The Magic of Nash Social Welfare in Optimization: Do Not Sum, Just Multiply!

Charkhgard, Hadi; Keshanian, Kimia; Esmaeilbeigi, Rasul; Charkhgard, Parisa

doi:10.1017/s1446181122000074

Cited by 3 publications

(9 citation statements)

References 21 publications

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“…This idea goes back to J. Nash's famous solution concept to the cooperative bargaining problem. The WNSWS is not only to provide an important quality criterion, but also to successfully converge to the Nash-optimal outcome in a distributed negotiation model [13]- [14].…”

Section: Technical Concepts and Main Contribu-tionsmentioning

confidence: 99%

Collaborative Coded Distributed Computing Scheme: A Two-Phase Cooperative Game Approach

Kim

2023

IEEE Access

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As a modern communication paradigm, Artificial intelligence based Internet of Things (AIoT) can provide an interactive platform across the globe to enrich the quality of networking services. With the AIoT paradigm, coded distributed computing (CDC) has recently emerged to be a promising solution to address the straggling effects in conventional distributed computing systems. In this article, we propose a novel CDC control scheme in the AIoT platform. Based on the cooperative game theory, the main challenges of our scheme are i) the 𝑘 value decision for the CDC process, and ii) edge node resource allocation for offloading tasks. Using the ideas of coalition game and weighted Nash social welfare solution (WNSWS), our proposed scheme is developed as a two-phase game model to achieve a mutually desirable solution. At the first phase, a dynamic coalition formation is proceeded to select the most adaptable edge nodes for the offloading subtasks. At the second phase, the WNSWS is adopted to effectively share each edge node's computing resource. Based on the jointly design of these two cooperative games, we explore the synergy effect to optimize the CDC process. In the edge assisted distributed computing infrastructure, our reciprocal combinative approach can provide a fair-efficient solution through the sequential interactions of edge nodes and AIoT devices. In the performance evaluation, we provide extensive simulation analyses to show our scheme's superiority by comparing with the existing baseline protocols.

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Section: Technical Concepts and Main Contribu-tionsmentioning

confidence: 99%

Collaborative Coded Distributed Computing Scheme: A Two-Phase Cooperative Game Approach

Kim

2023

IEEE Access

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“…The Social Welfare Program (SWP) [20,12] provides a framework in the context of multi-objective optimization to analyze the trade-off between the objectives, which in our case are utility and fairness. Concretely, a Social Welfare Program for (MMO) is any optimization problem of the form…”

Section: The Social Welfare Programmentioning

confidence: 99%

“…Thus, by solving different SWPs, various points of the Pareto frontier may be computed. As discussed in Charkhgarda et al [12], there are inherent weaknesses that come with this SWP approach.…”

Section: The Social Welfare Programmentioning

confidence: 99%

“…The Nash Social Welfare Program (NSWP) [12] is an improvement over the SWP since it addresses the weaknesses of the previous approach by balancing the objectives of Problem (MMO). Mathematically, it has the form:…”

Section: The Nash Social Welfare Programmentioning

confidence: 99%

“…Our second contribution attempts to bridge two objectives (one utilitarian and the other, fairness-related) in a multi-objective setting, adapting the fairness schemes to the different goals of KEPs. Specifically, we apply a framework known as the Nash Social Welfare Program (NSWP) [12] to a KEP instance and optimize its objective. We briefly review the advantages of this approach for multi-objective programming and we describe our third contribution: a column generation procedure to efficiently solve the NSWP (itself a conic program) in the context of KEPs.…”

Section: Introductionmentioning

confidence: 99%

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Adaptation, Comparison and Practical Implementation of Fairness Schemes in Kidney Exchange Programs

St-Arnaud¹,

Carvalho²,

Farnadi³

2022

Preprint

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The privileged treatment for patients suffering from end-stage renal disease is transplantation. In Kidney Exchange Programs (KEPs), each participating patient is registered together with an incompatible donor. Then, KEPs maximize overall patient benefit through donor exchanges. Compatibility requirements can severely restrict these programs, with certain patients waiting long to be selected for an exchange. Thus, the policy governing the selection of exchanges requires a careful balance between fairness in terms of individual access to transplantation and utilitarian criteria (e.g., total number of transplants). In this work, we review several fairness schemes, interpret them in the context of KEPs and describe their weaknesses. To overcome those drawbacks, we propose a novel scheme based on the Nash Social Welfare Program that simultaneously optimizes the fairness and the utilitarian objectives. Because the application of fairness schemes and a utilitarian objective implies solving conic programs of exponential size, we design a decomposition methodology to efficiently run them on KEP instances. Finally, we make an extensive comparison of the different schemes and validate the scalability of our methodology for benchmark instances from the literature.

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A two-stage stochastic game model for elective surgical capacity planning and investment

Acuna,

Cantarino,

Martinez

et al. 2024

Socio-Economic Planning Sciences

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The Magic of Nash Social Welfare in Optimization: Do Not Sum, Just Multiply!

Cited by 3 publications

References 21 publications

Collaborative Coded Distributed Computing Scheme: A Two-Phase Cooperative Game Approach

Collaborative Coded Distributed Computing Scheme: A Two-Phase Cooperative Game Approach

Adaptation, Comparison and Practical Implementation of Fairness Schemes in Kidney Exchange Programs

A two-stage stochastic game model for elective surgical capacity planning and investment

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