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Documents authored by Sandholm, Tuomas

Document
DOI: 10.4230/LIPIcs.ITCS.2024.5
On the Complexity of Computing Sparse Equilibria and Lower Bounds for No-Regret Learning in Games

Authors: Ioannis Anagnostides, Alkis Kalavasis, Tuomas Sandholm, and Manolis Zampetakis

Published in: LIPIcs, Volume 287, 15th Innovations in Theoretical Computer Science Conference (ITCS 2024)

Abstract
Characterizing the performance of no-regret dynamics in multi-player games is a foundational problem at the interface of online learning and game theory. Recent results have revealed that when all players adopt specific learning algorithms, it is possible to improve exponentially over what is predicted by the overly pessimistic no-regret framework in the traditional adversarial regime, thereby leading to faster convergence to the set of coarse correlated equilibria (CCE) - a standard game-theoretic equilibrium concept. Yet, despite considerable recent progress, the fundamental complexity barriers for learning in normal- and extensive-form games are poorly understood. In this paper, we make a step towards closing this gap by first showing that - barring major complexity breakthroughs - any polynomial-time learning algorithms in extensive-form games need at least 2^{log^{1/2 - o(1)} |𝒯|} iterations for the average regret to reach below even an absolute constant, where |𝒯| is the number of nodes in the game. This establishes a superpolynomial separation between no-regret learning in normal- and extensive-form games, as in the former class a logarithmic number of iterations suffices to achieve constant average regret. Furthermore, our results imply that algorithms such as multiplicative weights update, as well as its optimistic counterpart, require at least 2^{(log log m)^{1/2 - o(1)}} iterations to attain an O(1)-CCE in m-action normal-form games under any parameterization. These are the first non-trivial - and dimension-dependent - lower bounds in that setting for the most well-studied algorithms in the literature. From a technical standpoint, we follow a beautiful connection recently made by Foster, Golowich, and Kakade (ICML '23) between sparse CCE and Nash equilibria in the context of Markov games. Consequently, our lower bounds rule out polynomial-time algorithms well beyond the traditional online learning framework, capturing techniques commonly used for accelerating centralized equilibrium computation.
Cite as

Ioannis Anagnostides, Alkis Kalavasis, Tuomas Sandholm, and Manolis Zampetakis. On the Complexity of Computing Sparse Equilibria and Lower Bounds for No-Regret Learning in Games. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 5:1-5:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{anagnostides_et_al:LIPIcs.ITCS.2024.5,
  author =	{Anagnostides, Ioannis and Kalavasis, Alkis and Sandholm, Tuomas and Zampetakis, Manolis},
  title =	{{On the Complexity of Computing Sparse Equilibria and Lower Bounds for No-Regret Learning in Games}},
  booktitle =	{15th Innovations in Theoretical Computer Science Conference (ITCS 2024)},
  pages =	{5:1--5:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-309-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{287},
  editor =	{Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.5},
  URN =		{urn:nbn:de:0030-drops-195334},
  doi =		{10.4230/LIPIcs.ITCS.2024.5},
  annote =	{Keywords: No-regret learning, extensive-form games, multiplicative weights update, optimism, lower bounds}
}
Document
DOI: 10.4230/LIPIcs.CP.2022.3
Improved Sample Complexity Bounds for Branch-And-Cut

Authors: Maria-Florina Balcan, Siddharth Prasad, Tuomas Sandholm, and Ellen Vitercik

Published in: LIPIcs, Volume 235, 28th International Conference on Principles and Practice of Constraint Programming (CP 2022)

Abstract
The branch-and-cut algorithm for integer programming has a wide variety of tunable parameters that have a huge impact on its performance, but which are challenging to tune by hand. An increasingly popular approach is to use machine learning to configure these parameters based on a training set of integer programs from the application domain. We bound how large the training set should be to ensure that for any configuration, its average performance over the training set is close to its expected future performance. Our guarantees apply to parameters that control the most important aspects of branch-and-cut: node selection, branching constraint selection, and cut selection, and are sharper and more general than those from prior research.
Cite as

