# Tight Performance Bounds for Approximate Modified Policy Iteration with Non-Stationary Policies

1 MAIA - Autonomous intelligent machine
Inria Nancy - Grand Est, LORIA - AIS - Department of Complex Systems, Artificial Intelligence & Robotics
Abstract : We consider approximate dynamic programming for the infinite-horizon stationary $\gamma$-discounted optimal control problem formalized by Markov Decision Processes. While in the exact case it is known that there always exists an optimal policy that is stationary, we show that when using value function approximation, looking for a non-stationary policy may lead to a better performance guarantee. We define a non-stationary variant of MPI that unifies a broad family of approximate DP algorithms of the literature. For this algorithm we provide an error propagation analysis in the form of a performance bound of the resulting policies that can improve the usual performance bound by a factor $O\left(1-\gamma\right)$, which is significant when the discount factor $\gamma$ is close to 1. Doing so, our approach unifies recent results for Value and Policy Iteration. Furthermore, we show, by constructing a specific deterministic MDP, that our performance guarantee is tight.
Keywords :
Document type :
Preprints, Working Papers, ...

Cited literature [16 references]

https://hal.inria.fr/hal-00815996
Contributor : Bruno Scherrer <>
Submitted on : Friday, April 19, 2013 - 3:54:01 PM
Last modification on : Tuesday, December 18, 2018 - 4:40:21 PM
Long-term archiving on : Monday, April 3, 2017 - 7:56:17 AM

### Files

report.pdf
Files produced by the author(s)

### Identifiers

• HAL Id : hal-00815996, version 1
• ARXIV : 1304.5610

### Citation

Boris Lesner, Bruno Scherrer. Tight Performance Bounds for Approximate Modified Policy Iteration with Non-Stationary Policies. 2013. ⟨hal-00815996⟩

Record views