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The Multiplicative Weights Update Method: a Meta-Algorithm and Applications

Sanjeev Arora, Elad Hazan, Satyen Kale
2012 Theory of Computing  
Algorithms in varied fields use the idea of maintaining a distribution over a certain set and use the multiplicative update rule to iteratively change these weights.  ...  We feel that since this meta-algorithm and its analysis are so simple, and its applications so broad, it should be a standard part of algorithms courses, like "divide and conquer."  ...  In addition, since a preprint of this paper was available on the Internet for several years prior to publication, a number of people have read it and suggested improvements; we cannot list them all but  ... 
doi:10.4086/toc.2012.v008a006 dblp:journals/toc/AroraHK12 fatcat:hbikmeaflraqhgxl2pectrb2bq

Deterministic Discrepancy Minimization via the Multiplicative Weight Update Method [article]

Avi Levy, Harishchandra Ramadas, Thomas Rothvoss
2017 arXiv   pre-print
We propose an elegant deterministic polynomial time algorithm that is inspired by Lovett-Meka as well as the Multiplicative Weight Update method.  ...  The algorithm iteratively updates a fractional coloring while controlling the exponential weights that are assigned to the set constraints.  ...  The multiplicative weight update method is a meta-algorithm that originated in game theory but has found numerous recent applications in theoretical computer science and machine learning.  ... 
arXiv:1611.08752v3 fatcat:bwgjbh5lhffnhlw4vcyyi5fuxa

The multiplicative weights update algorithm for mixed integer nonlinear programming: theory, applications, and limitations

Luca Mencarelli
2018 4OR  
IV Conclusions 89 91 Appendix 93 95 97 A C R O N Y M S BB Branch-and-Bound BC Branch-and-Cut DGP Distance Geometry Problem HUC Hydro Unit Commitment KKT Karush-Kuhn-Tucker LMI Linear Matrix Inequality  ...  This PhD thesis has been realized with the L A T E X distribution on Mac OS X using the ClassicThesis style by André Miede, inspired by the book "The Elements of Typographic Style" [34] by Robert Bringhurst  ...  The Multiplicative Weights Update (MWU) algorithm is a "meta-algorithm", i.e., it could be adapted to many different settings, with a broad application in Optimization, Machine Learning, and Game Theory  ... 
doi:10.1007/s10288-018-0372-8 fatcat:6lgddfgrmbc6far2avo5x66a5e

On Multiplicative Weight Updates for Concave and Submodular Function Maximization

Chandra Chekuri, T.S. Jayram, Jan Vondrak
2015 Proceedings of the 2015 Conference on Innovations in Theoretical Computer Science - ITCS '15  
We develop a continuous-time framework based on multiplicative weight updates to approximately solve continuous optimization problems.  ...  The framework allows for a simple and modular analysis for a variety of problems involving convex constraints and concave or submodular objective functions.  ...  Acknowledgments: We thank Ken Clarkson and Neal Young for several helpful discussions. References  ... 
doi:10.1145/2688073.2688086 dblp:conf/innovations/ChekuriJV15 fatcat:qh5rdgdmtnbu7c6ataszrho3eq

A Comparative Study on Meta Heuristic Algorithms for Solving Multilevel Lot-Sizing Problems [chapter]

Ikou Kaku, Yiyong Xiao, Yi H
2013 Recent Advances on Meta-Heuristics and Their Application to Real Scenarios  
Acknowledgements This work is supported by the Japan Society for the Promotion of Science JSPS under the grant No. .  ...  Author details Ikou Kaku * , Yiyong Xiao and Yi Han *"ddress all correspondence to kakuikou@tcu.ac.jp Department of Environmental and Information studies, Tokyo City University, Japan School of Reliability  ...  There may other different meta-heuristic algorithms have been proposed for solving the MLLS problems, but it can be considered that the algorithms updated above can cover almost fields of the meta-heuristic  ... 
doi:10.5772/55279 fatcat:ygnc2mn5enbopi5lj6kb2edek4

A Comparative Study of Meta-heuristic Algorithms for Solving Quadratic Assignment Problem

Gamal Abd, Abeer M., El-Sayed M.
2014 International Journal of Advanced Computer Science and Applications  
This paper presents a comparative study between Meta-heuristic algorithms: Genetic Algorithm, Tabu Search, and Simulated annealing for solving a real-life (QAP) and analyze their performance in terms of  ...  The results show that Genetic Algorithm has a better solution quality while Tabu Search has a faster execution time in comparison with other Meta-heuristic algorithms for solving QAP.  ...  There are multiple methods used to solve optimization problems of both the mathematical and combinatorial types.  ... 
doi:10.14569/ijacsa.2014.050101 fatcat:mmsh5mv2crde3i6a3e25nvahlu

Meta-Learning with Graph Neural Networks: Methods and Applications [article]

Debmalya Mandal, Sourav Medya, Brian Uzzi, Charu Aggarwal
2021 arXiv   pre-print
We categorize the literature based on proposed architectures, shared representations, and applications. Finally, we discuss several exciting future research directions and open problems.  ...  Meta-learning has been an important framework to address the lack of samples in machine learning, and in recent years, researchers have started to apply meta-learning to GNNs.  ...  We have also provided a thorough review, summary of methods, and applications in these categories.  ... 
arXiv:2103.00137v3 fatcat:odsdbw34hjazxg43slwvfz7nki

AttrHIN: Network Representation Learning Method for Heterogeneous Information Network

