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An O(log log m) Prophet Inequality for Subadditive Combinatorial Auctions [article]

Paul Dütting, Thomas Kesselheim, Brendan Lucier
2020 arXiv   pre-print
The question is whether there exists a prophet inequality for this problem that significantly beats the best known approximation factor of O(log m).  ...  A central open problem in this area concerns subadditive combinatorial auctions. Here n agents with subadditive valuation functions compete for the assignment of m items.  ...  Our Results and Techniques An O(log log m) Prophet Inequality. Our first result is an existential O(log log m)-approximate price-based prophet inequality for subadditive combinatorial auctions.  ... 
arXiv:2004.09784v1 fatcat:rm2z32es6ne3xdew7xijzqpley

Improved Prophet Inequalities for Combinatorial Welfare Maximization with (Approximately) Subadditive Agents

Hanrui Zhang, Peter Sanders, Grzegorz Herman, Fabrizio Grandoni
2020 European Symposium on Algorithms  
Instantiated with different parameters, our framework implies (1) an O(log m / log log m)-competitive prophet inequality for subadditive agents, improving over the O(log m) upper bound via item pricing  ...  , (2) an O(D log m / log log m)-competitive prophet inequality for D-approximately subadditive agents, where D ∈ {1, ... , m-1} measures the maximum number of items that complement each other, and (3)  ...  A Sublogarithmic Prophet Inequality for Subadditive Agents We give a framework for designing prophet inequalities for combinatorial welfare maximization, which implies an O(log m/ log log m)-approximate  ... 
doi:10.4230/lipics.esa.2020.82 dblp:conf/esa/Zhang20 fatcat:4urerxq725d2voqx2a22f6gd6e

Combinatorial Prophet Inequalities [article]

Aviad Rubinstein, Sahil Singla
2016 arXiv   pre-print
We introduce a novel framework of Prophet Inequalities for combinatorial valuation functions.  ...  Inspired by the proof of our subadditive prophet inequality, we also obtain an O( n ·^2 r)-competitive algorithm for the Secretary Problem with a monotone subadditive objective function subject to an arbitrary  ...  Acknowledgements The second author thanks Anupam Gupta for introducing him to submodular optimization.  ... 
arXiv:1611.00665v1 fatcat:qdks4q6gq5fr7dc7wocdlllckm

Table of Contents

2020 2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS)  
Cut-Equivalent Trees are Optimal for Min-Cut Queries 105  ...  An O(log log m) Prophet Inequality for Subadditive Combinatorial Auctions 306 Paul Dütting (London School of Economics, UK), Thomas Kesselheim (University of Bonn, Germany), and Brendan Lucier (Microsoft  ...  Saranurak (Toyota Technological Institute of Chicago) Session 3: Plenary Session An Equivalence Between Private Classification and Online Prediction 389 Mark Bun (Department of Computer Science University  ... 
doi:10.1109/focs46700.2020.00004 fatcat:qzmbpkvoybhbvcezkfc2d6hldq

Implementation in Advised Strategies: Welfare Guarantees from Posted-Price Mechanisms When Demand Queries Are NP-Hard

Linda Cai, Clay Thomas, S. Matthew Weinberg, Michael Wagner
2020 Innovations in Theoretical Computer Science  
M. Weinberg 61:5 Combinatorial Auctions in the Computational Model.  ...  State-of-the-art posted-price mechanisms for submodular bidders with m items achieve approximation guarantees of O((log log m) 3 ) [1].  ...  Yet, no truthful constant-factor approximations are known (the state-of-the-art is O((log log m) 3 ) for submodular/XOS [1] or O(log m log log m) for subadditive [12] ).  ... 
doi:10.4230/lipics.itcs.2020.61 dblp:conf/innovations/CaiTW20 fatcat:xmkaziuibbhqhjkcn337chhnge

Combinatorial Auctions via Posted Prices [article]

Michal Feldman, Nick Gravin, Brendan Lucier
2014 arXiv   pre-print
We study anonymous posted price mechanisms for combinatorial auctions in a Bayesian framework.  ...  As a corollary, we obtain the first polytime (in n and m) constant-factor DSIC mechanism for Bayesian submodular combinatorial auctions, given access to demand query oracles.  ...  However, there is an extra difficulty for MPH-k valuations, since the concept of the "contribution of an item to welfare" is not as straightforward as for XOS valuations.  ... 
arXiv:1411.4916v1 fatcat:xeyymphcgjcgtgoe5fq7urmegq

Asymptotically Optimal Welfare of Posted Pricing for Multiple Items with MHR Distributions [article]

Alexander Braun, Matthias Buttkus, Thomas Kesselheim
2021 arXiv   pre-print
We give mechanisms using dynamic prices that obtain a 1 - Θ( 1/log n)-fraction of the optimal social welfare in expectation.  ...  Furthermore, we devise mechanisms that only use static item prices and are 1 - Θ( logloglog n/log n)-competitive compared to the optimal social welfare.  ...  Acknowledgments We thank the anonymous reviewers for helpful comments on improving the presentation of the paper. References  ... 
arXiv:2107.00526v1 fatcat:l5xwdpoezbaztlve62oyrwxwau

Learning Multi-item Auctions with (or without) Samples [article]

Yang Cai, Constantinos Daskalakis
2017 arXiv   pre-print
The second is a more general max-min learning setting that we introduce, where we are given "approximate distributions," and we seek to compute an auction whose revenue is approximately optimal simultaneously  ...  additive, XOS, and subadditive.  ...  By the prophet inequality [41] , there exists an SPM for selling item j with a collection of prices {p ij } i∈[n] that achieves revenue at least OPT j /2.  ... 
arXiv:1709.00228v1 fatcat:73vxkk5zznehfhhguf2slj6vfy

