Blockchain plays a crucial role in ensuring the security and integrity of decentralized systems, with the proof-of-work (PoW) mechanism being fundamental for achieving distributed consensus. As PoW blockchains see broader adoption, an increasingly diverse set of miners with varying computing capabilities participate in the network. In this paper, we consider the PoWblockchain mining, where the miners are associated with resource uncertainties. To characterize the uncertainty computing resources at different mining participants, we establish an ambiguous set representing uncertainty of resource distributions. Then, the networked mining is formulated as a non-cooperative game, where distributionally robust performance is calculated for each individual miner to tackle the resource uncertainties. We prove the existence of the equilibrium of the distributionally robust mining game. To derive the equilibrium, we propose the conditional value-at-risk (CVaR)-based reinterpretation of the best response of each miner. We then solve the individual strategy with alternating optimization, which facilitates the iteration among miners towards the game equilibrium. Furthermore, we consider the case that the ambiguity of resource distribution reduces to Gaussian distribution and the case that another uncertainties vanish, and then characterize the properties of the equilibrium therein along with a distributed algorithm to achieve the equilibrium. Simulation results show that the proposed approaches effectively converge to the equilibrium, and effectively tackle the uncertainties in blockchain mining to achieve a robust performance guarantee.

Over-the-air computation (AirComp) is a promising technique that addresses big data collection and fast wireless data aggregation. However, in a network where wireless communication and AirComp coexist, mutual interference becomes a critical challenge. In this paper, we propose to employ an unmanned aerial vehicle (UAV) to enable integrated communication and AirComp, where we capitalize on UAV mobility with alleviated interference for performance enhancement. Particularly, we aim to maximize the sum of user transmission rate with the guaranteed AirComp accuracy requirement, where we jointly optimize the transmission strategy, signal normalizing factor, scheduling strategy, and UAV trajectory. We decouple the formulated problem into two layers where the outer layer is for UAV trajectory and scheduling, and the inner layer is for transmission and computation. Then, we solve the inner layer problem through alternating optimization, and the outer layer is solved through soft actor–critic-based deep reinforcement learning. Simulation results show the convergence of the proposed learning process and also demonstrate the performance superiority of our proposal as compared with the baselines in various situations.

In blockchain systems characterized by computation competition, allocating computation resources is of paramount significance for the economic benefits of nodes. Besides, uncer-tainties 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.

The Internet of Things (IoT) can be conveniently deployed while empowering various applications, where the IoT nodes can form clusters to finish certain missions collectively. In this paper, we propose to employ unmanned aerial vehicles (UAVs) to assist the clustered IoT data collection with blockchain-based security provisioning. In particular, the UAVs generate candidate blocks based on the collected data, which are then audited through a lightweight proof-of-stake consensus mechanism within the UAV-based blockchain network. To motivate efficient blockchain while reducing the operational cost, a stake pool is constructed at the active UAV while encouraging stake investment from other UAVs with profit sharing. The problem is formulated to maximize the overall profit through the blockchain system in unit time by jointly investigating the IoT transmission, incentives through investment and profit-sharing, and UAV deployment strategies. Then, the problem is solved in a distributed manner while being decoupled into two layers. The inner layer incorporates IoT transmission and incentive design, which are tackled with large-system approximation and one-leader-multi-follower Stackelberg game analysis, respectively. The outer layer for UAV deployment is undertaken with a multi-agent deep deterministic policy gradient approach. Results show the convergence of the proposed learning process and the UAV deployment, and also demonstrated the performance superiority of our proposal as compared with the baselines.

Internet of Things (IoT) can be conveniently de-ployed while empowering various applications, where the IoT nodes can form clusters to finish certain missions collectively. In this paper, we propose to employ unmanned aerial vehicles (UAVs) to assist the IoT data collection with blockchain-based security provisioning, towards efficient and safeguarded IoT operations. In particular, a blockchain with proof-of-stake (PoS) consensus mechanism is constructed among the UAVs with the collected IoT data. Correspondingly, we optimize the IoT communication and the UAV deployment for the maximum blockchain throughput considering the PoS procedure. The problem is solved with a deep deterministic policy gradient-based approach, where the power allocation is obtained with closed-form solutions and the UAV deployment is learned with actor-critic networks. Simulation results are provided to show the deployment and performance, corroborating the effectiveness of our proposal.