Supplementary information for Bayesian reinforcement learning and Bayesian deep learning for blockchains with mobile edge computing

Article abstract

We present a novel game-theoretic, Bayesian reinforcement learning (RL) and deep learning (DL) framework to represent interactions of miners in public and consortium blockchains with mobile edge computing (MEC). Within the framework, we formulate a stochastic game played by miners under incomplete information. Each miner can offload its block operations to one of the base stations (BSs) equipped with the MEC server. The miners select their offloading BSs and block processing rates simultaneously and independently, without informing other miners about their actions. As such, no miner knows the past and current actions of others and, hence, constructs its belief about these actions. Accordingly, we devise a Bayesian RL algorithm based on the partially-observable Markov decision process for miner's decision making that allows each miner to dynamically adjust its strategy and update its beliefs through repeated interactions with each other and with the mobile environment. We also propose a novel unsupervised Bayesian deep learning algorithm where the uncertainties about unobservable states are approximated with Bayesian neural networks. We show that the proposed Bayesian RL and DL algorithms converge to the stable states where the miners' actions and beliefs form the perfect Bayesian equilibrium (PBE) and myopic PBE, respectively.

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