Maria-Florina Balcan, Siddharth Prasad, Tuomas Sandholm, and Ellen Vitercik. Improved Sample Complexity Bounds for Branch-And-Cut. In 28th International Conference on Principles and Practice of Constraint Programming (CP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 235, pp. 3:1-3:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{balcan_et_al:LIPIcs.CP.2022.3,
  author =	{Balcan, Maria-Florina and Prasad, Siddharth and Sandholm, Tuomas and Vitercik, Ellen},
  title =	{{Improved Sample Complexity Bounds for Branch-And-Cut}},
  booktitle =	{28th International Conference on Principles and Practice of Constraint Programming (CP 2022)},
  pages =	{3:1--3:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-240-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{235},
  editor =	{Solnon, Christine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2022.3},
  URN =		{urn:nbn:de:0030-drops-166321},
  doi =		{10.4230/LIPIcs.CP.2022.3},
  annote =	{Keywords: Automated algorithm configuration, integer programming, machine learning theory, tree search, branch-and-bound, branch-and-cut, cutting planes, sample complexity, generalization guarantees, data-driven algorithm design}
}
Document
DOI: 10.4230/DagSemProc.07431.1
07431 Abstracts Collection – Computational Issues in Social Choice

Authors: Ulle Endriss, Jérôme Lang, Francesca Rossi, and Tuomas Sandholm

Published in: Dagstuhl Seminar Proceedings, Volume 7431, Computational Issues in Social Choice (2007)

Abstract
From the 21st to the 26th of October 2007, the Dagstuhl Seminar 07431 on ``Computational Issues in Social Choice'' was held at the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their recent research, and ongoing work and open problems were discussed. The abstracts of the talks given during the seminar are collected in this paper. The first section summarises the seminar topics and goals in general. Links to full papers are provided where available.
Cite as

Ulle Endriss, Jérôme Lang, Francesca Rossi, and Tuomas Sandholm. 07431 Abstracts Collection – Computational Issues in Social Choice. In Computational Issues in Social Choice. Dagstuhl Seminar Proceedings, Volume 7431, pp. 1-19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)

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@InProceedings{endriss_et_al:DagSemProc.07431.1,
  author =	{Endriss, Ulle and Lang, J\'{e}r\^{o}me and Rossi, Francesca and Sandholm, Tuomas},
  title =	{{07431 Abstracts Collection – Computational Issues in Social Choice}},
  booktitle =	{Computational Issues in Social Choice},
  pages =	{1--19},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{7431},
  editor =	{Ulle Endriss and J\'{e}r\^{o}me Lang and Francesca Rossi and Tuomas Sandholm},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07431.1},
  URN =		{urn:nbn:de:0030-drops-12736},
  doi =		{10.4230/DagSemProc.07431.1},
  annote =	{Keywords: Computational social choice, voting theory, fair division, mechanism design, coalition formation, complexity theory, preference representation, algorithms}
}
Document
DOI: 10.4230/DagSemProc.07431.2
07431 Executive Summary – Computational Issues in Social Choice

Authors: Ulle Endriss, Jérôme Lang, Francesca Rossi, and Tuomas Sandholm

Published in: Dagstuhl Seminar Proceedings, Volume 7431, Computational Issues in Social Choice (2007)

Abstract
Computational social choice is an interdisciplinary field of study at the interface of social choice theory and computer science, with knowledge flowing in either direction. On the one hand, computational social choice is concerned with importing concepts and procedures from social choice theory for solving questions that arise in computer science and AI application domains. This is typically the case for managing societies of autonomous agents, which calls for negotiation and voting procedures. On the other hand, computational social choice is concerned with importing notions and methods from computer science for solving questions originally stemming from social choice, for instance by providing new perspectives on the problem of manipulation and control in elections. This Dagstuhl Seminar has been devoted to the presentation of recent results and an exchange of ideas in this growing research field.
Cite as

