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Emphatic TD Bellman Operator is a Contraction

Machine Learning 2015-08-25 v2 Machine Learning

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 γ\sqrt{\gamma}-contraction modulus (where γ\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.

Cite

@article{arxiv.1508.03411,
  title  = {Emphatic TD Bellman Operator is a Contraction},
  author = {Assaf Hallak and Aviv Tamar and Shie Mannor},
  journal= {arXiv preprint arXiv:1508.03411},
  year   = {2015}
}
R2 v1 2026-06-22T10:33:31.995Z