Online shortest paths with confidence intervals for routing in a time varying random network

The increase in the world's population and rising standards of living is leading to an ever-increasing number of vehicles on the roads, and with it ever-increasing difficulties in traffic management. This traffic management in transport networks can be clearly optimized by using information and communication technologies referred as Intelligent Transport Systems (ITS). This management problem is usually reformulated as finding the shortest path in a time varying random graph. In this article, an online shortest path computation using stochastic gradient descent is proposed. This routing algorithm for ITS traffic management is based on the online Frank-Wolfe approach. Our improvement enables to find a confidence interval for the shortest path, by using the stochastic gradient algorithm for approximate Bayesian inference. The theory required to understand our approach is provided, as well as the implementation details.