  This paper extends the reinforcement learning ideas into the multi-agents
system, which is far more complicated than the previously studied single-agent
system. We studied two different multi-agents systems. One is the
fully-connected neural network consists of multiple single neurons. Another one
is the simplified mechanical arm system which is controlled by multiple
neurons. We suppose that each neuron is like an agent and it can do Gibbs
sampling of the posterior probability of stimulus features. The policy is
optimized in a way that the cumulative global rewards are maximized. The
algorithm for the second system is based on the same idea but we incorporate
the physics model into the constraints. The simulation results show that for
the first system our algorithm converges well. For the second system it does
not converge well in a reasonable simulation time length. In summary, we took
the initial endeavor to study the reinforcement learning for multi-agents
system. The computational complexity is always an issue and significant amount
of works have to be done in order to better understand the problem.
