### Abstract

We consider policy evaluation algorithms within the context of infinite-horizon dynamic programming problems with discounted cost. We focus on discrete-time dynamic systems with a large number of states, and we discuss two methods, which use simulation, temporal differences, and linear cost function approximation. The first method is a new gradient-like algorithm involving least-squares subproblems and a diminishing stepsize, which is based on the λ-policy iteration method of Bertsekas and Ioffe. The second method is the LSTD(λ) algorithm recently proposed by Boyan, which for λ = 0 coincides with the linear least-squares temporal-difference algorithm of Bradtke and Barto. At present, there is only a convergence result by Bradtke and Barto for the LSTD(0) algorithm. Here, we strengthen this result by showing the convergence of LSTD(λ), with probability 1, for every λε[0,1].

Original language | English (US) |
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Pages (from-to) | 79-110 |

Number of pages | 32 |

Journal | Discrete Event Dynamic Systems: Theory and Applications |

Volume | 13 |

Issue number | 1-2 |

DOIs | |

State | Published - Jan 1 2003 |

Externally published | Yes |

### ASJC Scopus subject areas

- Control and Systems Engineering
- Modeling and Simulation
- Electrical and Electronic Engineering

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## Cite this

*Discrete Event Dynamic Systems: Theory and Applications*,

*13*(1-2), 79-110. https://doi.org/10.1023/A:1022192903948