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Artificial Intelligence
 
Data Science
 
Algorithms

[Mechanism Design Theme invited talk] The Complexity of Symmetric Equilibria in Min-Max Optimization and Team Zero-Sum Games

Dates
2025-02-19 14:50 - 16:00
Venue
Artemidos 1 - Amphitheater
Title: The Complexity of Symmetric Equilibria in Min-Max Optimization and Team Zero-Sum Games

Speaker: Ioannis Panageas (UC Irvine)

Abstract:  We consider the problem of computing stationary points in min-max optimization, with a particular focus on the special case of computing Nash equilibria in (two-)team zero-sum games. We first show that computing ε-Nash equilibria in 3-player adversarial team games -- wherein a team of 2 players competes against a single adversary -- is CLS-complete, resolving the complexity of Nash equilibria in such settings. Our proof proceeds by reducing from symmetric ε-Nash equilibria in symmetric, identical-payoff, two-player games, by suitably leveraging the adversarial player so as to enforce symmetry -- without disturbing the structure of the game. In particular, the class of instances we construct comprises solely polymatrix games, thereby also settling a question left open by Hollender, Maystre, and Nagarajan (2024). We also provide some further results concerning equilibrium computation in adversarial team games. 
Moreover, we establish that computing symmetric (first-order) equilibria in \emph{symmetric} min-max optimization is PPAD-complete, even for quadratic functions. Building on this reduction, we further show that computing symmetric ε-Nash equilibria in symmetric, 6-player (3 vs. 3) team zero-sum games is also PPAD-complete, even for ϵ=poly(1/n). As an immediate corollary, this precludes the existence of symmetric dynamics -- which includes many of the algorithms considered in the literature -- converging to stationary points. Finally, we prove that computing a non-symmetric poly(1/n)-equilibrium in symmetric min-max optimization is FNP-hard.

Short Bio: Ioannis Panageas is an Assistant Professor of Computer Science at UC Irvine and a researcher at Archimedes Research unit. He is interested in the theory of computation, machine learning and its interface with non-convex optimization, dynamical systems, learning in games, statistics and multi-agent reinforcement learning. Before joining UCI, he was an Assistant Professor at Singapore University of Technology and Design. Prior to that he was a MIT postdoctoral fellow. He received his PhD in Algorithms, Combinatorics and Optimization from Georgia Tech in 2016, a Diploma in EECS from National Technical University of Athens, and a MS in Mathematics from Georgia Tech. He is the recipient of the 2019 NRF fellowship for AI.

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Vision

To position Greece as a leading player in AI and Data Science

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Mission

To build an AI Excellence Hub in Greece where the international research community can connect, groundbreaking ideas can thrive, and the next generation of scientists emerges, shaping a brighter future for Greece and the world

 

Welcome to ARCHIMEDES, a vibrant research hub connecting the global AI and Data Science research community fostering groundbreaking research in Greece and beyond. Its dedicated core team, comprising lead researchers, affiliated researchers, Post-Docs, PhDs and interns, is committed to advancing basic and applied research in Artificial Intelligence and its supporting disciplines, including Algorithms, Statistics, Learning Theory, and Game Theory organized around 8 core research areas. By collaborating with Greek and Foreign Universities and Research Institutes, ARCHIMEDES disseminates its research findings fostering knowledge exchange and providing enriching opportunities for students. Leveraging AI to address real-world challenges, ARCHIMEDES promotes innovation within the Greek ecosystem and extends its societal impact. Established in January 2022, as a research unit of the Athena Research Center with support from the Committee Greece 2021, ARCHIMEDES is funded for its first four years by the EU Recovery and Resilience Facility (RRF).

 
 

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The project “ARCHIMEDES Unit: Research in Artificial Intelligence, Data Science and Algorithms” with code OPS 5154714 is implemented by the National Recovery and Resilience Plan “Greece 2.0” and is funded by the European Union – NextGenerationEU.

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