Reinforcement Learning With Temporal Logic Rewards (1612.03471v2)

Abstract: Reinforcement learning (RL) depends critically on the choice of reward functions used to capture the de- sired behavior and constraints of a robot. Usually, these are handcrafted by a expert designer and represent heuristics for relatively simple tasks. Real world applications typically involve more complex tasks with rich temporal and logical structure. In this paper we take advantage of the expressive power of temporal logic (TL) to specify complex rules the robot should follow, and incorporate domain knowledge into learning. We propose Truncated Linear Temporal Logic (TLTL) as specifications language, that is arguably well suited for the robotics applications, together with quantitative semantics, i.e., robustness degree. We propose a RL approach to learn tasks expressed as TLTL formulae that uses their associated robustness degree as reward functions, instead of the manually crafted heuristics trying to capture the same specifications. We show in simulated trials that learning is faster and policies obtained using the proposed approach outperform the ones learned using heuristic rewards in terms of the robustness degree, i.e., how well the tasks are satisfied. Furthermore, we demonstrate the proposed RL approach in a toast-placing task learned by a Baxter robot.

• The paper introduces TLTL, a novel framework that embeds complex temporal logic rules into reinforcement learning reward functions.
• The paper employs a robustness degree metric to convert TL specifications into real-valued rewards, accelerating policy learning in simulations and real-world tasks.
• The paper integrates TLTL with REPS, demonstrating improved learning efficiency over traditional heuristics in robotic applications such as a toast-placing task.

Reinforcement Learning With Temporal Logic Rewards

The paper "Reinforcement Learning With Temporal Logic Rewards" by Xiao Li, Cristian-Ioan Vasile, and Calin Belta proposes a novel approach to reinforcement learning (RL) by incorporating Temporal Logic (TL) into reward structures. Traditional RL depends significantly on the design of reward functions, which are typically handcrafted and may not sufficiently capture the complexity of real-world tasks. The authors address this by leveraging the expressiveness of Temporal Logic, particularly introducing a specific form termed Truncated Linear Temporal Logic (TLTL), to define complex rules and incorporate domain knowledge directly into RL processes.

Contributions and Methodology

1. Introduction of TLTL: The authors propose TLTL as a specification language tailored for robotic applications, enabling the integration of complex task requirements using a finite number of temporal and logical operators. TLTL specifications provide a structure for defining both goals and constraints in a compact form. This approach captures intricate aspects of tasks that are often overlooked when using traditional heuristic-based reward functions.
2. Robustness Degree Quantification: A critical innovation in this research is the use of quantitative semantics called the robustness degree. This metric evaluates how well a trajectory satisfies or violates a TLTL specification, thereby transforming logical formulae into real-valued reward functions. The robustness degree serves as an alternative to the commonly used reward-shaping techniques and enables more nuanced feedback during the learning process.
3. Comparative Evaluation: Through comparative studies involving both simulated environments and a real-world task, the authors demonstrate the efficacy of TLTL-based rewards. In simulation tasks involving a 2D manipulator, TLTL-based reward functions significantly outperformed both discrete and continuous heuristic rewards in terms of learning speed and policy quality. The paper also includes an experimental validation where a Baxter robot successfully learns a toast-placing task defined through TLTL, encompassing spatial constraints and gripper action timing.
4. Integration with REPS: The reinforcement learning setup utilizes Relative Entropy Policy Search (REPS) methods, an approach suitable for continuous state and action spaces. The authors adapt both episodic and step-based versions of REPS to integrate TLTL constraints, leading to improved learning efficiencies compared to heuristic-driven alternatives.

Implications and Future Directions

The primary implication of this work is the potential for TLTL to enhance RL frameworks, particularly in tasks that require intricate temporal and logical understanding. By formalizing complex task dynamics within the reward function itself, practitioners can enable more reliable and interpretable learning processes in robots, potentially accelerating the deployment of RL in safety-critical applications.

Theoretically, this paper lends itself to further exploration into the expansion of TLTL and its robustness evaluation. For instance, adapting the robustness functions for more complex TL derivatives or integrating them with gradient-based learning approaches may yield even more efficient learning schemes. Another avenue for future research is the exploration of automata-based methods for guided exploration, leveraging the structured nature of TL specifications to facilitate optimal policy synthesis.

In conclusion, this paper provides a substantial contribution to the field of reinforcement learning by reimagining the role of reward functions through the lens of temporal logic. This introduces a new layer of sophistication and reliability, particularly valuable for robotic applications where tasks are not only complex but also require compliance with strict operational constraints.