A sampling method based on distributed learning automata for solving stochastic shortest path problem

Abstract

This paper studies an iterative stochastic algorithm for solving the stochastic shortest path problem. This algorithm, which uses a distributed learning automata, tries to find the shortest path by taking a sufficient number of samples from the edges of the graph. In this algorithm, which edges to be sampled are determined dynamically as the algorithm proceeds. At each iteration of this algorithm, a distributed learning automata used to determine which edges to be sampled. This sampling method, which uses distributed learning automata, reduces the number of samplings from those edges, which may not be along the shortest path, and resulting in a reduction in the number of the edges to be sampled. In this paper, we propose a new method for analysis of the algorithm. The method proposed in this paper, unlike the previous ones, which were based on the Martingale theory, is based on the sampling. The proof given in this paper, unlike the previous ones, which were for a specific input graph, is not restricted to the input graph and is general. We also show that as the number of samples taken from the edges increases, the probability of finding the shortest path also increases. Experimental results obtained from some benchmark stochastic graphs and some random graphs also confirm the theoretical results.