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The congestion game is a powerful model that encompasses a range ofengineering systems such as traffic networks and resource allocation. Itdescribes the behavior of a group of agents who share a common set of $F$facilities and take actions as subsets with $k$ facilities. In this work, westudy the online formulation of congestion games, where agents participate inthe game repeatedly and observe feedback with randomness. We proposeCongestEXP, a decentralized algorithm that applies the classic exponentialweights method. By maintaining weights on the facility level, the regret boundof CongestEXP avoids the exponential dependence on the size of possiblefacility sets, i.e., $\binom{F}{k} \approx F^k$, and scales only linearly with$F$. Specifically, we show that CongestEXP attains a regret upper bound of$O(kF\sqrt{T})$ for every individual player, where $T$ is the time horizon. Onthe other hand, exploiting the exponential growth of weights enables CongestEXPto achieve a fast convergence rate. If a strict Nash equilibrium exists, weshow that CongestEXP can converge to the strict Nash policy almostexponentially fast in $O(F\exp(-t^{1-\alpha}))$, where $t$ is the number ofiterations and $\alpha \in (1/2, 1)$.

Taming the Exponential Action Set: Sublinear Regret and Fast Convergence to Nash Equilibrium in Online Congestion Games