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Analysis of Off-Policy Multi-Step TD-Learning with Linear Function Approximation 63

Analysis of Off-Policy Multi-Step TD-Learning with Linear Fu...

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63rd IEEE Conference on Decision and Control, CDC 2024

作者： Lee, Donghwan Department of Electrical and Engineering Daejeon34141 Korea Republic of

ISBN: (纸本)9798350316339

This paper analyzes multi-step TD-learning algorithms within the 'deadly triad' scenario, characterized by linear function approximation, off-policy learning, and bootstrapping. In particular, we prove that n-step TD-learning algorithms converge to a solution as the sampling horizon n increases sufficiently. The paper is divided into two parts. In the first part, we comprehensively examine the fundamental properties of their model-based deterministic counterparts, including projected value iteration, gradient descent algorithms, and the control theoretic approach, which can be viewed as prototype deterministic algorithms whose analysis plays a pivotal role in understanding and developing their model-free reinforcement learning counterparts. In particular, we prove that these algorithms converge to meaningful solutions when n is sufficiently large. Based on these findings, two n-step TD-learning algorithms are proposed and analyzed, which can be seen as the model-free reinforcement learning counterparts of the gradient and control theoretic algorithms. © 2024 IEEE.

关键词： consensus algorithm

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Improved Bounds for Fractional Online Matching Problems 24

Improved Bounds for Fractional Online Matching Problems

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25th Conference on Economics and Computation, EC 2024

作者： Tang, Zhihao Gavin Zhang, Yuhao ITCS Key Laboratory of Interdisciplinary Research of Computation and Economics Shanghai University of Finance and Economics Shanghai China John Hopcroft Center for Computer Science Shanghai Jiao Tong University Shanghai China

ISBN: (纸本)9798400707049

Online bipartite matching with one-sided arrival and its variants have been extensively studied since the seminal work of Karp, Vazirani, and Vazirani (STOC 1990). Motivated by real-life applications with dynamic market structures, e.g., ride-sharing, two generalizations of the classical one-sided arrival model are proposed to allow non-bipartite graphs and to allow all vertices to arrive online. Namely, online matching with general vertex arrival is introduced by Wang and Wong (ICALP 2015), and fully online matching is introduced by Huang et al. (JACM 2020). In this paper, we study the fractional versions of the two models. We improve three out of the four state-of-the-art upper and lower bounds of the two models. For fully online matching, we design a 0.6-competitive algorithm and prove that no algorithm can be 0.613-competitive. For online matching with general vertex arrival, we prove that no algorithm can be 0.584-competitive. Moreover, we give an arguably more intuitive algorithm for the general vertex arrival model, compared to the algorithm of Wang and Wong, while attaining the same competitive ratio of 0.526 (in closed form). © 2024 Copyright held by the owner/author(s).

关键词： consensus algorithm

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Diagnosing Multi-Agent STRIPS Plans 35

Diagnosing Multi-Agent STRIPS Plans

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35th International Conference on Principles of Diagnosis and Resilient Systems, DX 2024

作者： Natan, Avraham Stern, Roni Kalech, Meir Yeoh, William Son, Tran Cao Ben-Gurion University of the Negev Beersheba Israel Washington University St. LouisMO United States New Mexico State University Las CrucesNM United States

ISBN: (纸本)9783959773560

The increasing use of multi-agent systems demands that many challenges be addressed. One such challenge is diagnosing failed multi-agent plan executions, sometimes in system setups where the different agents are not willing to disclose their private actions. One formalism for generating multi-agent plans is the well-known MA-STRIPS formalism. While there have been approaches for delivering as robust plans as possible, we focus on the plan execution stage. Specifically, we address the problem of diagnosing plans that failed their execution. We propose a Model-Based Diagnosis approach to solve this problem. Given an MA-STRIPS problem, a plan that solves it, and an observation that indicates execution failure, we define the MA-STRIPS diagnosis problem. We compile that problem into a boolean satisfiability problem (SAT) and then use an off-the-shelf SAT solver to obtain candidate diagnoses. We further expand this approach to address privacy by proposing a distributed algorithm that can find these same diagnoses in a decentralized manner. Additionally, we propose an enhancement to the distributed algorithm that uses information generated during the diagnosis process to provide significant speedups. We found that the improved algorithm runs more than 10 times faster than the basic decentralized version and, in one case, runs faster than the centralized algorithm. © Avraham Natan, Roni Stern, Meir Kalech, William Yeoh, and Tran Cao Son.

关键词： consensus algorithm

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Riemannian Accelerated Zeroth-order algorithm: Improved Robustness and Lower Query Complexity 41

Riemannian Accelerated Zeroth-order Algorithm: Improved Robu...

