Vehicles equipped with GPS localizers are an important sensory device for examining people’s movements and activities. Taxis equipped with GPS localizers serve the transportation needs of a large number of people driven by diverse needs; their traces can tell us where passengers were picked up and dropped off, which route was taken, and what steps the driver took to find a new passenger. In this article, we provide an exhaustive survey of the work on mining these traces. We first provide a formalization of the data sets, along with an overview of different mechanisms for preprocessing the data. We then classify the existing work into three main categories: social dynamics, traffic dynamics and operational dynamics. Social dynamics refers to the study of the collective behaviour of a city’s population, based on their observed movements; Traffic dynamics studies the resulting flow of the movement through the road network; Operational dynamics refers to the study and analysis of taxi driver’s modus operandi . We discuss the different problems currently being researched, the various approaches proposed, and suggest new avenues of research. Finally, we present a historical overview of the research work in this field and discuss which areas hold most promise for future research.

We present new algorithms for computing and approximating bisimulation metrics in Markov Decision Processes (MDPs). Bisimulation metrics are an elegant formalism that capture behavioral equivalence between states and provide strong theoretical guarantees on differences in optimal behaviour. Unfortunately, their computation is expensive and requires a tabular representation of the states, which has thus far rendered them impractical for large problems. In this paper we present a new version of the metric that is tied to a behavior policy in an MDP, along with an analysis of its theoretical properties. We then present two new algorithms for approximating bisimulation metrics in large, deterministic MDPs. The first does so via sampling and is guaranteed to converge to the true metric. The second is a differentiable loss which allows us to learn an approximation even for continuous state MDPs, which prior to this work had not been possible.

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