-logarithmically, in particular as a power of the total number of trials. We show that optimized UCB algorithms are also fragile in an additional sense, namely when the problem is even slightly mis-specified, the regret can grow much faster than the conventional theory suggests. Our arguments are based on standard change-of-measure ideas, and indicate that the most likely way that regret becomes larger than expected is when the optimal arm returns below-average rewards in the first few arm plays, thereby causing the algorithm to believe that the arm is sub-optimal. To alleviate the fragility issues exposed, we show that UCB algorithms can be modified so as to ensure a desired degree of robustness to mis-specification. In doing so, we also show a sharp trade-off between the amount of UCB exploration and the heaviness of the resulting regret distribution tail. Copyright © 2021, The Authors. All rights reserved.

关键词： optimization algorithms

Optimized 2-Approximation of Treewidth

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arXiv 2024年

作者： Belbasi, Mahdi Fürer, Martin Kumar, Medha Pennsylvania State University United States

This paper presents a linear FPT algorithm to find a tree decomposition with a 2-approximation of the treewidth with a significantly smaller exponential dependence on the treewidth in the running time than previously ... 详细信息

关键词： optimization algorithms

SIMULATION-BASED, OPTIMIZED SCHEDULING OF LIMITED BAR-BENDERS OVER MULTIPLE BUILDING SITES 08

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SIMULATION-BASED, OPTIMIZED SCHEDULING OF LIMITED BAR-BENDER...

Winter Simulation Conference (WSC 2008)

作者： Hoi-Ching Lam Ming Lu Hong Kong Polytechnic University Hong Kong China

ISBN: (纸本)9781424427086

In the construction industry, a specialist subcontractor manages a taskforce of single-skilled laborers to work on multiple construction sites, aiming to minimize the total cost and stay profitable and competitive. This paper presents a simulation-based approach to assist the subcontractor in scheduling the application of limited laborer resources to handle jobs over multiple concurring sites. Factoring in technological constraints, repetitive building cycles, alternative method options, and the limited quantity of skilled laborers, we resort to computer power (including simulation and optimization algorithms resulting from recent research) in search of the best combination of construction methods at individual sites along with the optimum size of labor force, aimed to find the least cost for completing the jobs at all sites. A case study of bar-bender scheduling over three sites by use of an in-house computer tool results in the optimum method combinations, the optimum crew size, and the optimum resource schedule.

关键词： Construction methods Buildings Labor Force Laborers optimization algorithms Construction Industry Total Costs Optimum multiple construction sites crew size jobs LIMITED QUANTITY