Convergence of mirror descent dynamics in the routing game
2015 European Control Conference (ECC)(2015)
摘要
We consider a routing game played on a graph, in which different populations of drivers (or packet routers) iteratively make routing decisions and seek to minimize their delays. The Nash equilibria of the game are known to be the minimizers of a convex potential function, over the product of simplexes which represent the strategy spaces of the populations. We consider a class of population dynamics which only uses local loss information, and which can be interpreted as a mirror descent on the convex potential. We show that for vanishing, non-summable learning rates, mirror descent dynamics are guaranteed to converge to the set of Nash equilibria, and derive convergence rates as a function of the learning rate sequences of each population, and illustrate these results on numerical examples.
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关键词
mirror-descent dynamics,convergence,routing game,graph theory,packet routers,delay minimization,Nash equilibria,convex potential function minimizers,simplex product,strategy space representation,population dynamics,local loss information,convex potential,nonsummable learning rates,convergence rates,learning rate sequence
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