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We present a multi-agent learning algorithm, ALMA-Learning, for efficient and fair allocations in large-scale systems. We circumvent the traditional pitfalls of multi-agent learning (e.g., the moving target problem, the curse of dimensionality, or the need for mutually consistent actions) by relying on the ALMA heuristic as a coordination mechanism for each stage game. ALMA-Learning is decentralized, observes only own action/reward pairs, requires no inter-agent communication, and achieves near-optimal (<5% loss) and fair coordination in a variety of synthetic scenarios and a real-world meeting scheduling problem. The lightweight nature and fast learning constitute ALMA-Learning ideal for on-device deployment.