Scalable Signal Temporal Logic Guided Reinforcement Learning via Value Function Space Optimization

The integration of reinforcement learning (RL) and formal methods has emerged as a promising framework for solving long-horizon planning problems. Conventional approaches typically involve abstraction of the state and action spaces and manually created labeling functions or predicates. However, the efficiency of these approaches deteriorates as the tasks become increasingly complex, which results in exponential growth in the size of labeling functions or predicates. To address these issues, we propose a scalable model-based RL framework, called VFSTL, which schedules pre-trained skills to follow unseen STL specifications without using hand-crafted predicates. Given a set of value functions obtained by goal-conditioned RL, we formulate an optimization problem to maximize the robustness value of Signal Temporal Logic (STL) defined specifications, which is computed using value functions as predicates. To further reduce the computation burden, we abstract the environment state space into the value function space (VFS). Then the optimization problem is solved by Model-Based Reinforcement Learning. Simulation results show that STL with value functions as predicates approximates the ground truth robustness and the planning in VFS directly achieves unseen specifications using data from sensors.