Global optimality of softmax policy gradient with single hidden layer neural networks in the mean-field regime

Understand

We study the problem of policy optimization for infinite-horizon discounted Markov Decision Processes with softmax policy and nonlinear function approximation trained with policy gradient algorithms.

• We concentrate on the training dynamics in the mean-field regime, modeling e.g., the behavior of wide single hidden layer neural networks, when exploration is encouraged through entropy regularization.
• The dynamics of these models is established as a Wasserstein gradient flow of distributions in parameter space.
• We further prove global optimality of the fixed points of this dynamics under mild conditions on their initialization.