261 research outputs found

    LIPIcs, Volume 251, ITCS 2023, Complete Volume

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    LIPIcs, Volume 251, ITCS 2023, Complete Volum

    Utilitarian Welfare Optimization in the Generalized Vertex Coloring Games: An Implication to Venue Selection in Events Planning

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    We consider a general class of multi-agent games in networks, namely the generalized vertex coloring games (G-VCGs), inspired by real-life applications of the venue selection problem in events planning. Certain utility responding to the contemporary coloring assignment will be received by each agent under some particular mechanism, who, striving to maximize his own utility, is restricted to local information thus self-organizing when choosing another color. Our focus is on maximizing some utilitarian-looking welfare objective function concerning the cumulative utilities across the network in a decentralized fashion. Firstly, we investigate on a special class of the G-VCGs, namely Identical Preference VCGs (IP-VCGs) which recovers the rudimentary work by \cite{chaudhuri2008network}. We reveal its convergence even under a completely greedy policy and completely synchronous settings, with a stochastic bound on the converging rate provided. Secondly, regarding the general G-VCGs, a greediness-preserved Metropolis-Hasting based policy is proposed for each agent to initiate with the limited information and its optimality under asynchronous settings is proved using theories from the regular perturbed Markov processes. The policy was also empirically witnessed to be robust under independently synchronous settings. Thirdly, in the spirit of ``robust coloring'', we include an expected loss term in our objective function to balance between the utilities and robustness. An optimal coloring for this robust welfare optimization would be derived through a second-stage MH-policy driven algorithm. Simulation experiments are given to showcase the efficiency of our proposed strategy.Comment: 35 Page

    A machine learning approach to constructing Ramsey graphs leads to the Trahtenbrot-Zykov problem.

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    Attempts at approaching the well-known and difficult problem of constructing Ramsey graphs via machine learning lead to another difficult problem posed by Zykov in 1963 (now commonly referred to as the Trahtenbrot-Zykov problem): For which graphs F does there exist some graph G such that the neighborhood of every vertex in G induces a subgraph isomorphic to F? Chapter 1 provides a brief introduction to graph theory. Chapter 2 introduces Ramsey theory for graphs. Chapter 3 details a reinforcement learning implementation for Ramsey graph construction. The implementation is based on board game software, specifically the AlphaZero program and its success learning to play games from scratch. The chapter ends with a description of how computing challenges naturally shifted the project towards the Trahtenbrot-Zykov problem. Chapter 3 also includes recommendations for continuing the project and attempting to overcome these challenges. Chapter 4 defines the Trahtenbrot-Zykov problem and outlines its history, including proofs of results omitted from their original papers. This chapter also contains a program for constructing graphs with all neighborhood-induced subgraphs isomorphic to a given graph F. The end of Chapter 4 presents constructions from the program when F is a Ramsey graph. Constructing such graphs is a non-trivial task, as Bulitko proved in 1973 that the Trahtenbrot-Zykov problem is undecidable. Chapter 5 is a translation from Russian to English of this famous result, a proof not previously available in English. Chapter 6 introduces Cayley graphs and their relationship to the Trahtenbrot-Zykov problem. The chapter ends with constructions of Cayley graphs Γ in which the neighborhood of every vertex of Γ induces a subgraph isomorphic to a given Ramsey graph, which leads to a conjecture regarding the unique extremal Ramsey(4, 4) graph

    Robustness, scalability and interpretability of equivariant neural networks across different low-dimensional geometries

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    In this thesis we develop neural networks that exploit the symmetries of four different low-dimensional geometries, namely 1D grids, 2D grids, 3D continuous spaces and graphs, through the consideration of translational, rotational, cylindrical and permutation symmetries. We apply these models to applications across a range of scientific disciplines demonstrating the predictive ability, robustness, scalability, and interpretability. We develop a neural network that exploits the translational symmetries on 1D grids to predict age and species of mosquitoes from high-dimensional mid-infrared spectra. We show that the model can learn to predict mosquito age and species with a higher accuracy than models that do not utilise any inductive bias. We also demonstrate that the model is sensitive to regions within the input spectra that are in agreement with regions identified by a domain expert. We present a transfer learning approach to overcome the challenge of working with small, real-world, wild collected data sets and demonstrate the benefit of the approach on a real-world application. We demonstrate the benefit of rotation equivariant neural networks on the task of segmenting deforestation regions from satellite images through exploiting the rotational symmetry present on 2D grids. We develop a novel physics-informed architecture, exploiting the cylindrical symmetries of the group SO+ (2, 1), which can invert the transmission effects of multi-mode optical fibres (MMFs). We develop a new connection between a physics understanding of MMFs and group equivariant neural networks. We show that this novel architecture requires fewer training samples to learn, better generalises to out-of-distribution data sets, scales to higher-resolution images, is more interpretable, and reduces the parameter count of the model. We demonstrate the capability of the model on real-world data and provide an adaption to the model to handle real-world deviations from theory. We also show that the model can scale to higher resolution images than was previously possible. We develop a novel architecture which provides a symmetry-preserving mapping between two different low-dimensional geometries and demonstrate its practical benefit for the application of 3D hand mesh generation from 2D images. This models exploits both the 2D rotational symmetries present in a 2D image and in a 3D hand mesh, and provides a mapping between the two data domains. We demonstrate that the model performs competitively on a range of benchmark data sets and justify the choice of inductive bias in the model. We develop an architecture which is equivariant to a novel choice of automorphism group through the use of a sub-graph selection policy. We demonstrate the benefit of the architecture, theoretically through proving the improved expressivity and improved scalability, and experimentally on a range of widely studied benchmark graph classification tasks. We present a method of comparison between models that had not been previously considered in this area of research, demonstrating recent SOTA methods are statistically indistinguishable

