Socially Optimal Energy Usage via Adaptive Pricing

A central challenge in using price signals to coordinate the electricity consumption of a group of users is the operator's lack of knowledge of the users due to privacy concerns. In this paper, we develop a two-time-scale incentive mechanism that alternately updates between the users and a system operator. As long as the users can optimize their own consumption subject to a given price, the operator does not need to know or attempt to learn any private information of the users for price design. Users adjust their consumption following the price and the system redesigns the price based on the users' consumption. We show that under mild assumptions, this iterative process converges to the social welfare solution. In particular, the cost of the users need not always be convex and its consumption can be the output of a machine learning-based load control algorithm.