  Anderson mixing has been heuristically applied to reinforcement learning (RL)
algorithms for accelerating convergence and improving the sampling efficiency
of deep RL. Despite its heuristic improvement of convergence, a rigorous
mathematical justification for the benefits of Anderson mixing in RL has not
yet been put forward. In this paper, we provide deeper insights into a class of
acceleration schemes built on Anderson mixing that improve the convergence of
deep RL algorithms. Our main results establish a connection between Anderson
mixing and quasi-Newton methods and prove that Anderson mixing increases the
convergence radius of policy iteration schemes by an extra contraction factor.
The key focus of the analysis roots in the fixed-point iteration nature of RL.
We further propose a stabilization strategy by introducing a stable
regularization term in Anderson mixing and a differentiable, non-expansive
MellowMax operator that can allow both faster convergence and more stable
behavior. Extensive experiments demonstrate that our proposed method enhances
the convergence, stability, and performance of RL algorithms.