Qingbiao Zhou, Chen Wang, Qi Li
2021 IEEE Access  
not pay enough attention to the weight information of the meta path.  ...  In this paper, we propose a novel heterogeneous network embedding method, called AttrHIN, which adopts weighted metapath-based random walks strategy, and can make full use of the attribute information  ...  (2) We design a weighted meta-path-based random walk method to generate node sequences and an attributed heterogeneous Skip-Gram model to embed the nodes.  ... 
doi:10.1109/access.2021.3110200 fatcat:tcjfy4kwebad7g6w25v53yi66i

Federated Learning: A Distributed Shared Machine Learning Method

Kai Hu, Yaogen Li, Min Xia, Jiasheng Wu, Meixia Lu, Shuai Zhang, Liguo Weng, Siew Ann Cheong
2021 Complexity  
On the basis of classical FL algorithms, several federated machine learning algorithms are briefly introduced, with emphasis on deep learning and classification and comparisons of those algorithms are  ...  In FL, multiple clients collaborate to solve traditional distributed ML problems under the coordination of the central server without sharing their local private data with others.  ...  Acknowledgments is research was supported by the National Natural Science Foundation of China (42075130, 61773219, and 61701244) and the Key Special Project of the National Key R&D Program (2018YFC1405703  ... 
doi:10.1155/2021/8261663 fatcat:ahr2rpg2indqzg4h3zzda3co5a

Dynamic Task Weighting Methods for Multi-task Networks in Autonomous Driving Systems [article]

Isabelle Leang, Ganesh Sistu, Fabian Burger, Andrei Bursuc, Senthil Yogamani
2020 arXiv   pre-print
Our method outperforms state-of-the-art methods by a significant margin on a two-task application.  ...  We then propose a novel method combining evolutionary meta-learning and task-based selective backpropagation, for computing task weights leading to reliable network training.  ...  In this work we benchmark multiple task-weighting methods for a better view on the progress so far.  ... 
arXiv:2001.02223v2 fatcat:5q3uqbbwkbhz7cxzssfel74z64

Abc-based stacking method for multi-label classification

2019 Turkish Journal of Electrical Engineering and Computer Sciences  
The artificial bee colony algorithm, along with a single-layer artificial neural network, is used to find suitable meta-level classifier configurations.  ...  Ensemble methods are effective in managing multilabel classification problems by creating a set of accurate, diverse classifiers and then combining their outputs to produce classifications.  ...  When applying a stacking method we need to consider two problems: 1) selection of multiple accurate and diverse base-level classifiers, and 2) construction of a suitable meta-classifier [17] .  ... 
doi:10.3906/elk-1902-188 fatcat:57qgcishqbcqjnggd5btr7qfvq

An Appraisal of Incremental Learning Methods

Yong Luo, Liancheng Yin, Wenchao Bai, Keming Mao
2020 Entropy  
This review aims to draw a systematic review of the state of the art of incremental learning methods.  ...  Each paper is reviewed according to the types: architectural strategy, regularization strategy and rehearsal and pseudo-rehearsal strategy. We compare and discuss different methods.  ...  Meta-learning Meta-learning aims at mastering the ability to learn so that an agent can master many tasks. Multi-task learning Learn multiple related but different tasks at the same time.  ... 
doi:10.3390/e22111190 pmid:33286958 pmcid:PMC7712976 fatcat:5oyebvrcczdkrohfnk4ygmuwdi

Penalty Method for Inversion-Free Deep Bilevel Optimization [article]

Akshay Mehra, Jihun Hamm
2021 arXiv   pre-print
Solving a bilevel optimization problem is at the core of several machine learning problems such as hyperparameter tuning, data denoising, meta- and few-shot learning, and training-data poisoning.  ...  In this work, we propose a novel algorithm for solving bilevel optimization problems based on the classical penalty function approach.  ...  We thank the anonymous reviewers for their insightful comments and suggestions. This work was supported by the NSF EPSCoR-Louisiana Materials Design Alliance (LAMDA) program #OIA-1946231.  ... 
arXiv:1911.03432v6 fatcat:uk2xs37pmnhy3kwav2pxlvp5oi

GeoAI: A Model-Agnostic Meta-Ensemble Zero-Shot Learning Method for Hyperspectral Image Analysis and Classification

Konstantinos Demertzis, Lazaros Iliadis
2020 Algorithms  
This research exploits the MAML++ algorithm in order to introduce the Model-Agnostic Meta-Ensemble Zero-shot Learning (MAME-ZsL) approach.  ...  Moreover, it leverages the use of first and second-order derivatives as pre-training methods.  ...  Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/a13030061 fatcat:7bhjezzzznbd5ab4q6dismvkfe

Model-Agnostic Meta-Learning using Runge-Kutta Methods [article]

Daniel Jiwoong Im, Yibo Jiang, Nakul Verma
2019 arXiv   pre-print
By leveraging this refined control, we demonstrate that there are multiple principled ways to update MAML and show that the classic MAML optimization is simply a special case of second-order Runge-Kutta  ...  This method enables us to gain fine-grained control over the optimization and helps us achieve both the adaptation and representation goals across tasks.  ...  Moreover, a setting of q 21 = 1 2 corresponds to a learning rate of innerupdate (i.e. α in Algorithm 1) to be 1 2 h and the learning rate of outer meta-update (i.e. β in Algorithm 1) to be h.  ... 
arXiv:1910.07368v2 fatcat:pyb5bpja5zh7vdhythu54akifi
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