TD Convergence: An Optimization Perspective
This provides a theoretical explanation for TD's success in reinforcement learning, but it is incremental as it builds on existing optimization perspectives.
The paper tackles the convergence behavior of temporal-difference (TD) learning by analyzing it as an iterative optimization algorithm, identifying two forces that determine convergence or divergence, and proving convergence in broader settings beyond linear approximation and squared loss.
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.