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41st International Conference on Machine Learning, ICML 2024

作者： He, Chang Pan, Zhaoye Wang, Xiao Jiang, Bo School of Information Management and Engineering Shanghai University of Finance and Economics China Key Laboratory of Interdisciplinary Research of Computation and Economics Shanghai University of Finance and Economics Ministry of Education China Dishui Lake Advanced Finance Institute Shanghai University of Finance and Economics China

Optimization problems with access to only zeroth-order information of the objective function on Riemannian manifolds arise in various applications, spanning from statistical learning to robot learning. While various zeroth-order algorithms have been proposed in Euclidean space, they are not inherently designed to handle the challenging constraints imposed by Riemannian manifolds. The proper adaptation of zeroth-order techniques to Riemannian manifolds remained unknown until the pioneering work of (Li et al., 2023a). However, zeroth-order algorithms are widely observed to converge slowly and be unstable in practice. To alleviate these issues, we propose a Riemannian accelerated zeroth-order algorithm with improved robustness. Regarding efficiency, our accelerated algorithm has the function query complexity of O(ϵ-7/4d) for finding an ϵ-approximate first-order stationary point. By introducing a small perturbation, it exhibits a function query complexity of Õ(ϵ-7/4d) for seeking a second-order stationary point with a high probability, matching state-of-the-art result in Euclidean space. Moreover, we further establish the almost sure convergence in the asymptotic sense through the Stable Manifold Theorem. Regarding robustness, our algorithm requires larger smoothing parameters in the order of Õ(ϵ7/8d-1/2), improving the existing result by a factor of Õ(ϵ3/4). Copyright 2024 by the author(s)

关键词： consensus algorithm

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Performance Comparative Analysis of OvA, AvA, and OvO algorithms in Multi-Class Classification 17

Performance Comparative Analysis of OvA, AvA, and OvO Algori...

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17th International Conference on Management of Large-Scale System Development, MLSD 2024

作者： Wolf, Daniyar A. Galin, Rinat R. V.A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences Laboratory of Cyber-Physical Systems 65 Profsoyuznaya Str. Moscow117997 Russia

ISBN: (纸本)9798350375718

The paper presents the result of comparative analysis of the main approaches to multi-class classification, synthesis of their mathematical models based on the considered algorithms is carried out. Their features, advantages, and disadvantages are presented, and the accuracy of multi-class classification is evaluated. Their features, advantages, and disadvantages are presented, and the accuracy of multi-class classification is evaluated. The dependence on accuracy and computational resource requirements is shown. The OvA algorithm can be a better way to solve problems with a small number of classes and limited resources. For tasks that require high classification accuracy and sufficient computational resources, AvA or OvO algorithms can be chosen. Synthesis of mathematical models and systematic generalization was carried out. © 2024 IEEE.

关键词： consensus algorithm

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Bipartizing (Pseudo-)Disk Graphs: Approximation with a Ratio Better than 3 27

Bipartizing (Pseudo-)Disk Graphs: Approximation with a Ratio...

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27th International Conference on Approximation algorithms for Combinatorial Optimization Problems, APPROX 2024 and the 28th International Conference on Randomization and Computation, RANDOM 2024

作者： Lokshtanov, Daniel Panolan, Fahad Saurabh, Saket Xue, Jie Zehavi, Meirav University of California Santa Barbara United States University of Leeds United Kingdom Institute of Mathematical Sciences India New York University Shanghai China Ben-Gurion University Israel

ISBN: (纸本)9783959773485

In a disk graph, every vertex corresponds to a disk in R2 and two vertices are connected by an edge whenever the two corresponding disks intersect. Disk graphs form an important class of geometric intersection graphs, which generalizes both planar graphs and unit-disk graphs. We study a fundamental optimization problem in algorithmic graph theory, Bipartization (also known as Odd Cycle Transversal), on the class of disk graphs. The goal of Bipartization is to delete a minimum number of vertices from the input graph such that the resulting graph is bipartite. A folklore (polynomial-time) 3-approximation algorithm for Bipartization on disk graphs follows from the classical framework of Goemans and Williamson [Combinatorica’98] for cycle-hitting problems. For over two decades, this result has remained the best known approximation for the problem (in fact, even for Bipartization on unit-disk graphs). In this paper, we achieve the first improvement upon this result, by giving a (3 − α)-approximation algorithm for Bipartization on disk graphs, for some constant α > 0. Our algorithm directly generalizes to the broader class of pseudo-disk graphs. Furthermore, our algorithm is robust in the sense that it does not require a geometric realization of the input graph to be given. © Daniel Lokshtanov, Fahad Panolan, Saket Saurabh, Jie Xue, and Meirav Zehavi.

关键词： consensus algorithm

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Reweighted Solutions for Weighted Low Rank Approximation 41

Reweighted Solutions for Weighted Low Rank Approximation

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41st International Conference on Machine Learning, ICML 2024

作者： Woodruff, David P. Yasuda, Taisuke School of Computer Science Carnegie Mellon University PittsburghPA United States

Weighted low rank approximation (WLRA) is an important yet computationally challenging primitive with applications ranging from statistical analysis, model compression, and signal processing. To cope with the NP-hardness of this problem, prior work considers heuristics, bicriteria, or fixed parameter tractable algorithms to solve this problem. In this work, we introduce a new relaxed solution to WLRA which outputs a matrix that is not necessarily low rank, but can be stored using very few parameters and gives provable approximation guarantees when the weight matrix has low rank. Our central idea is to use the weight matrix itself to reweight a low rank solution, which gives an extremely simple algorithm with remarkable empirical performance in applications to model compression and on synthetic datasets. Our algorithm also gives nearly optimal communication complexity bounds for a natural distributed problem associated with this problem, for which we show matching communication lower bounds. Together, our communication complexity bounds show that the rank of the weight matrix provably parameterizes the communication complexity of WLRA. We also obtain the first relative error guarantees for feature selection with a weighted objective. Copyright 2024 by the author(s)

关键词： consensus algorithm

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Reasoning in Structured Argumentation: Assumption-based Argumentation and ASPIC+ 5

Reasoning in Structured Argumentation: Assumption-based Argu...

