The variance-penalized stochastic shortest path problem
Abstract
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.
Cite
@article{arxiv.2204.12280,
title = {The variance-penalized stochastic shortest path problem},
author = {Jakob Piribauer and Ocan Sankur and Christel Baier},
journal= {arXiv preprint arXiv:2204.12280},
year = {2022}
}
Comments
This is the extended version of the conference version accepted for publication at ICALP 2022