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• The data-driven inverse optimization corrects the DR execution online. • The proposed strategy is realized in a distributed manner and free of initialization. • This paper provides rigorous stability proof for the proposed optimization. • D-PPDS algorithm solves the DR optimization with global inequality constrain. This paper provides an insight into the demand response (DR) optimization in distribution markets consisting of a retailer and multiple demand response aggregators (DRA), where a retailer determines DR incentives based on power consumption profile. Conventional DR optimization with global states and constraints is intractable to be implemented in a distributed framework, which restricts the application feasibility and the potential profit of DR. To handle these limitations, we design a multi-agent architecture for distributed demand response (DDR). An online data-mining method is developed to identify the characteristics of DR. A leader–follower structure decomposes the original problem into a leader problem with global variables and aggregators of sub-problems, where discrete singular consensus is designed to broadcast the leader's strategy to followers in real-time. The distributed perturbation primal–dual sub-gradient (D-PPDS) algorithm is proposed to solve the DDR problem with global inequality constraints in a completely distributed fashion. The proposed DDR strategy is tested by an actual case. The simulation results demonstrate that the asynchronous D-PPDS algorithm can obtain the near-optimal solution of the problem with global inequality constraints, and is robust against delay or plug-and-play. [ABSTRACT FROM AUTHOR]