Weak Convergence Analysis of Online Neural Actor-Critic Algorithms
arXiv:2403.16825v2 Announce Type: replace Abstract: We prove that a single-layer neural network trained with the online actor critic algorithm converges in distribution to a random ordinary differential equation (ODE) as the number of hidden units and the number of training steps $\rightarrow \infty$. In the online actor-critic algorithm, the distribution of the data samples dynamically changes as the model is updated, which is a key challenge for any convergence analysis. We establish the geometric ergodicity of the data samples under a fixed actor policy. Then, using a Poisson equation, we prove that the fluctuations of the model updates around the limit distribution due to the randomly-arriving data samples vanish as the number of parameter updates $\rightarrow \infty$. Using the Poisson equation and weak convergence techniques, we prove that the actor neural network and critic neural network converge to the solutions of a system of ODEs with random initial conditions. Analysis of t