Zeroth-order feedback-based optimization for distributed energy management1

Distributed energy management is a typical optimization problem that requires coordination among multiple agents to satisfy specific targets. However, existing distributed algorithms for this problem still face challenges, including unknown system models, nonconvexity, and privacy issues. To address these challenges, we propose and analyze two distributed algorithms, where the agents do not share their information and instead perform local updates using zeroth-order feedback from a central coordinator to estimate the gradient of the global objective function. One algorithm applies 2-point Gaussian smoothing-based gradient estimators and has the oracle complexity bounded by O(d/ϵ2) to get ϵ-error solutions under both convex and nonconvex settings (d is the dimension of decision space). In contrast, the other algorithm applies coordinate finite-difference gradient estimators and achieves a lower complexity bound O(d/ϵ). We conduct empirical experiments on a load curtailment problem to validate their performance.