Lightweight Monte Carlo Algorithm for Markov Decision Processes.
Axel Legay, Sean Sedwards · arXiv (Cornell University) · 2013
Markov decision processes are widely used to model optimisation problems and concurrent systems, but only relatively small models may be solved exactly, due to the typically intractable number of states of a system. By considering schedulers based on the states visited by simulations, algorithms exist to find approximate solutions, but the number of states visited also becomes rapidly intractable. We present a lightweight Monte Carlo algorithm that may be used for statistical model checking Markov decision processes and other models that mix nondeterminism with probabilistic transitions. The algorithm uses an O(1) memory representation of general schedulers, based on pseudo-random number generators and hash functions, and may be efficiently parallelised. We provide confidence bounds and propose novel ways in which the algorithm may be profitably extended.