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The Stochastic Shortest Path Problem: A polyhedral combinatorics perspective

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  • Guillot, Matthieu
  • Stauffer, Gautier

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.

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  • Guillot, Matthieu & Stauffer, Gautier, 2020. "The Stochastic Shortest Path Problem: A polyhedral combinatorics perspective," European Journal of Operational Research, Elsevier, vol. 285(1), pages 148-158.
    • Handle: RePEc:eee:ejores:v:285:y:2020:i:1:p:148-158
    DOI: 10.1016/j.ejor.2018.10.052
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    References listed on IDEAS

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    Cited by:

    1. Lee, Jisun & Joung, Seulgi & Lee, Kyungsik, 2022. "A fully polynomial time approximation scheme for the probability maximizing shortest path problem," European Journal of Operational Research, Elsevier, vol. 300(1), pages 35-45.

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