Dividing Good and Better Items Among Agents with Bivalued Submodular Valuations

• URL: http://arxiv.org/abs/2302.03087v3
• Date: Wed, 19 Jul 2023 21:50:59 GMT
• Title: Dividing Good and Better Items Among Agents with Bivalued Submodular Valuations
• Authors: Cyrus Cousins, Vignesh Viswanathan and Yair Zick
• Abstract summary: We study the problem of fairly allocating a set of indivisible goods among agents with bivalued submodular valuations. We show that neither the leximin nor the MNW allocation is guaranteed to be envy free up to one good.
• Score: 20.774185319381985
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the problem of fairly allocating a set of indivisible goods among agents with {\em bivalued submodular valuations} -- each good provides a marginal gain of either $a$ or $b$ ($a < b$) and goods have decreasing marginal gains. This is a natural generalization of two well-studied valuation classes -- bivalued additive valuations and binary submodular valuations. We present a simple sequential algorithmic framework, based on the recently introduced Yankee Swap mechanism, that can be adapted to compute a variety of solution concepts, including max Nash welfare (MNW), leximin and $p$-mean welfare maximizing allocations when $a$ divides $b$. This result is complemented by an existing result on the computational intractability of MNW and leximin allocations when $a$ does not divide $b$. We show that MNW and leximin allocations guarantee each agent at least $\frac25$ and $\frac{a}{b+2a}$ of their maximin share, respectively, when $a$ divides $b$. We also show that neither the leximin nor the MNW allocation is guaranteed to be envy free up to one good (EF1). This is surprising since for the simpler classes of bivalued additive valuations and binary submodular valuations, MNW allocations are known to be envy free up to any good (EFX).

Related papers

• Fair Submodular Cover [18.37610521373708]
  We present the study of Fair Submodular Cover (FSC), where given a ground set $U$, a monotone submodular function $f:2UtomathbbR_ge 0$, a threshold $tau$. We first introduce discrete algorithms for FSC that achieve a bicriteria approximation ratio of $(frac1epsilon, 1-O(epsilon))$. We then present a continuous algorithm that achieves a $(frac1epsilon, 1-O(epsilon))$-
  arXiv  Detail & Related papers  (2024-07-05T18:37:09Z)
• Mind the Gap: A Causal Perspective on Bias Amplification in Prediction & Decision-Making [58.06306331390586]
  We introduce the notion of a margin complement, which measures how much a prediction score $S$ changes due to a thresholding operation. We show that under suitable causal assumptions, the influences of $X$ on the prediction score $S$ are equal to the influences of $X$ on the true outcome $Y$.
  arXiv  Detail & Related papers  (2024-05-24T11:22:19Z)
• Efficient Frameworks for Generalized Low-Rank Matrix Bandit Problems [61.85150061213987]
  We study the generalized low-rank matrix bandit problem, proposed in citelu2021low under the Generalized Linear Model (GLM) framework. To overcome the computational infeasibility and theoretical restrain of existing algorithms, we first propose the G-ESTT framework. We show that G-ESTT can achieve the $tildeO(sqrt(d_1+d_2)3/2Mr3/2T)$ bound of regret while G-ESTS can achineve the $tildeO
  arXiv  Detail & Related papers  (2024-01-14T14:14:19Z)
• Statistical Learning under Heterogeneous Distribution Shift [71.8393170225794]
  Ground-truth predictor is additive $mathbbE[mathbfz mid mathbfx,mathbfy] = f_star(mathbfx) +g_star(mathbfy)$.
  arXiv  Detail & Related papers  (2023-02-27T16:34:21Z)
• Fair Shares: Feasibility, Domination and Incentives [6.878547831852427]
  We consider fair allocation of a set $M$ of indivisible goods to $n$ equally-entitled agents, with no monetary transfers. For additive valuations we present shares that are feasible, self-maximizing and time computable.
  arXiv  Detail & Related papers  (2022-05-16T08:52:42Z)
• (Almost) Envy-Free, Proportional and Efficient Allocations of an Indivisible Mixed Manna [10.933894827834825]
  We study the problem of finding fair and efficient allocations of a set of indivisible items to a set of agents. As fairness notions, we consider arguably the strongest possible relaxations of envy-freeness and proportionality.
  arXiv  Detail & Related papers  (2022-02-06T01:29:50Z)
• Under-bagging Nearest Neighbors for Imbalanced Classification [63.026765294759876]
  We propose an ensemble learning algorithm called textitunder-bagging $k$-NN (textitunder-bagging $k$-NN) for imbalanced classification problems.
  arXiv  Detail & Related papers  (2021-09-01T14:10:38Z)
• The Power of Subsampling in Submodular Maximization [51.629656762796564]
  We show that this approach leads to optimal/state-of-the-art results despite being much simpler than existing methods. We empirically demonstrate the effectiveness of our algorithms on video summarization, location summarization, and movie recommendation tasks.
  arXiv  Detail & Related papers  (2021-04-06T20:25:57Z)
• Fine-Grained Gap-Dependent Bounds for Tabular MDPs via Adaptive Multi-Step Bootstrap [84.66885506098724]
  This paper presents a new model-free algorithm for episodic finite-horizon Markov Decision Processes (MDP), Adaptive Multi-step Bootstrap (AMB) We show AMB achieves a gap-dependent regret bound that only scales with the sum of the inverse of the sub-optimality gaps. We also show AMB suffers an additional $frac|Z_mul|Delta_min$ regret, where $Z_mul$ is the set of state-action pairs $(s,a)$'s satisfying $a$ is a non-unique optimal action for
  arXiv  Detail & Related papers  (2021-02-09T07:46:34Z)
• Finding Fair and Efficient Allocations When Valuations Don't Add Up [25.962505544590947]
  We show that when agent valuations are matroid rank functions, a socially optimal (i.e. utilitarian social welfare-maximizing) achieves allocation that envy-freeness up to one item (EF1) exists and is computationally tractable. This is the first valuation function class not subsumed by additive valuations for which it has been established that an allocation maximizing Nash welfare is EF1.
  arXiv  Detail & Related papers  (2020-03-16T07:42:27Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.