The main focus of this talk is the analysis of high-dimensional stochastic control problems in which many agents cooperate to minimize a convex cost functional. Our main results are sharp yet general bounds on the optimality gap between the full-information problem, in which each agent observes the states of all other agents, versus the distributed problem, in which each agent observes only its own state. Being decidedly non-asymptotic, our approach avoids structural constraints like exchangeability which are normally required in order to identify limiting objects, but which rule out network-based models. A protagonist in our approach, dubbed the "independent projection," is the optimal approximation (in a precise sense) of a given high-dimensional diffusion process by one in which the coordinates are independent.