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Optimal algorithms for Augmented Testing of Discrete Distributions

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arXiv 2024年

作者： Aliakbarpour, Maryam Indyk, Piotr Rubinfeld, Ronitt Silwal, Sandeep Rice University United States MIT United States UW-Madison United States

We consider the problem of hypothesis testing for discrete distributions. In the standard model, where we have sample access to an underlying distribution p, extensive research has established optimal bounds for uniformity testing, identity testing (goodness of fit), and closeness testing (equivalence or two-sample testing). We explore these problems in a setting where a predicted data distribution, possibly derived from historical data or predictive machine learning models, is available. We demonstrate that such a predictor can indeed reduce the number of samples required for all three property testing tasks. The reduction in sample complexity depends directly on the predictor's quality, measured by its total variation distance from p. A key advantage of our algorithms is their adaptability to the precision of the prediction. Specifically, our algorithms can self-adjust their sample complexity based on the accuracy of the available prediction, operating without any prior knowledge of the estimation's accuracy (i.e. they are consistent). Additionally, we never use more samples than the standard approaches require, even if the predictions provide no meaningful information (i.e. they are also robust). We provide lower bounds to indicate that the improvements in sample complexity achieved by our algorithms are information-theoretically optimal. Furthermore, experimental results show that the performance of our algorithms on real data significantly exceeds our worst-case guarantees for sample complexity, demonstrating the practicality of our approach. © 2024, CC BY-NC-ND.

关键词： consensus algorithm

Two Linearized Implicit Local Structure-Preserving algorithms for the Allen-Cahn Equation

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SSRN

SSRN 2024年

作者： Wang, Jialing Zhengting, Zhou Shu, Siqi School of Mathematics and Statistics Nanjing University of Information Science and Technology Nanjing210044 China

In this paper, two linearized implicit local structure-preserving algorithms are proposed for the Allen-Cahn equation by using the concatenating method and proven to satisfy the local energy dissipation rate conservation in any local spacetime regions. Under the suitable boundary conditions, both the two algorithms maintain the total energy dissipation law at the discrete level, where the energy is exactly the original energy. Numerical experiments verify the theoretical analysis well. © 2024, The Authors. All rights reserved.

关键词： consensus algorithm

Uniform generation of large traces

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arXiv 2024年

作者： Université, Samy Abbes Jugé, Vincent Paris Cité IRIF CNRS UMR 8243 8 place Aurélie Nemours ParisF-75013 France Univ Gustave Eiffel CNRS LIGM Marne-la-ValléeF-77454 France

We introduce an algorithm for the uniform generation of infinite traces, i.e., infinite words up to commutation of some letters. The algorithm outputs on-the-fly approximations of a theoretical infinite trace, the latter being distributed according to the exact uniform probability measure. The average size of the approximation grows linearly with the time of execution of the algorithm, hence its output can be effectively used while running. Two versions of the algorithm are given. A version without rejection has a good production speed, provided that some precomputations have been done, but these may be costly. A version with rejection requires much fewer computations, at the expense of a production speed that can be small. We also show that, for some particular trace monoids, one or the other version of the algorithm can actually be very good: few computations for a good production speed. © 2024, CC BY.

关键词： consensus algorithm

UTILITARIAN algorithm CONFIGURATION FOR INFINITE PARAMETER SPACES

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arXiv 2024年

作者： Graham, Devon R. Leyton-Brown, Kevin Department of Computer Science University of British Columbia VancouverBC Canada

Utilitarian algorithm configuration is a general-purpose technique for automatically searching the parameter space of a given algorithm to optimize its performance, as measured by a given utility function, on a given set of inputs. Recently introduced utilitarian configuration procedures offer optimality guarantees about the returned parameterization while provably adapting to the hardness of the underlying problem. However, the applicability of these approaches is severely limited by the fact that they only search a finite, relatively small set of parameters. They cannot effectively search the configuration space of algorithms with continuous or uncountable parameters. In this paper we introduce a new procedure, which we dub COUP (Continuous, Optimistic Utilitarian Procrastination). COUP is designed to search infinite parameter spaces efficiently to find good configurations quickly. Furthermore, COUP maintains the theoretical benefits of previous utilitarian configuration procedures when applied to finite parameter spaces but is significantly faster, both provably and experimentally. © 2024, CC BY.

