Supervised learning for kinetic consensus control

In this paper, how to successfully and efficiently condition a target population of agents towards consensus is discussed. To overcome the curse dimensionality, mean field formulation control problem considered. Although such designed be independent number agents, it feasible solve only for moderate intrinsic dimensions space. For reason, solution approached by means Boltzmann procedure, i.e. quasi-invariant limit controlled binary interactions as approximation PDE. The need an efficient solver interaction motivates use supervised learning approach encode feedback map sampled at very high rate. A gradient augmented feedforward neural network Value function considered compared with direct law.