Supervised learning for kinetic consensus control

TL;DR

This paper introduces a supervised learning approach to efficiently approximate binary feedback controls for mean field consensus problems, enabling scalable solutions for high-dimensional agent systems.

Contribution

It proposes a neural network-based method to encode binary feedback maps, improving the efficiency of solving mean field control problems via Boltzmann procedures.

Findings

Neural network approach accurately approximates binary feedback controls.

Method reduces computational complexity for high-dimensional problems.

Supervised learning enhances scalability of consensus control solutions.

Abstract

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