The Stochastic Shortest Path Problem: A polyhedral combinatorics perspective

Matthieu Guillot and Gautier Stauffer

European Journal of Operational Research, 2020, vol. 285, issue 1, 148-158

Abstract: In this paper, we give a new framework for the stochastic shortest path problem in finite state and action spaces. Our framework generalizes both the frameworks proposed by Bertsekas and Tsitsiklis (1991) and by Bertsekas and Yu (2016). We prove that the problem is well-defined and (weakly) polynomial when (i) there is a way to reach the target state from any initial state and (ii) there is no transition cycle of negative costs (a generalization of negative cost cycles). These assumptions generalize the standard assumptions for the deterministic shortest path problem and our framework encapsulates the latter problem (in contrast with prior works). In this new setting, we can show that (a) one can restrict to deterministic and stationary policies, (b) the problem is still (weakly) polynomial through linear programming, (c) Value Iteration and Policy Iteration converge, and (d) we can extend Dijkstra’s algorithm.

Keywords: Markov processes; Stochastic shortest path; Value iteration; Policy iteration; Dijkstra (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:285:y:2020:i:1:p:148-158

DOI: 10.1016/j.ejor.2018.10.052

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