Emphatic TD Bellman Operator is a Contraction

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.

References in corpus (2)

• On Convergence of Emphatic Temporal-Difference Learning
• Emphatic Temporal-Difference Learning

Cited by in corpus (1)

• Offline Reinforcement Learning: Tutorial, Review, and Perspectives on Open Problems