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The variance-penalized stochastic shortest path problem


The stochastic shortest path problem (SSPP) asks to resolve the non-deterministic choices in a Markov decision process (MDP) such that the expected accumulated weight before reaching a target state is maximized. This paper addresses the optimization of the variance-penalized expectation (VPE) of the accumulated weight, which is a variant of the SSPP in which a multiple of the variance of accumulated weights is incurred as a penalty. It is shown that the optimal VPE in MDPs with non-negative weights as well as an optimal deterministic finite-memory scheduler can be computed in exponential space. The threshold problem whether the maximal VPE exceeds a given rational is shown to be EXPTIME-hard and to lie in NEXPTIME. Furthermore, a result of interest in its own right obtained on the way is that a variance-minimal scheduler among all expectation-optimal schedulers can be computed in polynomial time.
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hal-03776449 , version 1 (13-09-2022)


  • HAL Id : hal-03776449 , version 1


Jakob Piribauer, Ocan Sankur, Christel Baier. The variance-penalized stochastic shortest path problem. ICALP 2022 - 49th International Colloquium on Automata, Languages, and Programming, Jul 2022, Paris / Hybrid, France. pp.1-19. ⟨hal-03776449⟩
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