Label-setting methods for Multimode Stochastic Shortest Path problems on graphs
It extends efficient label-setting methods to a broader class of stochastic shortest path problems, benefiting researchers in stochastic control and related fields.
The paper defines a class of Multimode Stochastic Shortest Path problems and develops sufficient conditions for applying label-setting methods (e.g., Dijkstra's algorithm) to solve them, illustrating the approach on discrete stochastic control examples.
Stochastic shortest path (SSP) problems arise in a variety of discrete stochastic control contexts. An optimal solutions to such a problem is typically computed using the value function, which can be found by solving the corresponding dynamic programming equations. In the deterministic case, these equations can be often solved by the highly efficient label-setting methods (such as Dijkstra's and Dial's algorithms). In this paper we define and study a class of Multimode Stochastic Shortest Path problems and develop sufficient conditions for the applicability of label-setting methods. We illustrate our approach on a number of discrete stochastic control examples. We also discuss the relationship of SSPs with discretizations of static Hamilton-Jacobi equations and provide an alternative derivation for several fast (non-iterative) numerical methods for these PDEs.