Ulle Endriss, Jérôme Lang, Francesca Rossi, and Tuomas Sandholm. 07431 Executive Summary – Computational Issues in Social Choice. In Computational Issues in Social Choice. Dagstuhl Seminar Proceedings, Volume 7431, pp. 1-3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)

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@InProceedings{endriss_et_al:DagSemProc.07431.2,
  author =	{Endriss, Ulle and Lang, J\'{e}r\^{o}me and Rossi, Francesca and Sandholm, Tuomas},
  title =	{{07431 Executive Summary – Computational Issues in Social Choice}},
  booktitle =	{Computational Issues in Social Choice},
  pages =	{1--3},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{7431},
  editor =	{Ulle Endriss and J\'{e}r\^{o}me Lang and Francesca Rossi and Tuomas Sandholm},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07431.2},
  URN =		{urn:nbn:de:0030-drops-12749},
  doi =		{10.4230/DagSemProc.07431.2},
  annote =	{Keywords: Computational social choice, voting theory, fair division, mechanism design, coalition formation, complexity theory, preference representation, algorithms}
}
Document
DOI: 10.4230/DagSemProc.05011.5
Automated Mechanism Design

Authors: Tuomas Sandholm

Published in: Dagstuhl Seminar Proceedings, Volume 5011, Computing and Markets (2005)

Abstract
Mechanisms design has traditionally been a manual endeavor. In 2002, Conitzer and Sandholm introduced the automated mechanism design (AMD) approach, where the mechanism is computationally created for the specific problem instance at hand. This has several advantages: 1) it can yield better mechanisms than the ones known to date, 2) it applies beyond the problem classes studied manually to date, 3) it can circumvent seminal economic impossibility results that hold for classes of problems but not all instances, and 4) it shifts the burden of design from man to machine. In this talk I will overview our results on AMD to date. I will cover problem representations and the computational complexity of different variants of the design problem. Initial applications include revenue-maximizing combinatorial auctions and (combinatorial) public goods problems. Algorithms for AMD will be discussed. To reduce the computational complexity of designing optimal combinatorial auctions, I introduce an incentive compatible, individually rational subfamily called Virtual Valuations Combinatorial Auctions. The auction mechanism's revenue can be boosted (started, for example, from the VCG) by hill-climbing in this subspace. I will also present computational complexity and communication complexity results that motivate multi-stage and non-truth-promoting mechanisms. Finally, I present our first steps toward automatically designing multi-stage mechanisms.
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Tuomas Sandholm. Automated Mechanism Design. In Computing and Markets. Dagstuhl Seminar Proceedings, Volume 5011, pp. 1-2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2005)

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@InProceedings{sandholm:DagSemProc.05011.5,
  author =	{Sandholm, Tuomas},
  title =	{{Automated Mechanism Design}},
  booktitle =	{Computing and Markets},
  pages =	{1--2},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2005},
  volume =	{5011},
  editor =	{Daniel Lehmann and Rudolf M\"{u}ller and Tuomas Sandholm},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.05011.5},
  URN =		{urn:nbn:de:0030-drops-2677},
  doi =		{10.4230/DagSemProc.05011.5},
  annote =	{Keywords: Automated mechanism design, mechanism design}
}
Document
DOI: 10.4230/DagSemProc.05011.1
05011 Abstracts Collection – Computing and Markets

Authors: Daniel Lehmann, Rudolf Müller, and Tuomas Sandholm

Published in: Dagstuhl Seminar Proceedings, Volume 5011, Computing and Markets (2005)

Abstract
From 03.01.05 to 07.01.05, the Dagstuhl Seminar 05011``Computing and Markets'' was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available.
Cite as

