Representing Entropy : A short proof of the equivalence between soft Q-learning and policy gradients

Anonymous

Nov 07, 2017 (modified: Nov 07, 2017) ICLR 2018 Conference Blind Submission readers: everyone Show Bibtex
  • Abstract: Two main families of reinforcement learning algorithms, Q-learning and policy gradients, have recently been proven to be equivalent when using a softmax relaxation on one part, and an entropic regularization on the other. We relate this result to the well-known convex duality of Shannon entropy and the softmax function. Such a result is also known as the Donsker-Varadhan formula. This provides a short proof of the equivalence. We then interpret this duality further, and use ideas of convex analysis to prove a new policy inequality relative to soft Q-learning.
  • TL;DR: A short proof of the equivalence of soft Q-learning and policy gradients.
  • Keywords: soft Q-learning, policy gradients, entropy, Legendre transformation, duality, convex analysis, Donsker-Varadhan

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