# Probabilistically Guaranteed Satisfaction of Temporal Logic Constraints During Reinforcement Learning

arXiv: https://arxiv.org/abs/2102.10063 · HTML: https://mlsanity.com/paper/2102.10063/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Feb 2021.

## Built on by (most cited first, 6 of 6)

- [Model-Free Learning of Safe yet Effective Controllers](https://mlsanity.com/paper/2103.14600/) (2021)
- [Reinforcement Learning Under Probabilistic Spatio-Temporal Constraints with Time Windows](https://mlsanity.com/paper/2307.15910/) (2023)
- [Safety-Critical Learning of Robot Control with Temporal Logic Specifications](https://mlsanity.com/paper/2109.02791/) (2021)
- [Probabilistic Satisfaction of Temporal Logic Constraints in Reinforcement Learning via Adaptive Policy-Switching](https://mlsanity.com/paper/2410.08022/) (2024)
- [Shielded Reinforcement Learning Under Dynamic Temporal Logic Constraints](https://mlsanity.com/paper/2603.17152/) (2026)
- [Hyperproperty-Constrained Secure Reinforcement Learning](https://mlsanity.com/paper/2508.00106/) (2025)

## Abstract (arXiv)

We propose a novel constrained reinforcement learning method for finding optimal policies in Markov Decision Processes while satisfying temporal logic constraints with a desired probability throughout the learning process. An automata-theoretic approach is proposed to ensure the probabilistic satisfaction of the constraint in each episode, which is different from penalizing violations to achieve constraint satisfaction after a sufficiently large number of episodes. The proposed approach is based on computing a lower bound on the probability of constraint satisfaction and adjusting the exploration behavior as needed. We present theoretical results on the probabilistic constraint satisfaction achieved by the proposed approach. We also numerically demonstrate the proposed idea in a drone scenario, where the constraint is to perform periodically arriving pick-up and delivery tasks and the objective is to fly over high-reward zones to simultaneously perform aerial monitoring.