Convergence of policy gradient for entropy regularized MDPs with neural network approximation in the mean-field regime. (arXiv:2201.07296v1 [math.OC])

We study the global convergence of policy gradient for infinite-horizon,
continuous state and action space, entropy-regularized Markov decision
processes (MDPs). We consider a softmax policy with (one-hidden layer) neural
network approximation in a mean-field regime. Additional entropic
regularization in the associated mean-field probability measure is added, and
the corresponding gradient flow is studied in the 2-Wasserstein metric. We show
that the objective function is increasing along the gradient flow. Further, we
prove that if the regularization in terms of the …

arxiv entropy gradient math network neural network policy