This letter develops a novel multi-agent deep reinforcement learning (MADRL)-based local control method that can achieve coordinated scheduling of large-scale PV inverters using local information. This is achieved by the development of a system state inference-aided actor structure for each agent and implementation of random sequential updating within centralized-training-decentralized-execution framework. To enhance the coordination between agents utilizing local observation, a state latent inductive reasoning-based composite loss is further designed for the optimization of the inference models. Simulation tests on IEEE 123-node network demonstrate the superiority of the developed local control method when there is a large number of PV inverters.