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Optimal k-Secretary with Logarithmic Memory

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arXiv 2025年

作者： Qiao, Mingda Zhang, Wei Massachusetts Institute of Technology United States

We study memory-bounded algorithms for the k-secretary problem. The algorithm of Kleinberg [Kle05] achieves an optimal competitive ratio of 1 − O(1/√k), yet a straightforward implementation requires Ω(k) memory. Our main result is a k-secretary algorithm that matches the optimal competitive ratio using O(log k) words of memory. We prove this result by establishing a general reduction from k-secretary to (random-order) quantile estimation, the problem of finding the k-th largest element in a stream. We show that a quantile estimation algorithm with an O(kα) expected error (in terms of the rank) gives a (1 − O(1/k1−α))-competitive k-secretary algorithm with O(1) extra words. We then introduce a new quantile estimation algorithm that achieves an O(√k) expected error bound using O(log k) memory. Of independent interest, we give a different algorithm that uses O(√k) words and finds the k-th largest element exactly with high probability, generalizing a result of Munro and Paterson [MP80]. Copyright © 2025, The Authors. All rights reserved.

关键词： consensus algorithm

Enhancing Medical IOT data using Blockchain

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Enhancing Medical IOT data using Blockchain

Emerging Smart Computing and Informatics (ESCI), Conference on

作者： N. Giridharan Yashwin G. M Logeshwaran B Bharaniraja R Department of Artificial Intelligence and Data Science K.S.Rangasamy College of Technology Tiruchengode India

ISBN: (数字)9798331515683

ISBN: (纸本)9798331515690

The potential of blockchain technology is very high in terms of transforming healthcare management systems, especially in safety, interoperability, and the integrity of health data. This revolutionary ability comes from the decentralized and immutable nature of blockchain architecture that enhances secure transactions. The implementation of SHA-256 algorithm greatly strengthens data against malicious attacks. This ensures that it cannot be hacked into unauthorized hands for sensitive information of patients. The use of smart contracts along with existing health data formats improves interoperability among various healthcare systems. Such level of interoperability increases both the communication and the swapping of health information across different platforms. However, the introduction of blockchain in healthcare faces several challenges about acceptance by users, scalability to ensure workability, and compliance with regulatory standards. A good insight related to the emerging landscape in which healthcare data management takes place can be derived from the present study. This can be achieved by studying the potential benefits blockchain technology would bring along with its integration into health management systems and the challenges that may come up in the process.

关键词： Workability Smart contracts Medical services consensus algorithm Blockchains Safety Internet of Things Security Interoperability Standards

A Blockchain-Based Approach to WoT Device Access Control

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A Blockchain-Based Approach to WoT Device Access Control

Computational Intelligence Approaches and Applications (ICCIAA), International Conference on

作者： Someah Alangari Computer Science Department College of Computing and IT Shaqra University Shaqra Saudi Arabia

ISBN: (数字)9798331523657

ISBN: (纸本)9798331523664

The Web of Things (WoT) represents an interconnected network of sensors and smart devices. It faces significant security and privacy challenges, including potential data breaches, unauthorized access issues, and concerning scalability problems. This paper introduces a blockchain-based solution that aims to enhance the security and reliability of the WoT. Taking advantage of the inherent transparency of blockchain's distributed ledger, the elimination of single points of failure through consensus algorithms, the enforcement of access control and privacy through smart contracts, and the assurance of data confidentiality through encryption, I propose an innovative design for the WoT that could guarantee enhanced security and trust. I also incorporate the use of a homomorphic hash function to further boost data privacy and integrity. This paper presents a comprehensive framework that employs blockchain technology to transform the current WoT into a more secure and trusted network, which I term the “Web of Trust”.

