arXiv Machine Learning By Chris Nota, Philip S. Thomas

Is the Policy Gradient a Gradient?

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The paper investigates whether the policy gradient update used in many reinforcement learning algorithms—specifically the episode-summed, on‑policy update that omits the outer discount factor—can be interpreted as the gradient of any objective function. The authors prove that this update does not necessarily correspond to the gradient of any function and provide a counterexample where the update drives the policy toward a globally pessimal deterministic limit while the parameters diverge. They also highlight that this theoretical ambiguity has led to widespread misstatements in the literature, even in highly cited works from top conferences.

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