Efficient Learning for Decomposing and Optimizing Random Networks

• Main Authors: Li, Haidong, Peng, Yijie, Xu, Xiaoyun, Heidergott, Bernd F, Chen, Chun-Hung
• Format: text
• Published: Archīum Ateneo 2022
• Subjects: Bayesian learning; Random network; Markov chain; Dynamic decomposition; Ranking and selection; Mathematics; Physical Sciences and Mathematics; Statistics and Probability
• Online Access: https://archium.ateneo.edu/gsb-pubs/75; https://doi.org/10.1016/j.fmre.2022.01.018
• Institution: Ateneo De Manila University

In this study, we consider the problem of node ranking in a random network. A Markov chain is defined for the network, and its transition probability matrix is unknown but can be learned by sampling random interactions among nodes. Our objective is to decompose the Markov chain into several ergodic classes and select the best node in each ergodic class. We propose a dynamic sampling procedure, which gives a probability guarantee on correct decomposition and maximizes a weighted probability of correct selection of the best node in each ergodic class. Numerical experiment results demonstrate the efficiency of the proposed sampling procedure.