关键词： consensus algorithm

Distributed weak independent sets in hypergraphs: Upper and lower bounds

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arXiv 2024年

作者： Adamson, Duncan Rosenbaum, Will Spirakis, Paul G. School of Computer Science University of St Andrews United Kingdom Department of Computer Science University of Liverpool United Kingdom

In this paper, we consider the problem of finding weak independent sets in a distributed network represented by a hypergraph. In this setting, each edge contains a set of r vertices rather than simply a pair, as in a standard graph. A k-weak independent set in a hypergraph is a set where no edge contains more than k vertices in the independent set. We focus two variations of this problem. First, we study the problem of finding k-weak maximal independent sets, k-weak independent sets where each vertex belongs to at least one edge with k vertices in the independent set. Second we introduce a weaker variant that we call (α, β)-independent sets where the independent set is β-weak, and each vertex belongs to at least one edge with at least α vertices in the independent set. Finally, we consider the problem of finding a (2, k)-ruling set on hypergraphs, i.e. independent sets where no vertex is a distance of more than k from the nearest member of the set. Given a hypergraph H of rank r and maximum degree ∆, we provide a LLL formulation for finding an (α, β)-independent set when (β−α)2/(β+α) ≥ 6 log(16r∆), an O(∆r/(β−α+1)+log∗ n) round deterministic algorithm finding an (α, β)-independent set, and a O(∆2(r − k) log r + ∆ log r log∗ r + log∗ n) round algorithm for finding a k-weak maximal independent set. Additionally, we provide zero round randomized algorithms for finding (α, β) independent sets, when (β−α)2/(β+α) ≥ 6clog n+6 for some constant c, and finding an m-weak independent set for some m ≥ r/2k where k is a given parameter. Finally, we provide lower bounds of Ω(∆ + log∗ n) and Ω(r + log∗ n) on the problems of finding a k-weak maximal independent sets for some values of k. © 2024, CC BY.

关键词： consensus algorithm

Fully Dynamic Matching and Ordered Ruzsa-Szemerédi Graphs

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arXiv 2024年

作者： Behnezhad, Soheil Ghafari, Alma Northeastern University United States

We study the fully dynamic maximum matching problem. In this problem, the goal is to efficiently maintain an approximate maximum matching of a graph that is subject to edge insertions and deletions. Our focus is particularly on algorithms that maintain the edges of a (1 − Ε)-approximate maximum matching for an arbitrarily small constant Ε > 0. Until recently, the fastest known algorithm for this problem required Θ(n) time per update where n is the number of vertices. This bound was slightly improved to n/(log∗ n)Ω(1) by Assadi, Behnezhad, Khanna, and Li [STOC’23] and very recently to n/2Ω(√log n) by Liu [FOCS’24]. Whether this can be improved to n1−Ω(1) remains a major open problem. In this paper, we introduce Ordered Ruzsa-Szemerédi (ORS) graphs (a generalization of Ruzsa-Szemerédi graphs) and show that the complexity of dynamic matching is closely tied to them. For δ > 0, define ORS(δn) to be the maximum number of matchings M1, . . ., Mt, each of size δn, that one can pack in an n-vertex graph such that each matching Mi is an induced matching in subgraph M1 ∪ . . . ∪ Mi. We show that there is a randomized algorithm that maintains a (1 − Ε)-approximate maximum matching of a fully dynamic graph in Õ(√ n 1+Ε · ORS(ΘΕ(n)) ) amortized update-time. While the value of ORS(Θ(n)) remains unknown and is only upper bounded by n1−o(1), the densest construction known from more than two decades ago only achieves ORS(Θ(n)) ≥ n1/Θ(log log n) = no(1) [Fischer et al. STOC’02]. If this is close to the right bound, then our algorithm achieves an update-time of √n1+O(Ε), resolving the aforementioned longstanding open problem in dynamic algorithms in a strong sense. Copyright © 2024, The Authors. All rights reserved.