Daniel Lehmann, Rudolf Müller, and Tuomas Sandholm. 05011 Abstracts Collection – Computing and Markets. In Computing and Markets. Dagstuhl Seminar Proceedings, Volume 5011, pp. 1-26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2005)

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@InProceedings{lehmann_et_al:DagSemProc.05011.1,
  author =	{Lehmann, Daniel and M\"{u}ller, Rudolf and Sandholm, Tuomas},
  title =	{{05011 Abstracts Collection – Computing and Markets}},
  booktitle =	{Computing and Markets},
  pages =	{1--26},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2005},
  volume =	{5011},
  editor =	{Daniel Lehmann and Rudolf M\"{u}ller and Tuomas Sandholm},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.05011.1},
  URN =		{urn:nbn:de:0030-drops-2250},
  doi =		{10.4230/DagSemProc.05011.1},
  annote =	{Keywords: Algorithms, complexity, game theory, social choice, auctions, equilibrium}
}
Document
DOI: 10.4230/DagSemProc.05011.2
05011 Executive Summary – Computing and Markets

Authors: Daniel Lehmann, Rudolf Müller, and Tuomas Sandholm

Published in: Dagstuhl Seminar Proceedings, Volume 5011, Computing and Markets (2005)

Abstract
The seminar Computing and Markets facilitated a very fruitful interaction between economists and computer scientists, which intensified the understanding of the other disciplines' tool sets. The seminar helped to pave the way to a unified theory of markets that takes into account both the economic and the computational issues---and their deep interaction.
Cite as

Daniel Lehmann, Rudolf Müller, and Tuomas Sandholm. 05011 Executive Summary – Computing and Markets. In Computing and Markets. Dagstuhl Seminar Proceedings, Volume 5011, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2005)

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@InProceedings{lehmann_et_al:DagSemProc.05011.2,
  author =	{Lehmann, Daniel and M\"{u}ller, Rudolf and Sandholm, Tuomas},
  title =	{{05011 Executive Summary – Computing and Markets}},
  booktitle =	{Computing and Markets},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2005},
  volume =	{5011},
  editor =	{Daniel Lehmann and Rudolf M\"{u}ller and Tuomas Sandholm},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.05011.2},
  URN =		{urn:nbn:de:0030-drops-2248},
  doi =		{10.4230/DagSemProc.05011.2},
  annote =	{Keywords: Algorithms, complexity, game theory, social choice, auctions, equilibrium}
}
Document
DOI: 10.4230/DagSemProc.05011.16
Sequences of Take-It-or-Leave-It Offers: Near-Optimal Auctions Without Full Valuation Revelation

Authors: Tuomas Sandholm and Andrew Gilpin

Published in: Dagstuhl Seminar Proceedings, Volume 5011, Computing and Markets (2005)

Abstract
We introduce take-it-or-leave-it auctions (TLAs) as an allocation mechanism that allows buyers to retain much of their private valuation information, yet generates close-to-optimal expected utility for the seller. We show that if each buyer receives at most one offer, each buyers dominant strategy is to act truthfully. In more general TLAs, the buyers optimal strategies are more intricate, and we derive the perfect Bayesian equilibrium for the game. We develop algorithms for finding the equilibrium and also for optimizing the offers so as to maximize the sellers expected utility. In several example settings we show that the sellers expected utility already is close to optimal for a small number of offers. As the number of buyers increases, the sellers expected utility increases, and becomes increasingly (but not monotonically) more competitive with Myersons expected utility maximizing auction.
Cite as

Tuomas Sandholm and Andrew Gilpin. Sequences of Take-It-or-Leave-It Offers: Near-Optimal Auctions Without Full Valuation Revelation. In Computing and Markets. Dagstuhl Seminar Proceedings, Volume 5011, pp. 1-17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2005)