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5th International Workshop on Systems and algorithms for Formal Argumentation, SAFA 2024

作者： Wallner, Johannes P. Institute of Software Technology Graz University of Technology Austria

Research in computational argumentation, as a branch in Artificial Intelligence (AI), is dedicated to study representations of arguments and to develop automated argumentative reasoning. The subfield of structured argumentation comprises of several approaches, which describe how to perform rational and automated argumentative reasoning, usually based on rule-based knowledge bases. From such bases arguments, and relations among arguments, are instantiated. Subsequently, reasoning can be carried out on the constructed arguments, oftentimes without the need to consider the internal structure of these arguments. In this way, argumentation semantics drive the reasoning process on such abstracted arguments. In recent years, research on computational aspects, i.e., developing theoretical foundations, algorithmic approaches, and systems, for structured argumentation has gained significant traction in the research community. We give an overview of recent strands of research on two prominent structured argumentation formalisms: assumption-based argumentation (ABA) and ASPIC+. We look at issues and benefits arising from instantiation or explication of arguments, discuss complexity results and algorithms for reasoning in ABA and ASPIC+, and consider how incorporation of preferences changes the picture. We close with open issues and possible directions for future research. © 2024 Copyright for this paper by its authors.

关键词： consensus algorithm

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Self-Stabilizing MIS Computation in the Beeping Model 38

Self-Stabilizing MIS Computation in the Beeping Model

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38th International Symposium on Distributed Computing, DISC 2024

作者： Giakkoupis, George Turau, Volker Ziccardi, Isabella Inria Univ. Rennes CNRS IRISA France Institute of Telematics Hamburg University of Technology Germany Bocconi University BIDSA Milan Italy

ISBN: (纸本)9783959773522

We consider self-stabilizing algorithms to compute a Maximal Independent Set (MIS) in the extremely weak beeping communication model. The model consists of an anonymous network with synchronous rounds. In each round, each vertex can optionally transmit a signal to all its neighbors (beep). After the transmission of a signal, each vertex can only differentiate between no signal received, or at least one signal received. We also consider an extension of this model where vertices can transmit signals through two distinguishable beeping channels. We assume that vertices have some knowledge about the topology of the network. We revisit the not self-stabilizing algorithm proposed by Jeavons, Scott, and Xu (2013), which computes an MIS in the beeping model. We enhance this algorithm to be self-stabilizing, and explore three different variants, which differ in the knowledge about the topology available to the vertices and the number of beeping channels. In the first variant, every vertex knows an upper bound on the maximum degree ∆ of the graph. For this case, we prove that the proposed self-stabilizing version maintains the same run-time as the original algorithm, i.e., it stabilizes after O(log n) rounds w.h.p. on any n-vertex graph. In the second variant, each vertex only knows an upper bound on its own degree. For this case, we prove that the algorithm stabilizes after O(log n · log log n) rounds on any n-vertex graph, w.h.p. In the third variant, we consider the model with two beeping channels, where every vertex knows an upper bound of the maximum degree of the nodes in the 1-hop neighborhood. We prove that this variant stabilizes w.h.p. after O(log n) rounds. © George Giakkoupis, Volker Turau, and Isabella Ziccardi.

关键词： consensus algorithm

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Faster Cycle Detection in the Congested Clique 38

Faster Cycle Detection in the Congested Clique

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38th International Symposium on Distributed Computing, DISC 2024

作者： Censor-Hillel, Keren Even, Tomer Williams, Virginia Vassilevska Department of Computer Science Technion Haifa Israel Massachusetts Institute of Technology CambridgeMA United States

ISBN: (纸本)9783959773522

We provide a fast distributed algorithm for detecting h-cycles in the Congested Clique model, whose running time decreases as the number of h-cycles in the graph increases. In undirected graphs, constant-round algorithms are known for cycles of even length. Our algorithm greatly improves upon the state of the art for odd values of h. Moreover, our running time applies also to directed graphs, in which case the improvement is for all values of h. Further, our techniques allow us to obtain a triangle detection algorithm in the quantum variant of this model, which is faster than prior work. A key technical contribution we develop to obtain our fast cycle detection algorithm is a new algorithm for computing the product of many pairs of small matrices in parallel, which may be of independent interest. © Keren Censor-Hillel, Tomer Even, and Virginia Vassilevska Williams.

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