We examine an adaptive learning framework for nonatomic congestion games where the players' cost functions may be subject to exogenous fluctuations (e.g., due to disturbances in the network, variations in the traffic going through a link). In this setting, the popular multiplicative/ exponential weights algorithm enjoys an $\mathcal{O}(1/\sqrt{T})$ equilibrium convergence rate; however, this rate is suboptimal in static environments---i.e., when the network is not subject to randomness. In this static regime, accelerated algorithms achieve an $\mathcal{O}(1/T^{2})$ convergence speed, but they fail to converge altogether in stochastic problems. To fill this gap, we propose a novel, adaptive exponential weights method---dubbed AdaWeight---that seamlessly interpolates between the $\mathcal{O}(1/T^{2})$ and $\mathcal{O}(1/\sqrt{T})$ rates in the static and stochastic regimes respectively. Importantly, this best-of-both-worlds guarantee does not require any prior knowledge of the problem's parameters or tuning by the optimizer; in addition, the method's convergence speed depends subquadratically on the size of the network (number of vertices and edges), so it scales gracefully to large, real-life urban networks.

The Multiplicative Weights Update (MWU) method is a ubiquitous meta-algorithm that works as follows: A distribution is maintained on a certain set, and at each step the probability assigned to action $\gamma$ is multiplied by $(1 -\epsilon C(\gamma))> 0$ where $C(\gamma)$ is the ``cost of action $\gamma$ and then rescaled to ensure that the new values form a distribution. We analyze MWU in congestion games where agents use \textit{arbitrary admissible constants} as learning rates $\epsilon$ and prove convergence to \textit{exact Nash equilibria}. Interestingly, this convergence result does not carry over to the nearly homologous MWU variant where at each step the probability assigned to action $\gamma$ is multiplied by $(1 -\epsilon)^{C(\gamma)}$ even for the simplest case of two-agent, two-strategy load balancing games, where such dynamics can provably lead to limit cycles or even chaotic behavior.

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To help address these issues, a natural approach is to consider games with special structures. In this paper, we focus on congestion games.

In Facility Location problems there are agents that should be connected to facilities and locations where facilities may be opened so that agents can connect to them. We depart from Uncapacitated Facility Location and by assuming that the connection costs of agents to facilities are congestion dependent, we define a novel problem, namely, Facility Location for Congesting (Selfish) Commuters. The connection costs of agents to facilities come as a result of how the agents commute to reach the facilities in an underlying network with cost functions on the edges. Inapproximability results follow from the related literature and thus approximate solutions is all we can hope for. For when the cost functions are nondecreasing we employ in a novel way an approximate version of Caratheodory's Theorem [5] to show how approximate solutions for different versions of the problem can be derived. For when the cost functions are nonincreasing we show how this problem generalizes the Cost-Distance problem [38] and provide an algorithm that for this more general case achieves the same approximation guarantees.

Urban traffic congestion stems from the misalignment between self-interested routing decisions and socially optimal flows. Intersections, as critical bottlenecks, amplify these inefficiencies because existing control schemes often neglect drivers' strategic behavior. Autonomous intersections, enabled by vehicle-to-infrastructure communication, permit vehicle-level scheduling based on individual requests. Leveraging this fine-grained control, we propose a non-monetary mechanism that strategically adjusts request timestamps-delaying or advancing passage times-to incentivize socially efficient routing. We present a hierarchical architecture separating local scheduling by roadside units from network-wide timestamp adjustments by a central planner. We establish an experimentally validated analytical model, prove the existence and essential uniqueness of equilibrium flows and formulate the planner's problem as an offline bilevel optimization program solvable with standard tools. Experiments on the Sioux Falls network show up to a 68% reduction in the efficiency gap between equilibrium and optimal flows, demonstrating scalability and effectiveness.