Path planning with user route preference - A reward surface approximation approach using orthogonal Legendre polynomials

As self driving cars become more ubiquitous, users would look for natural ways of informing the car AI about their personal choice of routes. This choice is not always dictated by straightforward logic such as shortest distance or shortest time, and can be influenced by hidden factors, such as comfort and familiarity. This paper presents a path learning algorithm for such applications, where from limited positive demonstrations, an autonomous agent learns the user's path preference and honors that choice in its route planning, but has the capability to adopt alternate routes, if the original choice(s) become impractical. The learning problem is modeled as a Markov decision process. The states (way-points) and actions (to move from one way-point to another) are pre-defined according to the existing network of paths between the origin and destination and the user's demonstration is assumed to be a sample of the preferred path. The underlying reward function which captures the essence of the demonstration is computed using an inverse reinforcement learning algorithm and from that the entire path mirroring the expert's demonstration is extracted. To alleviate the problem of state space explosion when dealing with a large state space, the reward function is approximated using a set of orthogonal polynomial basis functions with a fixed number of coefficients regardless of the size of the state space. A six fold reduction in total learning time is achieved compared to using simple basis functions, that has dimensionality equal to the number of distinct states.