We study cooperative multi-agent reinforcement learning (MARL) problems in which agents evolve under decoupled noisy dynamics but share a population objective. A canonical example is a mobility operator that orchestrates a fleet of vehicles to meet customer demand. The stochastic and time-varying nature of these problems calls for learning approaches, yet existing MARL algorithms do not scale: learning assignment and routing jointly over the full state-action space becomes prohibitive as the number of agents grows. Formulating the problem over the space of probability measures, we prove a separation principle: the population cost-to-go function is upper bounded by an optimal transport problem whose transportation cost is the target-conditioned single-agent cost-to-go function. This simplifies the multi-agent problem to learning a single-agent policy and coordinating the agents via optimal transport. Building on this principle, we introduce SALT (Separation-based Assignment and Learning via optimal Transport), a family of algorithms that learn a target-conditioned single-agent policy using any standard reinforcement learning algorithm, and then coordinate the agents via optimal transport. Since learning occurs at the single-agent level, SALT scales to fleet sizes where MARL baselines become intractable and transfers without retraining to fleet sizes unseen during training. In a vehicle-delivery experiment on the southern Manhattan road network, where MARL baselines are computationally prohibitive, SALT improves travel time by 15-21% over a shortest-path routing heuristic. In stochastic grid worlds, SALT reduces average travel times by 23-61% relative to MARL baselines and scales to population sizes where these methods fail.

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