关键词： Access control Data privacy Distributed ledger Scalability consensus algorithm Computer architecture Transforms Standardization Blockchains Encryption

Runtime Analysis of the Compact Genetic algorithm on the LeadingOnes Benchmark

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arXiv 2025年

作者： Chwialkowski, Marcel Doerr, Benjamin Krejca, Martin S. École Polytechnique Institut Polytechnique de Paris Palaiseau France Palaiseau France

The compact genetic algorithm (cGA) is one of the simplest estimation-of-distribution algorithms (EDAs). Next to the univariate marginal distribution algorithm (UMDA)—another simple EDA—, the cGA has been subject to extensive mathematical runtime analyses, often showcasing a similar or even superior performance to competing approaches. Surprisingly though, up to date and in contrast to the UMDA and many other heuristics, we lack a rigorous runtime analysis of the cGA on the LEADINGONES benchmark—one of the most studied theory benchmarks in the domain of evolutionary computation. We fill this gap in the literature by conducting a formal runtime analysis of the cGA on LEADINGONES. For the cGA’s single parameter—called the hypothetical population size—at least polylogarithmically larger than the problem size, we prove that the cGA samples the optimum of LEADINGONES with high probability within a number of function evaluations quasi-linear in the problem size and linear in the hypothetical population size. For the best hypothetical population size, our result matches, up to polylogarithmic factors, the typical quadratic runtime that many randomized search heuristics exhibit on LEADINGONES. Our analysis exhibits some noteworthy differences in the working principles of the two algorithms which were not visible in previous works. © 2025, CC BY.

关键词： consensus algorithm

Convergence Analysis of the Wasserstein Proximal algorithm beyond Geodesic Convexity

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arXiv 2025年

作者： Zhu, Shuailong Chen, Xiaohui Section of Computer Science Ecole Polytechnique Fédérale de Lausanne Switzerland Department of Mathematics University of Southern California United States

The proximal algorithm is a powerful tool to minimize nonlinear and nonsmooth functionals in a general metric space. Motivated by the recent progress in studying the training dynamics of the noisy gradient descent algorithm on two-layer neural networks in the mean-field regime, we provide in this paper a simple and self-contained analysis for the convergence of the general-purposeWasserstein proximal algorithm without assuming geodesic convexity of the objective functional. Under a natural Wasserstein analog of the Euclidean Polyak-Lojasiewicz inequality, we establish that the proximal algorithm achieves an unbiased and linear convergence rate. Our convergence rate improves upon existing rates of the proximal algorithm for solving Wasserstein gradient flows under strong geodesic convexity. We also extend our analysis to the inexact proximal algorithm for geodesically semiconvex objectives. In our numerical experiments, proximal training demonstrates a faster convergence rate than the noisy gradient descent algorithm on mean-field neural networks. © 2025, CC BY-NC-SA.

关键词： consensus algorithm

Decision-Theoretic Approaches in Learning-Augmented algorithms∗

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arXiv 2025年

作者： Angelopoulos, Spyros Dürr, Christoph Melidi, Georgii Sorbonne University CNRS LIP6 Paris France International Laboratory on Learning Systems Montreal Canada

In this work, we initiate the systemic study of decision-theoretic metrics in the design and analysis of algorithms with machine-learned predictions. We introduce approaches based on both deterministic measures such as distance-based evaluation, that help us quantify how close the algorithm is to an ideal solution, as well as stochastic measures that allow us to balance the trade-off between the algorithm’s performance and the risk associated with the imperfect oracle. These approaches help us quantify the algorithmic performance across the entire spectrum of prediction error, unlike several previous works that focus on few, and often extreme values of the error. We apply these techniques to two well-known problems from resource allocation and online decision making, namely contract scheduling and 1-max search. © 2025, CC BY.

