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We consider the traffic assignment problem in nonatomic routing games wherethe players' cost functions may be subject to random fluctuations (e.g.,weather disturbances, perturbations in the underlying network, etc.). We tacklethis problem from the viewpoint of a control interface that makes routingrecommendations based solely on observed costs and without any furtherknowledge of the system's governing dynamics -- such as the network's costfunctions, the distribution of any random events affecting the network, etc. Inthis online setting, learning methods based on the popular exponential weightsalgorithm converge to equilibrium at an $\mathcal{O}({1/\sqrt{T}})$ rate: thisrate is known to be order-optimal in stochastic networks, but it is otherwisesuboptimal in static networks. In the latter case, it is possible to achieve an$\mathcal{O}({1/T^{2}})$ equilibrium convergence rate via the use of finelytuned accelerated algorithms; on the other hand, these accelerated algorithmsfail to converge altogether in the presence of persistent randomness, so it isnot clear how to achieve the "best of both worlds" in terms of convergencespeed. Our paper seeks to fill this gap by proposing an adaptive routingalgortihm with the following desirable properties: $(i)$ it seamlesslyinterpolates between the $\mathcal{O}({1/T^{2}})$ and$\mathcal{O}({1/\sqrt{T}})$ rates for static and stochastic environmentsrespectively; $(ii)$ its convergence speed is polylogarithmic in the number ofpaths in the network; ${(iii)}$ the method's per-iteration complexity andmemory requirements are both linear in the number of nodes and edges in thenetwork; and ${(iv)}$ it does not require any prior knowledge of the problem'sparameters.

Routing in an Uncertain World: Adaptivity, Efficiency, and Equilibrium