Emphatic TD Bellman Operator is a Contraction

Assaf Hallak; Aviv Tamar; Shie Mannor

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arXiv · 1508.03411

Emphatic TD Bellman Operator is a Contraction

Assaf Hallak·Aviv Tamar·Shie Mannor

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Abstract

Recently, \citet{SuttonMW15} introduced the emphatic temporal differences (ETD) algorithm for off-policy evaluation in Markov decision processes. In this short note, we show that the projected fixed-point equation that underlies ETD involves a contraction operator, with a $\sqrt{\gamma}$-contraction modulus (where $\gamma$ is the discount factor). This allows us to provide error bounds on the approximation error of ETD. To our knowledge, these are the first error bounds for an off-policy evaluation algorithm under general target and behavior policies.

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Assaf Hallak, Aviv Tamar, Shie Mannor. 2015-08-14. Emphatic TD Bellman Operator is a Contraction. https://arxiv.org/abs/1508.03411

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