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Coalitions naturally exist in many real-world systems involving multiple decision makers such as ridesharing, security, and online ad auctions, but the coalition structure among the agents is often unknown. We propose and study an important yet previously overseen problem -- Coalition Structure Learning (CSL), where we aim to carefully design a series of games for the agents and infer the underlying coalition structure by observing their interactions in those games. We establish a lower bound on the sample complexity -- defined as the number of games needed to learn the structure -- of any algorithms for CSL and propose the Iterative Grouping (IG) algorithm for designing normal-form games to achieve the lower bound. We show that IG can be extended to other succinct games such as congestion games and graphical games. Moreover, we solve CSL in a more restrictive and practical setting: auctions. We show a variant of IG to solve CSL in the auction setting even if we cannot design the bidder valuations. Finally, we conduct experiments to evaluate IG in the auction setting and the results align with our theoretical analysis.
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Learning in Congestion Games with Bandit Feedback
In this paper, we investigate Nash-regret minimization in congestion games, a class of games with benign theoretical structure and broad real-world applications. We first propose a centralized algorithm based on the optimism in the face of uncertainty principle for congestion games with (semi-)bandit feedback, and obtain finite-sample guarantees. Then we propose a decentralized algorithm via a novel combination of the Frank-Wolfe method and G-optimal design. By exploiting the structure of the congestion game, we show the sample complexity of both algorithms depends only polynomially on the number of players and the number of facilities, but not the size of the action set, which can be exponentially large in terms of the number of facilities. We further define a new problem class, Markov congestion games, which allows us to model the non-stationarity in congestion games. We propose a centralized algorithm for Markov congestion games, whose sample complexity again has only polynomial dependence on all relevant problem parameters, but not the size of the action set.
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- Award ID(s):
- 2023166
- PAR ID:
- 10443269
- Date Published:
- Journal Name:
- Advances in neural information processing systems
- Issue:
- 35
- ISSN:
- 1049-5258
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
- Conference Paper:
- The DOI is not currently available.
