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

• URL: http://arxiv.org/abs/2010.11858v1
• Date: Thu, 22 Oct 2020 16:47:22 GMT
• Title: Global optimality of softmax policy gradient with single hidden layer neural networks in the mean-field regime
• Authors: Andrea Agazzi, Jianfeng Lu
• Abstract summary: We study the problem of policy optimization for infinite-horizon discounted Markov Decision Processes with softmax policy and nonlinear function approximation trained with policy 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.
• Score: 10.882573368659516
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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