关键词： consensus algorithm

TESTING THE FAIRNESS-ACCURACY IMPROVABILITY OF algorithmS

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arXiv 2024年

作者： Auerbach, Eric Liang, Annie Okumura, Kyohei Tabord-Meehan, Max Department of Economics Northwestern University United States Department of Economics University of Chicago United States

Many organizations use algorithms that have a disparate impact, i.e., the benefits or harms of the algorithm fall disproportionately on certain social groups. Addressing an algorithm’s disparate impact can be challenging, however, because it is often unclear whether it is possible to reduce this impact without sacrificing other objectives of the organization, such as accuracy or profit. Establishing the improvability of algorithms with respect to multiple criteria is of both conceptual and practical interest: in many settings, disparate impact that would otherwise be prohibited under US federal law is permissible if it is necessary to achieve a legitimate business interest. The question is how an analyst can formally substantiate, or refute, this "necessity" defense. In this paper, we provide an econometric framework for testing the hypothesis that it is possible to improve on the fairness of an algorithm without compromising on other pre-specified objectives. Our proposed test is simple to implement and can be applied under any exogenous constraint on the algorithm space. We establish the large-sample validity and consistency of our test, and microfound the test’s robustness to manipulation based on a game between a policymaker and the analyst. Finally, we apply our approach to evaluate a healthcare algorithm originally considered by Obermeyer et al. (2019), and quantify the extent to which the algorithm’s disparate impact can be reduced without compromising the accuracy of its predictions. © 2024, CC BY.

关键词： consensus algorithm

Best-Arm Identification in Unimodal Bandits

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arXiv 2024年

作者： Poiani, Riccardo Jourdan, Marc Kaufmann, Emilie Degenne, Rémy Bocconi University Milan Italy EPFL Lausanne Switzerland Univ. Lille Inria CNRS Centrale Lille UMR 9189-CRIStAL France

We study the fixed-confidence best-arm identification problem in unimodal bandits, in which the means of the arms increase with the index of the arm up to their maximum, then decrease. We derive two lower bounds on the stopping time of any algorithm. The instance-dependent lower bound suggests that due to the unimodal structure, only three arms contribute to the leading confidence-dependent cost. However, a worst-case lower bound shows that a linear dependence on the number of arms is unavoidable in the confidence-independent cost. We propose modifications of Track-and-Stop and a Top Two algorithm that leverage the unimodal structure. Both versions of Track-and-Stop are asymptotically optimal for one-parameter exponential families. The Top Two algorithm is asymptotically near-optimal for Gaussian distributions and we prove a non-asymptotic guarantee matching the worse-case lower bound. The algorithms can be implemented efficiently and we demonstrate their competitive empirical performance. © 2024, CC BY.

关键词： consensus algorithm

How to Make the Gradients Small Privately: Improved Rates for Differentially Private Non-Convex Optimization

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arXiv 2024年

作者： Lowy, Andrew Ullman, Jonathan Wright, Stephen J. Wisconsin Institute for Discovery University of Wisconsin-Madison United States Khoury College of Computer Sciences Northeastern University United States Department of Computer Sciences University of Wisconsin–Madison United States

We provide a simple and flexible framework for designing differentially private algorithms to find approximate stationary points of non-convex loss functions. Our framework is based on using a private approximate risk minimizer to "warm start" another private algorithm for finding stationary points. We use this framework to obtain improved, and sometimes optimal, rates for several classes of non-convex loss functions. First, we obtain improved rates for finding stationary points of smooth non-convex empirical loss functions. Second, we specialize to quasar-convex functions, which generalize star-convex functions and arise in learning dynamical systems and training some neural nets. We achieve the optimal rate for this class. Third, we give an optimal algorithm for finding stationary points of functions satisfying the Kurdyka-Lojasiewicz (KL) condition. For example, over-parameterized neural networks often satisfy this condition. Fourth, we provide new state-of-the-art rates for stationary points of non-convex population loss functions. Fifth, we obtain improved rates for non-convex generalized linear models. A modification of our algorithm achieves nearly the same rates for second-order stationary points of functions with Lipschitz Hessian, improving over the previous state-of-the-art for each of the above problems. © 2024, CC BY.

关键词： consensus algorithm