  In this paper, we present a reinforcement learning approach to designing a
control policy for a "leader" agent that herds a swarm of "follower" agents,
via repulsive interactions, as quickly as possible to a target probability
distribution over a strongly connected graph. The leader control policy is a
function of the swarm distribution, which evolves over time according to a
mean-field model in the form of an ordinary difference equation. The dependence
of the policy on agent populations at each graph vertex, rather than on
individual agent activity, simplifies the observations required by the leader
and enables the control strategy to scale with the number of agents. Two
Temporal-Difference learning algorithms, SARSA and Q-Learning, are used to
generate the leader control policy based on the follower agent distribution and
the leader's location on the graph. A simulation environment corresponding to a
grid graph with 4 vertices was used to train and validate the control policies
for follower agent populations ranging from 10 to 100. Finally, the control
policies trained on 100 simulated agents were used to successfully redistribute
a physical swarm of 10 small robots to a target distribution among 4 spatial
regions.