    LIPIcs, Volume 261, ICALP 2023, Complete Volume

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    LIPIcs, Volume 261, ICALP 2023, Complete Volum

    Integrality and cutting planes in semidefinite programming approaches for combinatorial optimization

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    Many real-life decision problems are discrete in nature. To solve such problems as mathematical optimization problems, integrality constraints are commonly incorporated in the model to reflect the choice of finitely many alternatives. At the same time, it is known that semidefinite programming is very suitable for obtaining strong relaxations of combinatorial optimization problems. In this dissertation, we study the interplay between semidefinite programming and integrality, where a special focus is put on the use of cutting-plane methods. Although the notions of integrality and cutting planes are well-studied in linear programming, integer semidefinite programs (ISDPs) are considered only recently. We show that manycombinatorial optimization problems can be modeled as ISDPs. Several theoretical concepts, such as the Chvátal-Gomory closure, total dual integrality and integer Lagrangian duality, are studied for the case of integer semidefinite programming. On the practical side, we introduce an improved branch-and-cut approach for ISDPs and a cutting-plane augmented Lagrangian method for solving semidefinite programs with a large number of cutting planes. Throughout the thesis, we apply our results to a wide range of combinatorial optimization problems, among which the quadratic cycle cover problem, the quadratic traveling salesman problem and the graph partition problem. Our approaches lead to novel, strong and efficient solution strategies for these problems, with the potential to be extended to other problem classes

    Self-supervised learning techniques for monitoring industrial spaces

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    Dissertação de mestrado em Matemática e ComputaçãoEste documento é uma Dissertação de Mestrado com o título ”Self-Supervised Learning Techniques for Monitoring Industrial Spaces”e foi realizada e ambiente empresarial na empresa Neadvance - Machine Vision S.A. em conjunto com a Universidade do Minho. Esta dissertação surge de um grande projeto que consiste no desenvolvimento de uma plataforma de monitorização de operações específicas num espaço industrial, denominada SMARTICS (Plataforma tecnoló gica para monitorização inteligente de espaços industriais abertos). Este projeto continha uma componente de investigação para explorar um paradigma de aprendizagem diferente e os seus métodos - self-supervised learning, que foi o foco e principal contributo deste trabalho. O supervised learning atingiu um limite, pois exige anotações caras e dispendiosas. Em problemas reais, como em espaços industriais nem sempre é possível adquirir um grande número de imagens. O self-supervised learning ajuda nesses problemas, ex traindo informações dos próprios dados e alcançando bom desempenho em conjuntos de dados de grande escala. Este trabalho fornece uma revisão geral da literatura sobre a estrutura de self-supervised learning e alguns métodos. Também aplica um método para resolver uma tarefa de classificação para se assemelhar a um problema em um espaço industrial.This document is a Master’s Thesis with the title ”Self-Supervised Learning Techniques for Monitoring Industrial Spaces” and was carried out in a business environment at Neadvance - Machine Vision S.A. together with the University of Minho. This dissertation arises from a major project that consists of developing a platform to monitor specific operations in an industrial space, named SMARTICS (Plataforma tecnológica para monitorização inteligente de espaços industriais abertos). This project contained a research component to explore a different learning paradigm and its methods - self-supervised learning, which was the focus and main contribution of this work. Supervised learning has reached a bottleneck as they require expensive and time-consuming annotations. In real problems, such as in industrial spaces it is not always possible to require a large number of images. Self-supervised learning helps these issues by extracting information from the data itself and has achieved good performance in large-scale datasets. This work provides a comprehensive literature review of the self supervised learning framework and some methods. It also applies a method to solve a classification task to resemble a problem in an industrial space and evaluate its performance

    LIPIcs, Volume 274, ESA 2023, Complete Volume

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    LIPIcs, Volume 274, ESA 2023, Complete Volum
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