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Gamekeeper: Online Learning for Admission Control of Networked Open Multiagent Systems | IEEE Journals & Magazine | IEEE Xplore

Gamekeeper: Online Learning for Admission Control of Networked Open Multiagent Systems


Abstract:

We consider open games where players arrive according to a Poisson process with rate \lambda and stay in the game for an exponential random duration with rate \mu. Th...Show More

Abstract:

We consider open games where players arrive according to a Poisson process with rate \lambda and stay in the game for an exponential random duration with rate \mu. The game evolves in continuous time, where each player n sets an exponential random clock and updates his/her action a_{n}\in \lbrace 0,\ldots,K\rbrace when it expires. The players take independent actions according to local decision rules that, uninterrupted, are designed to converge to an equilibrium. When \lambda is small, the game spends most of the time in a (time-varying) equilibrium. This equilibrium exhibits predictable behavior and can have performance guarantees by design. However, when \lambda is too small, the system is underutilized since not many players are in the game on average. Choosing the maximal \lambda that the game can support while still spending a target fraction 0< \rho < 1 of the time at equilibrium requires knowing the reward functions. To overcome that, we propose an online learning algorithm that the gamekeeper uses to adjust the probability \theta to admit an incoming player. The gamekeeper only observes whether an action was changed without observing the action or who played it. We prove that our algorithm learns, with probability 1, a \theta ^{*} such that the game is at equilibrium for at least \rho fraction of the time, and no more than \rho +\varepsilon(\mu,\rho)< 1, where we specify \varepsilon(\mu,\rho). Our algorithm is a black-box method to transfer performance guarantees of distributed protocols from closed systems to open systems.
Published in: IEEE Transactions on Automatic Control ( Volume: 69, Issue: 11, November 2024)
Page(s): 7694 - 7709
Date of Publication: 08 May 2024

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