Extended distributed learning automata: An automata-based framework for solving stochastic graph optimization problems

In this paper, a new structure for cooperative learning automata called extended learning automata (eDLA) is introduced. Based on the new structure, an iterative randomized heuristic algorithm using sampling is proposed for finding an optimal subgraph in a stochastic edge-weighted graph. Stochastic graphs are graphs in which the weights of edges have an unknown probability distribution. The proposed algorithm uses an eDLA to find a policy that leads to a subgraph that satisfy some restrictions such as minimum or maximum weight (length). At each stage of the proposed algorithm, the eDLA determines which edges should be sampled. The proposed eDLA-based sampling method may reduce unnecessary samples and hence decrease the time required for finding an optimal subgraph. It is shown that the proposed method converges to an optimal solution, the probability of which can be made arbitrarily close to 1 by using a sufficiently small learning parameter. A new variance-aware threshold value is also proposed that can significantly improve the convergence rate of the proposed eDLA-based algorithm. It is further shown that our algorithm is competitive in terms of the quality of the solution. © 2014, Springer Science+Business Media New York.