This paper proposes a novel equilibrium-inspired multiagent optimizer (EMO) with extreme transfer learning for decentralized optimal carbon-energy combined-flow (OCECF) of large-scale power systems. The original large-scale power system is firstly divided into several small-scale subsystems, in which each subsystem is regarded as an agent, such that a decentralized OCECF can be achieved via a Nash game among all the agents. Then, a knowledge matrix associated with a state-action chain is presented for knowledge storing of the previous optimization tasks, which can be updated by a continuous interaction with the external environment. Furthermore, an extreme learning machine is adopted for an efficient transfer learning, such that the convergence rate of a new task can be dramatically accelerated by properly exploiting the prior knowledge of the source tasks. EMO has been thoroughly evaluated for the decentralized OCECF on IEEE 57-bus system, IEEE 300-bus system, and a practical Shenzhen power grid of southern China. Case studies and engineering application verify that EMO can effectively handle the decentralized OCECF of large-scale power systems. (C) 2016 Elsevier Ltd. All rights reserved.