Learning specifications for reactive synthesis with safety constraints

Abstract: This paper presents a novel approach to learning from demonstration that enables robots to autonomously execute complex tasks in dynamic environments. We model latent tasks as probabilistic formal languages and introduce a tailored reactive synthesis framework that balances robot costs with user task preferences. Our methodology focuses on safety-constrained learning and inferring formal task specifications as Probabilistic Deterministic Finite Automata (PDFA). We adapt existing evidence-driven state merging algorithms and incorporate safety requirements throughout the learning process to ensure that the learned PDFA always complies with safety constraints. Furthermore, we introduce a multi-objective reactive synthesis algorithm that generates deterministic strategies that are guaranteed to satisfy the PDFA task while optimizing the trade-offs between user preferences and robot costs, resulting in a Pareto front of optimal solutions. Our approach models the interaction as a two-player game between the robot and the environment, accounting for dynamic changes. We present a computationally-tractable value iteration algorithm to generate the Pareto front and the corresponding deterministic strategies. Comprehensive experimental results demonstrate the effectiveness of our algorithms across various robots and tasks, showing that the learned PDFA never includes unsafe behaviors and that synthesized strategies consistently achieve the task while meeting both the robot cost and user-preference requirements.