Optimal control of partially observable Markov decision processes with finite linear temporal logic constraints
Krishna C. Kalagarla, Kartik Dhruva, Dongming Shen, Rahul Jain, Ashutosh Nayyar, Pierluigi Nuzzo
Abstract
Autonomous agents often operate in environments where the state is partially observed. In addition to maximizing their cumulative reward, agents must execute complex tasks with rich temporal and logical structures. These tasks can be expressed using temporal logic languages like finite linear temporal logic. This paper, for the first time, provides a structured framework for designing agent policies that maximize the reward while ensuring that the probability of satisfying the temporal logic specification is sufficiently high. We reformulate the problem as a constrained partially observable Markov decision process (POMDP) and provide a novel approach that can leverage off-the-shelf unconstrained POMDP solvers for solving it. Our approach guarantees approximate optimality and constraint satisfaction with high probability. We demonstrate its effectiveness by implementing it on several models of interest.
BibTeX
@InProceedings{pmlr-v180-kalagarla22a,
title = {Optimal control of partially observable Markov decision processes with finite linear temporal logic constraints},
author = {Kalagarla, Krishna C. and Dhruva, Kartik and Shen, Dongming and Jain, Rahul and Nayyar, Ashutosh and Nuzzo, Pierluigi},
booktitle = {Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence},
pages = {949--958},
year = {2022},
editor = {Cussens, James and Zhang, Kun},
volume = {180},
series = {Proceedings of Machine Learning Research},
month = {01--05 Aug},
publisher = {PMLR},
pdf = {https://proceedings.mlr.press/v180/kalagarla22a/kalagarla22a.pdf},
url = {https://proceedings.mlr.press/v180/kalagarla22a.html},
abstract = {Autonomous agents often operate in environments where the state is partially observed. In addition to maximizing their cumulative reward, agents must execute complex tasks with rich temporal and logical structures. These tasks can be expressed using temporal logic languages like finite linear temporal logic. This paper, for the first time, provides a structured framework for designing agent policies that maximize the reward while ensuring that the probability of satisfying the temporal logic specification is sufficiently high. We reformulate the problem as a constrained partially observable Markov decision process (POMDP) and provide a novel approach that can leverage off-the-shelf unconstrained POMDP solvers for solving it. Our approach guarantees approximate optimality and constraint satisfaction with high probability. We demonstrate its effectiveness by implementing it on several models of interest.}
}