What are the optimal times for an Internet of Things (IoT) device to act as a blockchain miner? The aim is to minimize the energy consumed by low-power IoT devices that log their data into a secure (tamper-proof) distributed ledger. We formulate the energy-efficient blockchain mining for IoT devices as a multiple-stopping time partially observed Markov decision process (POMDP) to maximize the probability of adding a block in the blockchain; we also present a model to optimize the number of stops (mining instants). In general, POMDPs are computationally intractable to solve, but we show mathematically using submodularity that the optimal mining policy has a useful structure: 1) it is monotone in belief space, and 2) it exhibits a threshold structure, which divides the belief space into two connected sets. Exploiting the structural results, we formulate a computationally-efficient linear mining policy for the blockchain-enabled IoT device. We present a policy gradient technique to optimize the parameters of the linear mining policy. Finally, we use synthetic and real Bitcoin datasets to study the performance of our proposed mining policy. We demonstrate the energy efficiency achieved by the optimal linear mining policy in contrast to other heuristic strategies.

翻译：物联网设备充当区块链矿工的最佳时机是什么？本文旨在最小化将数据记录到安全（防篡改）分布式账本中的低功耗物联网设备所消耗的能量。我们将物联网设备的节能区块链挖矿问题建模为一种多停时部分可观测马尔可夫决策过程（POMDP），以最大化在区块链中成功添加区块的概率；同时，我们提出了一种优化停时次数（挖矿时刻）的模型。通常，POMDP在计算上难以求解，但我们利用子模性从数学上证明了最优挖矿策略具有以下有用结构：（1）该策略在信念空间上是单调的；（2）其具有阈值结构，将信念空间划分为两个连通集合。利用这些结构性质，我们为区块链赋能的物联网设备设计了一种计算高效的线性挖矿策略。我们提出了一种策略梯度方法来优化线性挖矿策略的参数。最后，我们使用合成数据集和真实的比特币数据集对所提挖矿策略的性能进行了研究。我们验证了最优线性挖矿策略相较于其他启发式策略所实现的节能效果。