Imitation Learning with Temporal Logic Constraints

Designing reinforcement learning agents to satisfy complex temporal objectives expressed in Linear Temporal Logic (LTL), presents significant challenges, particularly in ensuring sample efficiency and task alignment over infinite horizons. Recent works have shown that by leveraging the corresponding Limit Deterministic Büchi Automaton (LDBA) representation, LTL formulas can be translated into variable discounting schemes over LDBA-accepting states to maximize a lower bound on the probability of formula satisfaction. However, the resulting reward signals are inherently sparse, making exploration of LDBA-accepting states increasingly difficult as task horizons lengthen to infinity. In this work, we address these challenges by leveraging finite-length demonstrations to overcome the exploration bottleneck for LTL objectives over infinite horizons. We segment demonstrations and agent exploratory trajectories at LDBA-accepting states and iteratively guide the agent within each segment to learn to reach these accepting states. By incentivizing the agent to visit LDBA-accepting states from arbitrary states, our approach increases the probability of LTL formula satisfaction without the need for extensive or lengthy demonstrations. We demonstrate the applicability of our method across a variety of high-dimensional continuous control domains. It achieves faster convergence and consistently outperforms baseline approaches.