# Optimal Control of Partially Observable Markov Decision Processes with Finite Linear Temporal Logic Constraints

arXiv: https://arxiv.org/abs/2203.09038 · HTML: https://mlsanity.com/paper/2203.09038/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Mar 2022.

## Built on by (most cited first, 5 of 5)

- [C-MCTS: Safe Planning with Monte Carlo Tree Search](https://mlsanity.com/paper/2305.16209/) (2023)
- [Optimal Control of Logically Constrained Partially Observable and Multi-Agent Markov Decision Processes](https://mlsanity.com/paper/2305.14736/) (2023)
- [Recursively-Constrained Partially Observable Markov Decision Processes](https://mlsanity.com/paper/2310.09688/) (2023)
- [Sound Heuristic Search Value Iteration for Undiscounted POMDPs with Reachability Objectives](https://mlsanity.com/paper/2406.02871/) (2024)
- [Ensuring Logic in the Fog: Sound POMDP Synthesis with LTL Objectives](https://mlsanity.com/paper/2605.12581/) (2026)

## Abstract (arXiv)

Autonomous agents often operate in scenarios 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 (LTL_f). 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.