# Rate of Convergence and Error Bounds for LSTD($\lambda$)

1 MAIA - Autonomous intelligent machine
Inria Nancy - Grand Est, LORIA - AIS - Department of Complex Systems, Artificial Intelligence & Robotics
Abstract : We consider LSTD($\lambda$), the least-squares temporal-difference algorithm with eligibility traces algorithm proposed by Boyan (2002). It computes a linear approximation of the value function of a fixed policy in a large Markov Decision Process. Under a $\beta$-mixing assumption, we derive, for any value of $\lambda \in (0,1)$, a high-probability estimate of the rate of convergence of this algorithm to its limit. We deduce a high-probability bound on the error of this algorithm, that extends (and slightly improves) that derived by Lazaric et al. (2012) in the specific case where $\lambda=0$. In particular, our analysis sheds some light on the choice of $\lambda$ with respect to the quality of the chosen linear space and the number of samples, that complies with simulations.
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Reports
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Cited literature [12 references]

https://hal.inria.fr/hal-00990525
Contributor : Bruno Scherrer <>
Submitted on : Tuesday, May 13, 2014 - 3:49:54 PM
Last modification on : Tuesday, December 18, 2018 - 4:40:21 PM
Long-term archiving on : Monday, April 10, 2017 - 10:16:10 PM

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### Identifiers

• HAL Id : hal-00990525, version 1
• ARXIV : 1405.3229

### Citation

Manel Tagorti, Bruno Scherrer. Rate of Convergence and Error Bounds for LSTD($\lambda$). [Research Report] 2014. ⟨hal-00990525⟩

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