We study a primal-dual (PD) reinforcement learning (RL) algorithm for online constrained Markov decision processes (CMDPs). Despite its widespread practical use, the existing theoretical literature on PD-RL algorithms...
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Erdős and Graham found it conceivable that the best n-term Egyptian underapproximation of almost every positive number for sufficiently large n gets constructed in a greedy manner, i.e., from the best (n−1)-term Egyp...
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This paper develops the first decentralized online Riemannian optimization algorithm on Hadamard manifolds. Our algorithm, the decentralized projected Riemannian gradient descent, iteratively performs local updates us...
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The quality of enumeration algorithms is often measured by their delay, that is, the maximal time spent between the output of two distinct solutions. If the goal is to enumerate t distinct solutions for any given t, t...
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We consider the fundamental problem of solving a large-scale system of linear equations in a distributed/federated manner. The taskmaster solves the system with the help of a set of machines, each possessing a subset ...
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We consider the fundamental problem of solving a large-scale system of linear equations in a distributed/federated manner. The taskmaster solves the system with the help of a set of machines, each possessing a subset of the equations. While there exist several approaches for solving this problem, missing is a rigorous comparison between the convergence rates of two different classes of algorithms, namely, the projection-based methods and the optimization-based ones. In this paper, we provide a comprehensive analysis and comparison of these two classes of algorithms, with a particular focus on the most efficient method from each class, i.e., the recently proposed Accelerated Projection-Based consensus (APC) [1] and the Distributed Heavy-Ball Method (D-HBM). To this end, we first introduce a novel, geometric notion of data heterogeneity called angular heterogeneity and discuss its generality. Using this notion, we characterize and compare the optimal convergence rates of several well-known algorithms and capture the effects of the number of machines, the number of equations, and both cross-machine and local data heterogeneity on these rates. Our analysis not only establishes the superiority of APC for realistic scenarios where there is a large data heterogeneity, but also provides several insights into the effect of angular heterogeneity on the efficiencies of the studied methods. Additionally, we leverage existing results in numerical linear algebra to obtain distributed algorithms for the efficient computation of the proposed angular heterogeneity metrics. Lastly, as a by-product of our investigation, we obtain a tight bound on the condition number of an arbitrary square matrix in terms of the Euclidean norms of its rows and the angles between them. Our theoretical findings are validated through numerical analyses, confirming the superior performance of APC in typical real-world settings and providing a deeper understanding of the effects of angular heterogeneity on
Since arrival of new era of socialism with Chinese characteristics, living standards and quality of life of people have gradually improved. Farmers hope to obtain physical signs of livestock without causing stress rea...
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ISBN:
(数字)9798350368888
ISBN:
(纸本)9798350368895
Since arrival of new era of socialism with Chinese characteristics, living standards and quality of life of people have gradually improved. Farmers hope to obtain physical signs of livestock without causing stress reactions, and this demand is gradually increasing. Moreover, animal protection personnel hope to gradually increase requirement for measuring physical characteristics of animals without disturbing them. Therefore, method proposed in this article enables breeders and animal protection personnel to achieve hope of non-contact measurement to obtain animal signs. Contactless measurement has always been one of main research directions in machine vision, using point cloud segmentation method to filter out background point cloud ground and railing of pigs under complex conditions. Point cloud segmentation is a prerequisite for all basic applications, not only for point cloud reconstruction but also for segmentation and classification applications. In point cloud segmentation, a random sampling consensus algorithm (RANSAC) combined with conditional Euclidean clustering segmentation algorithm is proposed. Using single choice point cloud segmentation to divide entire point cloud into two parts, effectively obtaining target point cloud information.
We revisit the 3SUM problem in the preprocessed universes setting. We present an algorithm that, given three sets A, B, C of n integers, preprocesses them in quadratic time, so that given any subsets A′ ⊆ A, B′ ⊆ B...
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Negotiation is useful for resolving conflicts in multiagent systems. We explore autonomous negotiation in a setting where two self-interested rational agents sequentially trade items from a finite set of categories. E...
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This paper considers the problem of computing the operator norm of a linear map between finite dimensional Hilbert spaces when only evaluations of the linear map are available and under restrictive storage assumptions...
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