  We study the convergence behavior of the celebrated temporal-difference (TD)
learning algorithm. By looking at the algorithm through the lens of
optimization, we first argue that TD can be viewed as an iterative optimization
algorithm where the function to be minimized changes per iteration. By
carefully investigating the divergence displayed by TD on a classical counter
example, we identify two forces that determine the convergent or divergent
behavior of the algorithm. We next formalize our discovery in the linear TD
setting with quadratic loss and prove that convergence of TD hinges on the
interplay between these two forces. We extend this optimization perspective to
prove convergence of TD in a much broader setting than just linear
approximation and squared loss. Our results provide a theoretical explanation
for the successful application of TD in reinforcement learning.
