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Creators/Authors contains: "Merten, Samuel"

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  1. ; ; (, 27th European Symposium on Programming (ESOP))
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  2. ; ; (, Journal of Formalized Reasoning)
    We report on the formalization in Ssreflect/Coq of a number of concepts and results from algorithmic game theory, including potential games, smooth games, solution concepts such as Pure and Mixed Nash Equilibria, Coarse Correlated Equilibria, epsilon-approximate equilibria, and behavioral models of games such as best-response dynamics. We apply the formalization to prove Price of Stability bounds for, and convergence under best-response dynamics of, the Atomic Routing game, which has applications in computer networking. Our second application proves that Affine Congestion games are (5/3, 1/3)-smooth, and therefore have Price of Anarchy 5/2. Our formalization is available online. 
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  3. ; ; (, PODC '17: Proceedings of the ACM Symposium on Principles of Distributed Computing)
    The Multiplicative Weights Update method (MWU) is a simple yet powerful algorithm for learning linear classifiers, for ensemble learning a la boosting, for approximately solving linear and semidefinite systems, for computing approximate solutions to multicommodity flow problems, and for online convex optimization, among other applications. In this brief announcement, we apply techniques from interactive theorem proving to define and prove correct the first formally verified implementation of MWU (specifically, we show that our MWU is no regret). Our primary application -- and one justification of the relevance of our work to the PODC community -- is to verified multi-agent systems, such as distributed multi-agent network flow and load balancing games, for which verified MWU provides a convenient method for distributed computation of approximate Coarse Correlated Equilibria. 
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