Distributionally Robust Mining for Proof-of-Work Blockchain Under Resource Uncertainties

In blockchain systems characterized by computation competition, allocating computation resources is of paramount significance for the economic benefits of nodes. Besides, uncertainties of computation resources also affect the node's profits. In this paper, we address the computation resource allocation issue within a proof-of-work (PoW) blockchain system without exact information on the available resources, which impedes the direct investigation of the maximum mining profit. Correspondingly, we establish the chance-constrained threshold for maximum achievable profit through the blockchain in an uncertain environment and maximize this threshold under a given outage probability. Particularly, the uncertain computation resource is modeled only with its first and second statistics, which lack the exact distribution information. In this respect, we propose the distributionally robust approach to tackle the chance-constrained resource allocation strategy, which guarantees the intended profit threshold regardless of the actual distribution. We show that the considered problem admits a conditional value-at-risk (CVaR) approximation reformulation, which can be handled by alternately optimizing the resource allocation strategy and the profit threshold. Simulation results demonstrate that the proposed design is robust against the uncertainty distribution, and effectively guarantees the profits of miners.