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In this work, we introduce a new variant of online gradient descent, whichprovably converges to Nash Equilibria and simultaneously attains sublinearregret for the class of congestion games in the semi-bandit feedback setting.Our proposed method admits convergence rates depending only polynomially on thenumber of players and the number of facilities, but not on the size of theaction set, which can be exponentially large in terms of the number offacilities. Moreover, the running time of our method has polynomial-timedependence on the implicit description of the game. As a result, our workanswers an open question from (Du et. al, 2022).

Semi Bandit Dynamics in Congestion Games: Convergence to Nash Equilibrium and No-Regret Guarantees