Mean field control (MFC) theory allows us to conclude that certain high-dimensional control problems are "approximately distributed", in the sense that (i) we can construct a "distributed control" (a feedback whose ith component depends only on the position of the ith particle) which is approximately optimal and (ii) the law of the optimally controlled state process is approximately a product measure. Of course, this analysis applies only when the controller's cost functional is symmetric. Nevertheless, it makes sense to ask when we can expect non-symmetric control problems to be approximately distributed as well. In an ongoing joint work with Daniel Lacker, we provide an answer to this question through several explicit estimates. When specialized to the mean field setting, our estimates give a new approach to the (quantitative) convergence problem for MFC which does not require an analysis of the relevant HJB equation on the space of measures. Speaker(s): Joseph Jackson (UT Austin)
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