Using price signals to coordinate the electricity consumption of a group of users has been studied extensively. Typically, a system operator broadcasts a price, and users optimizes their own actions subject to the price and internal cost functions. A central challenge is the operator's lack of knowledge of the users, since users may not want to share private information. In addition, learning algorithms are being increasingly used to load control, and users maybe unable to provide their costs in analytical form. In this paper, we develop a two time-scale incentive mechanism that alternately updates between the users and a system operator. The system operator selects a price, and the users optimize their consumption. Based on the consumption, a new price is then computed by the system operator. As long as the users can optimize their own consumption for a given price, the operator does not need to know or attempt to learn any private information of the users. We show that under a wide range of assumptions, this iterative process converges to the social welfare solution. In particular, the cost of the users need not be strictly convex and its consumption can be the output of a learning algorithm.

翻译：通过价格信号协调用户群体的电力消耗已得到广泛研究。通常，系统运营商广播定价，用户根据价格及其内部成本函数优化自身行为。核心挑战在于运营商缺乏对用户的了解，因为用户可能不愿共享隐私信息。此外，学习算法正越来越多地应用于负荷控制，用户可能无法以解析形式提供其成本函数。本文提出了一种双时间尺度激励机制，在用户与系统运营商之间交替更新。系统运营商选择价格，用户优化其用电量，运营商再基于用电量计算新价格。只要用户能够针对给定价格优化其用电量，运营商无需知晓或试图学习用户的任何隐私信息。我们证明，在多种假设条件下，该迭代过程能够收敛至社会福利最优解。特别地，用户成本函数无需严格凸性，其用电量也可以是学习算法的输出结果。