10.4230/LIPIcs.FSTTCS.2012.461
Chatterjee, Krishnendu
Krishnendu
Chatterjee0000-0002-4561-241X
Joglekar, Manas
Manas
Joglekar
Shah, Nisarg
Nisarg
Shah
Average case analysis of the classical algorithm for Markov decision processes with Büchi objectives
LIPIcs
Schloss Dagstuhl - Leibniz-Zentrum für Informatik
2012
2018-12-11T11:59:13Z
2020-01-17T09:32:05Z
conference
https://research-explorer.app.ist.ac.at/record/2715
https://research-explorer.app.ist.ac.at/record/2715.json
519040 bytes
application/pdf
We consider Markov decision processes (MDPs) with specifications given as Büchi (liveness) objectives. We consider the problem of computing the set of almost-sure winning vertices from where the objective can be ensured with probability 1. We study for the first time the average case complexity of the classical algorithm for computing the set of almost-sure winning vertices for MDPs with Büchi objectives. Our contributions are as follows: First, we show that for MDPs with constant out-degree the expected number of iterations is at most logarithmic and the average case running time is linear (as compared to the worst case linear number of iterations and quadratic time complexity). Second, for the average case analysis over all MDPs we show that the expected number of iterations is constant and the average case running time is linear (again as compared to the worst case linear number of iterations and quadratic time complexity). Finally we also show that given that all MDPs are equally likely, the probability that the classical algorithm requires more than constant number of iterations is exponentially small.