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Proper Policies in Infinite-State Stochastic Shortest Path Problems.
- Source :
- IEEE Transactions on Automatic Control; Nov2018, Vol. 63 Issue 11, p3787-3792, 6p
- Publication Year :
- 2018
-
Abstract
- We consider stochastic shortest path problems with infinite state and control spaces, a nonnegative cost per stage, and a termination state. We extend the notion of a proper policy, a policy that terminates within a finite expected number of steps, from the context of finite state space to the context of infinite state space. We consider the optimal cost function $J^*$ , and the optimal cost function $\hat{J}$ over just the proper policies. We show that $J^*$ and $\hat{J}$ are the smallest and largest solutions of Bellman's equation, respectively, within a suitable class of Lyapounov-like functions. If the cost per stage is bounded, these functions are those that are bounded over the effective domain of $\hat{J}$. The standard value iteration algorithm may be attracted to either $J^*$ or $\hat{J}$ , depending on the initial condition. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00189286
- Volume :
- 63
- Issue :
- 11
- Database :
- Complementary Index
- Journal :
- IEEE Transactions on Automatic Control
- Publication Type :
- Periodical
- Accession number :
- 132684900
- Full Text :
- https://doi.org/10.1109/TAC.2018.2811781