Zeroth-Order Feedback-Based Optimization for Distributed Demand Response

Distributed demand response is a typical distributed optimization problem that requires coordination among multiple agents to satisfy demand response requirements. However, existing distributed algorithms for this problem still face challenges such as unknown system models, nonconvexity, privacy issues, etc. To address these challenges, we propose and analyze two distributed algorithms, in which the agents do not share their information and instead perform local updates using zeroth-order feedback information to estimate the gradient of the global objective function. One algorithm applies to problems with general convex and compact feasible sets but has higher oracle complexity bounded by $O(d/\epsilon^2)$, while the other algorithm achieves lower complexity bound $O(d/\epsilon)$ but is only applicable to problems with box constraints. We conduct empirical experiments to validate their performance.