Combinatorial Auctions via Posted Prices [chapter]

Michal Feldman, Nick Gravin, Brendan Lucier
2014 Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms  
We study anonymous posted price mechanisms for combinatorial auctions in a Bayesian framework.  ...  As a corollary, we obtain the first polytime (in n and m) constant-factor DSIC mechanism for Bayesian submodular combinatorial auctions, given access to demand query oracles.  ...  Acknowledgments We are grateful to Shaddin Dughmi, David Kempe and Noam Nisan for helpful discussions. Michal  ... 
doi:10.1137/1.9781611973730.10 dblp:conf/soda/FeldmanGL15 fatcat:3fvodd234bcofmj4bkfhq2qvgy

Prophet Inequalities Made Easy: Stochastic Optimization by Pricing Non-Stochastic Inputs

Paul Duetting, Michal Feldman, Thomas Kesselheim, Brendan Lucier
2017 2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS)  
Our framework unifies and simplifies much of the existing literature on prophet inequalities and posted price mechanisms and is used to derive new and improved results for combinatorial markets (with and  ...  The framework establishes prophet inequalities by constructing price-based online approximation algorithms, a natural extension of threshold algorithms for settings beyond binary selection.  ...  It also yields an O(log m)-approximate prophet inequality for subadditive valuations by approximating subadditive valuations with XOS valuations [18, 9] . 1.4. New and improved prophet inequalities.  ... 
doi:10.1109/focs.2017.56 dblp:conf/focs/DuettingFKL17 fatcat:nchibt3tnfdqjext4spo2aarti

Prophet Inequalities via the Expected Competitive Ratio [article]

Tomer Ezra and Stefano Leonardi and Rebecca Reiffenhäuser and Matteo Russo and Alexandros Tsigonias-Dimitriadis
2022 arXiv   pre-print
In a prophet inequality problem, a decision-maker sees a series of online elements and needs to decide immediately and irrevocably whether or not to select each element upon its arrival, subject to an  ...  We consider prophet inequalities under general downward-closed constraints.  ...  Below, we show an even stronger result for single-choice prophet.  ... 
arXiv:2207.03361v2 fatcat:qvabhh72u5duvlm355gnhhcl5u

Prophet Inequalities Made Easy: Stochastic Optimization by Pricing Non-Stochastic Inputs [article]

Paul Dütting, Michal Feldman, Thomas Kesselheim, Brendan Lucier
2017 arXiv   pre-print
Our framework unifies and simplifies much of the existing literature on prophet inequalities and posted price mechanisms, and is used to derive new and improved results for combinatorial markets (with  ...  The framework establishes prophet inequalities by constructing price-based online approximation algorithms, a natural extension of threshold algorithms for settings beyond binary selection.  ...  It also yields a O(log m)-approximate prophet inequality for subadditive valuations by approximating subadditive valuations with XOS valuations [17, 9] .  ... 
arXiv:1612.03161v2 fatcat:exaa5jinkbdshbq2bl7dvzb3vq

Simple Mechanisms for a Subadditive Buyer and Applications to Revenue Monotonicity [article]

Aviad Rubinstein, S. Matthew Weinberg
2018 arXiv   pre-print
), as well as buyers who are fractionally subadditive with item multipliers drawn independently.  ...  We study the revenue maximization problem of a seller with n heterogeneous items for sale to a single buyer whose valuation function for sets of items is unknown and drawn from some distribution D.  ...  ACKNOWLEDGMENT We would like to thank Moshe Babaioff, Hu Fu, Nicole Immorlica, and Brendan Lucier for numerous suggestions and helpful discussions.  ... 
arXiv:1501.07637v2 fatcat:2ptuerjxnbcejoenpmuw2veut4

Single-Sample Prophet Inequalities via Greedy-Ordered Selection [article]

Constantine Caramanis, Paul Dütting, Matthew Faw, Federico Fusco, Philip Lazos, Stefano Leonardi, Orestis Papadigenopoulos, Emmanouil Pountourakis, Rebecca Reiffenhäuser
2021 arXiv   pre-print
matroids), and capture new settings (such as budget additive combinatorial auctions).  ...  We study single-sample prophet inequalities (SSPIs), i.e., prophet inequalities where only a single sample from each prior distribution is available.  ...  A number of works have obtained prophet inequalities for matchings and combinatorial auctions [Alaei et al., 2012 , Feldman et al., 2014 , Ehsani et al., 2018 , Gravin and Wang, 2019 , Dütting et al.,  ... 
arXiv:2111.03174v1 fatcat:on4hvjmgavev3cjqv76ur6chz4

On Submodular Prophet Inequalities and Correlation Gap [article]

Chandra Chekuri, Vasilis Livanos
2021 arXiv   pre-print
Rubinstein and Singla developed a notion of combinatorial prophet inequalities in order to generalize the standard prophet inequality setting to combinatorial valuation functions such as submodular and  ...  For non-negative submodular functions they demonstrated a constant factor prophet inequality for matroid constraints.  ...  Acknowledgements: The authors thank Sahil Singla for clarifications on [37] . CC thanks Vondrák and VL thanks Maria Siskaki, Kesav Krishnan and Venkata Sai Bavisetty for helpful discussions.  ... 
arXiv:2107.03662v1 fatcat:r6eazxwdtbannmlkz5gxvvk5ta
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