On the Max-Min Fair Stochastic Allocation of Indivisible Goods

Kawase, Yasushi; Sumita, Hanna

doi:10.1609/aaai.v34i02.5580

Cited by 6 publications

(7 citation statements)

References 47 publications

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“…Specifically, we prove that a 1 3 -approximation 10 can be obtained deterministically, whereas a (e−1) 2 e 2 −e+1 ≈ 0.52-approximation can be obtained w.h.p. As a reference point, it is worth noting that the problem of maximizing the egalitarian welfare in the same settings has been shown to be NP-hard to approximate to a (multiplicative) factor better than 1 − 1 e ≈ 0.632 [13]. However, as an α-approximation to leximin is first and foremost an α-approximation to the egalitarian welfare 11 , the same hardness result applies to our problem as well.…”

Section: Stochastic Allocations Of Indivisible Goodssupporting

confidence: 54%

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Leximin Approximation: From Single-Objective to Multi-Objective

Hartman,

Hassidim,

Aumann

et al. 2023

Frontiers in Artificial Intelligence and Applications

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Leximin is a common approach to multi-objective optimization, frequently employed in fair division applications. In leximin optimization, one first aims to maximize the smallest objective value; subject to this, one maximizes the second-smallest objective; and so on. Often, even the single-objective problem of maximizing the smallest value cannot be solved accurately. What can we hope to accomplish for leximin optimization in this situation? Recently, Henzinger et al. (2022) defined a notion of approximate leximin optimality. Their definition, however, considers only an additive approximation. In this work, we first define the notion of approximate leximin optimality, allowing both multiplicative and additive errors. We then show how to compute, in polynomial time, such an approximate leximin solution, using an oracle that finds an approximation to a single-objective problem. The approximation factors of the algorithms are closely related: an (α,ϵ)-approximation for the single-objective problem (where α ∈ (0,1] and ϵ ≥ 0 are the multiplicative and additive factors respectively) translates into an (α2/(1 − α + α2), ϵ/(1 − α + α2))-approximation for the multi-objective leximin problem, regardless of the number of objectives. Finally, we apply our algorithm to obtain an approximate leximin solution for the problem of stochastic allocations of indivisible goods.

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Section: Stochastic Allocations Of Indivisible Goodssupporting

confidence: 54%

“…We apply our results to the problem of stochastic allocations of indivisible goods. When agents have submodular utilities, approximating the egalitarian value to a (multiplicative) factor better than 1− 1 e ≈ 0.632 is NP-hard [13]. That is, even the first-objective of leximin, i.e., maximizing the smallest objective, is NP-hard.…”

Section: Introductionmentioning

confidence: 99%

Leximin Approximation: From Single-Objective to Multi-Objective

Hartman,

Hassidim,

Aumann

et al. 2023

Frontiers in Artificial Intelligence and Applications

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“…Nishimura and Sumita (2023) established the connection of maximum Nash welfare with a stronger variant of EFM when agents' utilities are binary and linear for each good, and a weaker variant of EFM when agents' utilities are general additive. Kawase, Nishimura, and Sumita (2023) studied fair mixed-goods allocations whose utility vectors minimizes a symmetric convex function.…”

Section: Mixed Divisible and Indivisible Goodsmentioning

confidence: 99%

Mixed Fair Division: A Survey

Liu,

Lu,

Suzuki

et al. 2024

AAAI

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The fair allocation of resources to agents is a fundamental problem in society and has received significant attention and rapid developments from the game theory and artificial intelligence communities in recent years. The majority of the fair division literature can be divided along at least two orthogonal directions: goods versus chores, and divisible versus indivisible resources. In this survey, besides describing the state of the art, we outline a number of interesting open questions in three mixed fair division settings: (i) indivisible goods and chores, (ii) divisible and indivisible goods (i.e., mixed goods), and (iii) fair division of indivisible goods with subsidy.

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“…The particular case of identical agents has been studied for decades as the online machine covering problem in the context of scheduling [40,15,50,79]. Moreover, there is a line of work studying an offline version of the max-min fair allocation problem (the case when all utilities are known in advance), which is referred to as the Santa Claus problem [63,13,60,28,52,46,33,54].…”

Section: Introductionmentioning

confidence: 99%

Uniformly Bounded Regret in Dynamic Fair Allocation

Balseiro¹,

Xia²

2022

Preprint

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We study a dynamic allocation problem in which T sequentially arriving divisible resources need to be allocated to n fixed agents with additive utilities. Agents' utilities are drawn stochastically from a known distribution, and decisions are made immediately and irrevocably. Most works on dynamic resource allocation aim to maximize the utilitarian welfare of the agents, which may result in unfair concentration of resources at select agents while leaving others' demands under-fulfilled. In this paper, we consider the egalitarian welfare objective instead, which aims at balancing the efficiency and fairness of the allocation. To this end, we first study a fluid-based policy derived from a deterministic approximation to the underlying problem and show that it attains a regret of order Θ( √ T ) against the hindsight optimum, i.e., the optimal egalitarian allocation when all utilities are known in advance. We then propose a new policy, called Backward Infrequent Re-solving with Thresholding (BIRT), which consists of re-solving the fluid problem at most O(log log T ) times. We prove the BIRT policy attains O(1) regret against the hindsight optimum, independently of the time horizon length T and initial welfare. We also present numerical experiments to illustrate the significant performance improvement against several benchmark policies.

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On the Max-Min Fair Stochastic Allocation of Indivisible Goods

Cited by 6 publications

References 47 publications

Leximin Approximation: From Single-Objective to Multi-Objective

Leximin Approximation: From Single-Objective to Multi-Objective

Mixed Fair Division: A Survey

Uniformly Bounded Regret in Dynamic Fair Allocation

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