Label-setting methods for Multimode Stochastic Shortest Path problems on graphs

TL;DR

This paper extends label-setting methods to a class of Multimode Stochastic Shortest Path problems, providing conditions for their applicability and exploring connections with Hamilton-Jacobi equations.

Contribution

It introduces sufficient conditions for applying label-setting algorithms to Multimode SSPs and relates these problems to discretized Hamilton-Jacobi equations.

Findings

Established conditions for label-setting applicability to Multimode SSPs

Demonstrated the approach on stochastic control examples

Connected SSPs with discretizations of Hamilton-Jacobi equations

Abstract

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.