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We study high-dimensional stochastic optimal control problems in which manyagents cooperate to minimize a convex cost functional. We consider both thefull-information problem, in which each agent observes the states of all otheragents, and the distributed problem, in which each agent observes only its ownstate. Our main results are sharp non-asymptotic bounds on the gap betweenthese two problems, measured both in terms of their value functions and optimalstates. Along the way, we develop theory for distributed optimal stochasticcontrol in parallel with the classical setting, by characterizing optimizers interms of an associated stochastic maximum principle and a Hamilton-Jacobi-typeequation. By specializing these results to the setting of mean field control,in which costs are (symmetric) functions of the empirical distribution ofstates, we derive the optimal rate for the convergence problem in thedisplacement convex regime.

Approximately optimal distributed stochastic controls beyond the mean field setting