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# Online Learning for Traffic Navigation in Congested Networks

*Proceedings of The 34th International Conference on Algorithmic Learning Theory*, PMLR 201:642-662, 2023.

#### Abstract

We develop an online learning algorithm for a navigation platform to route travelers in a congested network with multiple origin-destination (o-d) pairs while simultaneously learning unknown cost functions of road segments (edges) using the crowd-sourced data. The number of travel requests is randomly realized, and the travel time of each edge is stochastically distributed with the mean being a linear function that increases with the edge load (the number of travelers who take the edge). In each step of our algorithm, the platform updates the estimates of cost function parameters using the collected travel time data, and maintains a rectangular confidence interval of each parameter. The platform then routes travelers in the next step using an optimistic strategy based on the lower bound of the up-to-date confidence interval. The key aspects of our setting include (i) the size and the spatial distribution of collected travel time data depend on travelersâ€™ routing strategies; (ii) we evaluate the regret of our algorithm for platforms with different objectives, ranging from minimizing the social cost to minimizing the individual cost of self-interested users. We prove that the regret upper bound of our algorithm is $O(\sqrt{T}\log(T)|E|)$, where $T$ is the time horizon, and $|E|$ is the number of edges in the network. Furthermore, we show that the regret bound decreases as the number of travelers increases, which implies that the platform learns faster with a larger user population. Finally, we implement our algorithm on the network of New York City, and demonstrate the efficacy of the proposed algorithm.