Coordinating large populations of grid-edge devices requires learning methods that remain fully decentralised in deployment while still respecting three-phase AC distribution-network physics. This paper proposes gradient-based multi-agent proximal learning (GradMAP) to address this challenge. GradMAP trains independent neural-network policies for each agent without any parameter sharing, and each agent uses only its own local observation for online decision-making without communication. During offline training, GradMAP embeds a differentiable three-phase AC power-flow model in a primal-dual learning loop and uses implicit differentiation to propagate exact network-constraint violations to update the policy parameters. To speed up training, GradMAP reuses expensive environment gradients through a proximal surrogate within a trust region defined in the more direct policy-output (action) space, instead of the probability distribution space used in other works, such as PPO. In case studies with 1,000 agents managing batteries, heat pumps, and controllable generators on the IEEE 123-bus feeder, GradMAP learns decentralised policies that minimise three-phase AC load-flow constraint violations within 15 minutes of training on a single workstation-class NVIDIA RTX PRO 5000 Blackwell 48GB GPU. This is a 3--5x training speed-up over gradient-based self-supervised learning benchmarks and substantially better training efficiency than multi-agent reinforcement-learning benchmarks. In out-of-sample tests, GradMAP also delivers among the lowest operating cost and constraint violations.