Efficient Approximation of Optimal Control for Markov Games



Fearnley, John, Rabe, Markus, Schewe, Sven ORCID: 0000-0002-9093-9518 and Zhang, Lijun
(2010) Efficient Approximation of Optimal Control for Markov Games.

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Abstract

We study the time-bounded reachability problem for continuous-time Markov decision processes (CTMDPs) and games (CTMGs). Existing techniques for this problem use discretisation techniques to break time into discrete intervals, and optimal control is approximated for each interval separately. Current techniques provide an accuracy of O(\epsilon^2) on each interval, which leads to an infeasibly large number of intervals. We propose a sequence of approximations that achieve accuracies of O(\epsilon^3), O(\epsilon^4), and O(\epsilon^5), that allow us to drastically reduce the number of intervals that are considered. For CTMDPs, the performance of the resulting algorithms is comparable to the heuristic approach given by Buckholz and Schulz, while also being theoretically justified. All of our results generalise to CTMGs, where our results yield the first practically implementable algorithms for this problem. We also provide positional strategies for both players that achieve similar error bounds.

Item Type: Article
Uncontrolled Keywords: cs.GT, cs.GT, cs.SY, math.OC
Depositing User: Symplectic Admin
Date Deposited: 27 Jul 2018 15:27
Last Modified: 09 May 2022 15:11
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3009302