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Sublinear Approximation Algorithm for Nash Social Welfare with XOS Valuations [article]

Siddharth Barman, Anand Krishna, Pooja Kulkarni, Shivika Narang
2022 arXiv   pre-print
We develop the first sublinear approximation algorithm for maximizing Nash social welfare under XOS valuations, specified via demand and XOS oracles.  ...  Nash social welfare has been extensively studied in recent years for various valuation classes.  ...  Algorithm 1 Sublinear approximation for Nash social welfare under XOS valuations Input: Instance [n], [m], {v i } i∈[n] with demand and XOS oracle access to the (XOS) valuations v i s Output: Theorem  ... 
arXiv:2110.00767v2 fatcat:mrhhlyfdn5aadb6sjg4bm53ory

Uniform Welfare Guarantees Under Identical Subadditive Valuations

Siddharth Barman, Ranjani G. Sundaram
2020 Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence  
Hence, by way of a constant-factor approximation algorithm, we obtain novel results for maximizing Nash social welfare and egalitarian welfare for identical subadditive valuations.  ...  Parameterized by an exponent term p, generalized-mean welfares en- compass multiple well-studied objectives, such as social welfare, Nash social welfare, and egalitarian welfare.  ...  a polynomial-time 1.45-approximation algorithm for maximizing Nash social welfare [Barman et al., 2018a] .  ... 
doi:10.24963/ijcai.2020/7 dblp:conf/ijcai/BarmanS20 fatcat:fdaj4ifnkzaphadxp2bxlsm5ua

Barriers to Near-Optimal Equilibria

Tim Roughgarden
2014 2014 IEEE 55th Annual Symposium on Foundations of Computer Science  
Implications for Simple Auctions We saw in Section I-B how Theorem VI.1, in conjunction with known exponential lower bounds for nondeterministic communication protocols that approximately maximize welfare  ...  auctions with "black-box" bidder valuations; and welfaremaximization in combinatorial auctions with succinctly described valuations.  ...  ACKNOWLEDGMENT We thank Zhiyi Huang, Sanjeev Khanna, and Inbal Talgam-Cohen for helpful discussions, and the anonymous FOCS reviewers for their comments.  ... 
doi:10.1109/focs.2014.16 dblp:conf/focs/Roughgarden14 fatcat:zcksbe4eejcm7cx5dzxvdllc2i

Uniform Welfare Guarantees Under Identical Subadditive Valuations [article]

Siddharth Barman, Ranjani G. Sundaram
2020 arXiv   pre-print
Hence, by way of a constant-factor approximation algorithm, we obtain novel results for maximizing Nash social welfare and egalitarian welfare for identical subadditive valuations.  ...  Parameterized by an exponent term p, generalized-mean welfares encompass multiple well-studied objectives, such as social welfare, Nash social welfare, and egalitarian welfare.  ...  Indeed, with p equal to one, zero, and −∞, the p-mean welfare, respectively, corresponds to (average) social welfare, Nash social welfare, and egalitarian welfare.  ... 
arXiv:2005.00504v1 fatcat:j33kqdfn5rgi7jihepzskkpxba

Fair Division of Indivisible Goods: A Survey [article]

Georgios Amanatidis, Georgios Birmpas, Aris Filos-Ratsikas, Alexandros A. Voudouris
2022 arXiv   pre-print
Allocating resources to individuals in a fair manner has been a topic of interest since the ancient times, with most of the early rigorous mathematical work on the problem focusing on infinitely divisible  ...  Recently, there has been a surge of papers studying computational questions regarding various different notions of fairness for the indivisible case, like maximin share fairness (MMS) and envy-freeness  ...  Barman and Krishnamurthy [2020] and Ghodsi et al. [2022] designed algorithms for computing approximate MMS allocations for richer classes of valuations (such as submodular, XOS, and subadditive).  ... 
arXiv:2202.07551v2 fatcat:4iingy3g5rfjxgm3x2lbphag7a

Liquid Price of Anarchy [article]

Yossi Azar, Michal Feldman, Nick Gravin, Alan Roytman
2015 arXiv   pre-print
For pure Nash equilibria, we establish tight bounds on the LPoA for the larger class of fractionally-subadditive valuations.  ...  The social welfare function, which is the standard measure of efficiency in auctions, is inadequate for settings with budgets, since there may be a large disconnect between the value a bidder derives from  ...  The authors showed that, for second price auctions, the social welfare of every Bayesian Nash equilibrium is a 2-approximation to the optimal social welfare, even for players with fractionally-subadditive  ... 
arXiv:1511.01132v1 fatcat:7vjclyqrgfhrxpacbyl4tzqufa

Learning and Efficiency in Games with Dynamic Population [article]

Thodoris Lykouris, Vasilis Syrgkanis, Eva Tardos
2020 arXiv   pre-print
Previous work has only showed that high welfare is guaranteed for learning outcomes in static environments.  ...  In fact, in large markets learning players achieve asymptotically optimal social welfare despite high turnover.  ...  Acknowledgements We would like to thank Karthik Sridharan for pointing us to relevant adaptive regret learning literature and Janardhan Kulkarni for suggesting the direction of asymptotic optimality under  ... 
arXiv:1505.00391v4 fatcat:5ftj54r7ejcfredldfu4vfih5a

Combinatorial auctions with bidding constraints and network externalities

Martin Starnberger
2015 unpublished
selected by the mechanism maximizes social welfare; that is, the allocation maximizes the sum of the valuations.  ...  we first study settings with single-dimensional valuations and prove a positive result for randomized mechanisms and an impossibility result for deterministic mechanisms.  ...  Our work lead to an algorithm for approximating the optimal social welfare that has an approximation ratio that is sublinear in the out-degree ∆ of the conflict graph.  ... 
doi:10.25365/thesis.39602 fatcat:oiilykq7bncpncwzbusx7xjkhi

A Survey on Data Pricing: from Economics to Data Science [article]

Jian Pei
2020 arXiv   pre-print
We also consider a series of challenges and directions for future work.  ...  Moreover, the sublinear approximation for unweighted kNN classifiers is facilitated by locality sensitive hashing [51] .  ...  with general valuation functions.  ... 
arXiv:2009.04462v2 fatcat:pacfeqmi7rhdxnihcrnvqbfjay

Dagstuhl Reports, Volume 7, Issue 4, April 2017, Complete Issue [article]

2018
These mechanisms can be extended to two-sided combinatorial auctions with additive and XOS valuations on subsets of items.  ...  Related to sample complexity is the area of sublinear algorithms. For huge data sets, even linear-time algorithms are impractical. Hence, the area of sublinear algorithms has developed.  ...  In contrast, artificial intelligence (AI) is designed for scheduling. Humans are bad in dealing with notifications and set up their notification systems.  ... 
doi:10.4230/dagrep.7.4 fatcat:oiz7wwh4hbhtvkg773gx65qukm