论文标题
分布式随机嵌套优化通过立方正则化
Distributed Stochastic Nested Optimization via Cubic Regularization
论文作者
论文摘要
本文考虑了嵌套的随机分布式优化问题。在其中，利用了内部问题的实现的近似解决方案，以获得外部问题决策变量的分布式随机立方体化牛顿（DICN）更新。我们提供了一个示例，涉及电动汽车用户具有各种偏好，这些偏好表明该模型对于各种数据驱动的多代理设置而言是适当且足够复杂的，与非巢模型相比。本文的主要贡献是：（i）开发局部停止标准以解决内部优化问题，以确保外部问题更新足够准确，以及（ii）开发新的DICN算法来解决外部问题和理论上的理由。模拟表明，在高度非凸场中，这种方法比标准梯度和牛顿外部问题更新更稳定，并且收敛速度更快，并且我们还证明该方法扩展到EV充电方案，其中电阻电池损失和使用时间的定价模型在时间范围内被视为。
This paper considers a nested stochastic distributed optimization problem. In it, approximate solutions to realizations of the inner-problem are leveraged to obtain a Distributed Stochastic Cubic Regularized Newton (DiSCRN) update to the decision variable of the outer problem. We provide an example involving electric vehicle users with various preferences which demonstrates that this model is appropriate and sufficiently complex for a variety of data-driven multi-agent settings, in contrast to non-nested models. The main two contributions of the paper are: (i) development of local stopping criterion for solving the inner optimization problem which guarantees sufficient accuracy for the outer-problem update, and (ii) development of the novel DiSCRN algorithm for solving the outer-problem and a theoretical justification of its efficacy. Simulations demonstrate that this approach is more stable and converges faster than standard gradient and Newton outer-problem updates in a highly nonconvex scenario, and we also demonstrate that the method extends to an EV charging scenario in which resistive battery losses and a time-of-use pricing model are considered over a time horizon.
