  Actor-Critic based approaches were among the first to address reinforcement
learning in a general setting. Recently, these algorithms have gained renewed
interest due to their generality, good convergence properties, and possible
biological relevance. In this paper, we introduce an online temporal difference
based actor-critic algorithm which is proved to converge to a neighborhood of a
local maximum of the average reward. Linear function approximation is used by
the critic in order estimate the value function, and the temporal difference
signal, which is passed from the critic to the actor. The main distinguishing
feature of the present convergence proof is that both the actor and the critic
operate on a similar time scale, while in most current convergence proofs they
are required to have very different time scales in order to converge. Moreover,
the same temporal difference signal is used to update the parameters of both
the actor and the critic. A limitation of the proposed approach, compared to
results available for two time scale convergence, is that convergence is
guaranteed only to a neighborhood of an optimal value, rather to an optimal
value itself. The single time scale and identical temporal difference signal
used by the actor and the critic, may provide a step towards constructing more
biologically realistic models of reinforcement learning in the brain.
