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Documents authored by Schmid, Laura


Document
On the Convergence Time in Graphical Games: A Locality-Sensitive Approach

Authors: Juho Hirvonen, Laura Schmid, Krishnendu Chatterjee, and Stefan Schmid

Published in: LIPIcs, Volume 286, 27th International Conference on Principles of Distributed Systems (OPODIS 2023)


Abstract
Graphical games are a useful framework for modeling the interactions of (selfish) agents who are connected via an underlying topology and whose behaviors influence each other. They have wide applications ranging from computer science to economics and biology. Yet, even though an agent’s payoff only depends on the actions of their direct neighbors in graphical games, computing the Nash equilibria and making statements about the convergence time of "natural" local dynamics in particular can be highly challenging. In this work, we present a novel approach for classifying complexity of Nash equilibria in graphical games by establishing a connection to local graph algorithms, a subfield of distributed computing. In particular, we make the observation that the equilibria of graphical games are equivalent to locally verifiable labelings (LVL) in graphs; vertex labelings which are verifiable with constant-round local algorithms. This connection allows us to derive novel lower bounds on the convergence time to equilibrium of best-response dynamics in graphical games. Since we establish that distributed convergence can sometimes be provably slow, we also introduce and give bounds on an intuitive notion of "time-constrained" inefficiency of best responses. We exemplify how our results can be used in the implementation of mechanisms that ensure convergence of best responses to a Nash equilibrium. Our results thus also give insight into the convergence of strategy-proof algorithms for graphical games, which is still not well understood.

Cite as

Juho Hirvonen, Laura Schmid, Krishnendu Chatterjee, and Stefan Schmid. On the Convergence Time in Graphical Games: A Locality-Sensitive Approach. In 27th International Conference on Principles of Distributed Systems (OPODIS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 286, pp. 11:1-11:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{hirvonen_et_al:LIPIcs.OPODIS.2023.11,
  author =	{Hirvonen, Juho and Schmid, Laura and Chatterjee, Krishnendu and Schmid, Stefan},
  title =	{{On the Convergence Time in Graphical Games: A Locality-Sensitive Approach}},
  booktitle =	{27th International Conference on Principles of Distributed Systems (OPODIS 2023)},
  pages =	{11:1--11:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-308-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{286},
  editor =	{Bessani, Alysson and D\'{e}fago, Xavier and Nakamura, Junya and Wada, Koichi and Yamauchi, Yukiko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2023.11},
  URN =		{urn:nbn:de:0030-drops-195015},
  doi =		{10.4230/LIPIcs.OPODIS.2023.11},
  annote =	{Keywords: distributed computing, Nash equilibria, mechanism design, best-response dynamics}
}
Document
Flooding with Absorption: An Efficient Protocol for Heterogeneous Bandits over Complex Networks

Authors: Junghyun Lee, Laura Schmid, and Se-Young Yun

Published in: LIPIcs, Volume 286, 27th International Conference on Principles of Distributed Systems (OPODIS 2023)


Abstract
Multi-armed bandits are extensively used to model sequential decision-making, making them ubiquitous in many real-life applications such as online recommender systems and wireless networking. We consider a multi-agent setting where each agent solves their own bandit instance endowed with a different set of arms. Their goal is to minimize their group regret while collaborating via some communication protocol over a given network. Previous literature on this problem only considered arm heterogeneity and networked agents separately. In this work, we introduce a setting that encompasses both features. For this novel setting, we first provide a rigorous regret analysis for a standard flooding protocol combined with the classic UCB policy. Then, to mitigate the issue of high communication costs incurred by flooding in complex networks, we propose a new protocol called Flooding with Absorption (FwA). We provide a theoretical analysis of the resulting regret bound and discuss the advantages of using FwA over flooding. Lastly, we experimentally verify on various scenarios, including dynamic networks, that FwA leads to significantly lower communication costs despite minimal regret performance loss compared to other network protocols.

Cite as

Junghyun Lee, Laura Schmid, and Se-Young Yun. Flooding with Absorption: An Efficient Protocol for Heterogeneous Bandits over Complex Networks. In 27th International Conference on Principles of Distributed Systems (OPODIS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 286, pp. 20:1-20:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{lee_et_al:LIPIcs.OPODIS.2023.20,
  author =	{Lee, Junghyun and Schmid, Laura and Yun, Se-Young},
  title =	{{Flooding with Absorption: An Efficient Protocol for Heterogeneous Bandits over Complex Networks}},
  booktitle =	{27th International Conference on Principles of Distributed Systems (OPODIS 2023)},
  pages =	{20:1--20:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-308-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{286},
  editor =	{Bessani, Alysson and D\'{e}fago, Xavier and Nakamura, Junya and Wada, Koichi and Yamauchi, Yukiko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2023.20},
  URN =		{urn:nbn:de:0030-drops-195100},
  doi =		{10.4230/LIPIcs.OPODIS.2023.20},
  annote =	{Keywords: multi-armed bandits, multi-agent systems, collaborative learning, network protocol, flooding}
}
Document
The Evolutionary Price of Anarchy: Locally Bounded Agents in a Dynamic Virus Game

Authors: Laura Schmid, Krishnendu Chatterjee, and Stefan Schmid

Published in: LIPIcs, Volume 153, 23rd International Conference on Principles of Distributed Systems (OPODIS 2019)


Abstract
The Price of Anarchy (PoA) is a well-established game-theoretic concept to shed light on coordination issues arising in open distributed systems. Leaving agents to selfishly optimize comes with the risk of ending up in sub-optimal states (in terms of performance and/or costs), compared to a centralized system design. However, the PoA relies on strong assumptions about agents' rationality (e.g., resources and information) and interactions, whereas in many distributed systems agents interact locally with bounded resources. They do so repeatedly over time (in contrast to "one-shot games"), and their strategies may evolve. Using a more realistic evolutionary game model, this paper introduces a realized evolutionary Price of Anarchy (ePoA). The ePoA allows an exploration of equilibrium selection in dynamic distributed systems with multiple equilibria, based on local interactions of simple memoryless agents. Considering a fundamental game related to virus propagation on networks, we present analytical bounds on the ePoA in basic network topologies and for different strategy update dynamics. In particular, deriving stationary distributions of the stochastic evolutionary process, we find that the Nash equilibria are not always the most abundant states, and that different processes can feature significant off-equilibrium behavior, leading to a significantly higher ePoA compared to the PoA studied traditionally in the literature.

Cite as

Laura Schmid, Krishnendu Chatterjee, and Stefan Schmid. The Evolutionary Price of Anarchy: Locally Bounded Agents in a Dynamic Virus Game. In 23rd International Conference on Principles of Distributed Systems (OPODIS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 153, pp. 21:1-21:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)


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@InProceedings{schmid_et_al:LIPIcs.OPODIS.2019.21,
  author =	{Schmid, Laura and Chatterjee, Krishnendu and Schmid, Stefan},
  title =	{{The Evolutionary Price of Anarchy: Locally Bounded Agents in a Dynamic Virus Game}},
  booktitle =	{23rd International Conference on Principles of Distributed Systems (OPODIS 2019)},
  pages =	{21:1--21:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-133-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{153},
  editor =	{Felber, Pascal and Friedman, Roy and Gilbert, Seth and Miller, Avery},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2019.21},
  URN =		{urn:nbn:de:0030-drops-118071},
  doi =		{10.4230/LIPIcs.OPODIS.2019.21},
  annote =	{Keywords: Evolutionary Games, Virus Propagation, Price of Anarchy, Analysis}
}
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