关键词： consensus algorithm

Distributed Proximal-Correction algorithm for The Sum of Maximal Monotone Operators

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IEEE Transactions on Automatic Control 2024年

作者： Gong, Kai Zhang, Liwei The School of Mathematical Sciences Dalian University of Technology Liaoning 116024 China The National Frontiers Science Center for Industrial Intelligence and System Optimization the Key Laboratory of Data Analysis and Optimization for Smart Industry Ministry of Education Northeastern University Shenyang110819 China

This paper focuses on a class of inclusion problems of maximal monotone operators over directed multi-agent networks, where each agent is characterized by a splittable local operator. By integrating the ideas from correction, inexact proximal methods, and push-sum protocol, we proposed a distributed proximal-correction algorithm (referred to as DPCA-ϵik) to solve this inclusion problem of operators, where ϵik is an agent predetermined accuracy for approximately computing proximal mappings. Under mild assumptions on problem setup and agents specified precision ϵik, we proved the convergence and sublinear rate o(1/k) of DPCA-ϵik in terms of the first-order optimality residual. Furthermore, under the metric regularity of local operators of agents, we established its linear convergence rate. Numerical simulations and comparisons with other distributed algorithms illustrate the effectiveness of the proposed algorithm. ©1963-2012 IEEE.

关键词： consensus algorithm

Distributed algorithm for economic dispatch with transmission losses under digraph

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INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS 2023年第1期149卷

作者： Wang, Rui Li, Qi Zou, Juan Miao, Cuixia Qufu Normal Univ Sch Math Sci Jingxuan 57 Qufu 273100 Shan Dong Peoples R China

By taking transmission losses , directed communication into considered, a more practical scenario of economic dispatch problem is studied in the paper. It is formulated as a non-convex optimization problem. Using convex relaxation, the non-convex optimization problem is transformed into convex optimization problem , the conditions to ensure that they have the same solution are given. Then, a consensus-based distributed algorithm with time-varying feedback gains is presented, which can be used to the general directed communication networks. Especially, the convergence and optimality of the proposed algorithm are proved by using multi-parameter eigenvalue perturbation theory and graph theory. Finally, simulation results validate the theoretical results and illustrate the effectiveness and advantages of the proposed algorithm.

关键词： Economic dispatch problem Distributed algorithm consensus algorithm Transmission loss Smart grid

Shapley-Based Feature Selection for Online algorithm Selection

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Shapley-Based Feature Selection for Online Algorithm Select...

European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases, ECML PKDD 2023

作者： Becker, Patrick Bengs, Viktor Munich Germany Munich Germany Munich Germany

ISBN: (纸本)9783031746291

Online algorithm selection concerns the task of designing a dynamic algorithm selector that observes sequentially arriving problem instances of an algorithmic problem class for which it must select a suitable algorithm from a given pool of candidate algorithms. Typically the suitability of a candidate algorithm is determined by its average runtime for solving a problem instance. Recent work has shown that multi-armed bandit algorithms can be leveraged for specifying a suitable algorithm selector by taking available feature information of problem instances into account. In this paper, we investigate whether the performance of these bandit-based selection strategies can be further improved by incorporating feature selection. To this end, we use the concept of Shapley values from cooperative game theory to specify the contribution of the features with respect to the suitability of the candidate algorithms and adapt the bandit-based selection strategies to consider only features with the highest contribution. We present two different Shapley value-based approaches and show empirically that UCB-based bandit selection strategies can be improved, while Thompson sampling-based strategies actually deteriorate in terms of average runtime. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： consensus algorithm