Temporal Difference Learning as Gradient Splitting

• URL: http://arxiv.org/abs/2010.14657v1
• Date: Tue, 27 Oct 2020 22:50:39 GMT
• Title: Temporal Difference Learning as Gradient Splitting
• Authors: Rui Liu and Alex Olshevsky
• Abstract summary: We show that convergence proofs for gradient descent can be applied almost verbatim to temporal difference learning. We show that a minor variation on TD learning which estimates the mean of the value function separately has a convergence time where $1/(1-gamma)$ only multiplies anally negligible term.
• Score: 15.321579527891457
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Temporal difference learning with linear function approximation is a popular method to obtain a low-dimensional approximation of the value function of a policy in a Markov Decision Process. We give a new interpretation of this method in terms of a splitting of the gradient of an appropriately chosen function. As a consequence of this interpretation, convergence proofs for gradient descent can be applied almost verbatim to temporal difference learning. Beyond giving a new, fuller explanation of why temporal difference works, our interpretation also yields improved convergence times. We consider the setting with $1/\sqrt{T}$ step-size, where previous comparable finite-time convergence time bounds for temporal difference learning had the multiplicative factor $1/(1-\gamma)$ in front of the bound, with $\gamma$ being the discount factor. We show that a minor variation on TD learning which estimates the mean of the value function separately has a convergence time where $1/(1-\gamma)$ only multiplies an asymptotically negligible term.

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