Distributionally Robust Routing Problems
Date:
Abstract: Given a probability distribution over the cost function of edges in a graph, a stochastic routing optimisation problem finds a route in the graph that minimises a risk function of the route cost. In practise, it is rare that we have access to the true data-generating distribution over edge costs. Instead, we are given a set of empirical cost observations. From the observations, we can construct a (Bayesian) machine learning model of the costs, then do out-of-sample prediction with our model on new, unseen data. If the observations are noisy or in limited supply - or if our model is misspecified - we might not trust the posterior predictive distribution of the model. In this talk, we discuss routing optimisation algorithms that are robust with respect to an ambiguity set of distributions that are close to the predictive distribution of the model. Real-world applications to air pollution are demonstrated.