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@InProceedings{sandholm_et_al:DagSemProc.05011.16,
  author =	{Sandholm, Tuomas and Gilpin, Andrew},
  title =	{{Sequences of Take-It-or-Leave-It Offers: Near-Optimal Auctions Without Full Valuation Revelation}},
  booktitle =	{Computing and Markets},
  pages =	{1--17},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2005},
  volume =	{5011},
  editor =	{Daniel Lehmann and Rudolf M\"{u}ller and Tuomas Sandholm},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.05011.16},
  URN =		{urn:nbn:de:0030-drops-2075},
  doi =		{10.4230/DagSemProc.05011.16},
  annote =	{Keywords: compact representation of games, congestion games, local-effect games, action-graph gamescomputational markets; auctions; bidding strategiesNegotiatio}
}
Document
DOI: 10.4230/DagSemProc.05011.17
Spiteful Bidding in Sealed-Bid Auctions

Authors: Felix Brandt, Tuomas Sandholm, and Yoav Shoham

Published in: Dagstuhl Seminar Proceedings, Volume 5011, Computing and Markets (2005)

Abstract
We study the bidding behavior of spiteful agents who, contrary to the common assumption of self-interest, maximize the weighted difference of their own profit and their competitors' profit. This assumption is motivated by inherent spitefulness, or, for example, by competitive scenarios such as in closed markets where the loss of a competitor will likely result in future gains for oneself. We derive symmetric Bayes Nash equilibria for spiteful agents in first-price and second-price sealed-bid auctions. In first-price auctions, bidders become "more truthful" the more spiteful they are. Surprisingly, the equilibrium strategy in second-price auctions does not depend on the number of bidders. Based on these equilibria, we compare revenue in both auction types. It turns out that expected revenue in second-price auctions is higher than expected revenue in first-price auctions whenever agents have the slightest interest in reducing others' profit as long as they still care for their own profit. In other words, revenue equivalence only holds for auctions in which all agents are either self-interested or completely malicious.
Cite as

Felix Brandt, Tuomas Sandholm, and Yoav Shoham. Spiteful Bidding in Sealed-Bid Auctions. In Computing and Markets. Dagstuhl Seminar Proceedings, Volume 5011, pp. 1-16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2005)

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@InProceedings{brandt_et_al:DagSemProc.05011.17,
  author =	{Brandt, Felix and Sandholm, Tuomas and Shoham, Yoav},
  title =	{{Spiteful Bidding in Sealed-Bid Auctions}},
  booktitle =	{Computing and Markets},
  pages =	{1--16},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2005},
  volume =	{5011},
  editor =	{Daniel Lehmann and Rudolf M\"{u}ller and Tuomas Sandholm},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.05011.17},
  URN =		{urn:nbn:de:0030-drops-1987},
  doi =		{10.4230/DagSemProc.05011.17},
  annote =	{Keywords: Auctions , Externalities , Spite , Revenue}
}
Document
DOI: 10.4230/DagSemRep.344
Electronic Market Design (Dagstuhl Seminar 02241)

Authors: Daniel Lehmann, Rudolf Müller, Tuomas Sandholm, and Rakesh V. Vohra

Published in: Dagstuhl Seminar Reports. Dagstuhl Seminar Reports, Volume 1 (2021)

Abstract
Cite as

Daniel Lehmann, Rudolf Müller, Tuomas Sandholm, and Rakesh V. Vohra. Electronic Market Design (Dagstuhl Seminar 02241). Dagstuhl Seminar Report 344, pp. 1-18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2002)

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@TechReport{lehmann_et_al:DagSemRep.344,
  author =	{Lehmann, Daniel and M\"{u}ller, Rudolf and Sandholm, Tuomas and Vohra, Rakesh V.},
  title =	{{Electronic Market Design (Dagstuhl Seminar 02241)}},
  pages =	{1--18},
  ISSN =	{1619-0203},
  year =	{2002},
  type = 	{Dagstuhl Seminar Report},
  number =	{344},
  institution =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemRep.344},
  URN =		{urn:nbn:de:0030-drops-152250},
  doi =		{10.4230/DagSemRep.344},
}
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