Rich behavioural models: illustration on journey planning
I will illustrate rich behavioral models in games and Markov decision processes through applications to journey planning in an uncertain environment. The shortest path problem asks to find a path of minimal length between a source vertex and a destination vertex within a weighted graph. It can be used to model minimization of travel time between two places in a town where the environment (traffic, weather, etc) is perfectly predictable. I will first discuss how it can be generalized to more realistic stochastic environments, in which case one usually wants to minimize its expected time to destination, or to maximize its chances to reach the destination within a given time. To that end, I will use (discrete) Markov decision processes. Then, I will present recent extensions allowing to reason about richer types of travel strategies (choice of route, mean of transport, etc): strategies that take into account both the length of a journey and its cost, strategies that minimize the expected travel time while providing strong guarantees on the worst-case travel time (i.e., when considering the environment as an opponent in a two-player game), and more. I will focus on the modeling power of the different models through natural application scenarios of the everyday life.