Synthesis of Discounted-Reward Optimal Policies for Markov Decision Processes Under Linear Temporal Logic Specifications
arXiv:2011.00632
Abstract
We present a method to find an optimal policy with respect to a reward function for a discounted Markov decision process under general linear temporal logic (LTL) specifications. Previous work has either focused on maximizing a cumulative reward objective under finite-duration tasks, specified by syntactically co-safe LTL, or maximizing an average reward for persistent (e.g., surveillance) tasks. This paper extends and generalizes these results by introducing a pair of occupancy measures to express the LTL satisfaction objective and the expected discounted reward objective, respectively. These occupancy measures are then connected to a single policy via a novel reduction resulting in a mixed integer linear program whose solution provides an optimal policy. Our formulation can also be extended to include additional constraints with respect to secondary reward functions. We illustrate the effectiveness of our approach in the context of robotic motion planning for complex missions under uncertainty and performance objectives.
arXiv commentAccepted for ACC 2021
References in corpus (5)
- Playing Atari with Deep Reinforcement Learning
- Probably Approximately Correct MDP Learning and Control With Temporal Logic Constraints
- Control Synthesis from Linear Temporal Logic Specifications using Model-Free Reinforcement Learning
- A Sample-Efficient Algorithm for Episodic Finite-Horizon MDP with Constraints
- A Learning Based Optimal Human Robot Collaboration with Linear Temporal Logic Constraints