Verifiable Reinforcement Learning via Policy Extraction (1805.08328v2)

Abstract: While deep reinforcement learning has successfully solved many challenging control tasks, its real-world applicability has been limited by the inability to ensure the safety of learned policies. We propose an approach to verifiable reinforcement learning by training decision tree policies, which can represent complex policies (since they are nonparametric), yet can be efficiently verified using existing techniques (since they are highly structured). The challenge is that decision tree policies are difficult to train. We propose VIPER, an algorithm that combines ideas from model compression and imitation learning to learn decision tree policies guided by a DNN policy (called the oracle) and its Q-function, and show that it substantially outperforms two baselines. We use VIPER to (i) learn a provably robust decision tree policy for a variant of Atari Pong with a symbolic state space, (ii) learn a decision tree policy for a toy game based on Pong that provably never loses, and (iii) learn a provably stable decision tree policy for cart-pole. In each case, the decision tree policy achieves performance equal to that of the original DNN policy.

• The paper introduces a novel algorithm that extracts DNN policies into decision trees using imitation learning and model compression techniques.
• The extracted policies match DNN performance in tasks like Pong and cart-pole while significantly reducing verification overhead.
• The approach provides theoretical guarantees and scalable verification, paving the way for safe, real-world reinforcement learning applications.

Overview of Verifiable Reinforcement Learning via Policy Extraction

The paper "Verifiable Reinforcement Learning via Policy Extraction" presents a novel approach to reinforcement learning (RL) by focusing on the extraction of decision tree policies. Unlike traditional deep neural network (DNN) frameworks where safety verification can be computationally prohibitive, this work leverages the structured nature of decision trees to facilitate verifiable policies, addressing core challenges in RL applications that require stringent safety measures, such as autonomous driving and robotics.

The key idea presented in the paper is to develop an algorithm that successfully distills a complex DNN policy into a decision tree policy. This choice is deliberate; decision trees, which are nonparametric, can model complex policies while remaining inherently amenable to verification techniques due to their structured format. However, training decision tree policies presents significant hurdles. The authors propose a novel algorithm that incorporates elements from model compression and imitation learning, effectively using a DNN (referred to as the oracle) and its associated $Q$-function to guide the training of the decision tree.

Contributions and Methods

The paper introduces , a two-tiered algorithm. The initial phase, , uses imitation learning principles to extend capabilities by utilizing the oracle's $Q$-function for more informed and efficient training of decision trees. Building on this foundation, , further minimizes the size of the decision tree policies compared to earlier methods by imposing additional structural constraints and leveraging model-specific characteristics during the extraction process.

The practical implications of this approach are demonstrated through applications on simplified environments derived from Atari Pong and cart-pole scenarios. For instance, the paper outlines the derivation of a provably robust decision tree policy for a Pong variant, a decision tree policy that never loses in a toy Pong game, and a stable decision tree policy for cart-pole. Each evaluation confirms that the performance of these extracted policies matches that of their DNN counterparts, highlighting the practical viability of the proposed extraction method.

Numerical Results and Verification

The findings include several strong numerical results. Notably, the decision tree policies obtained performed within the same reward range as the oracle DNN policies across different tasks. These tasks include symbolic versions of Pong and cart-pole simulations, where the extracted policies are not only efficient but also conducive to formal verification techniques.

Moreover, the decision tree policies significantly ease verification efforts. The paper provides evidence of efficient scalability in verifying correctness, stability, and robustness—elements crucial for real-world deployment of RL systems. For example, the authors could model the system dynamics and verify the invariants for toy-tasks like Pong, demonstrating that the policies can be checked for safety with reduced computational overhead compared to DNN policies.

Theoretical Implications and Future Directions

The theoretical exposition in the paper establishes a performance bound for the proposed algorithm, demonstrating its favorable comparison against existing works. An interesting theoretical advancement is the introduction of a unique loss function that better captures critical states in an MDP, thereby improving training fidelity over Ross's past algorithms.

Looking forward, the paper suggests meaningful pathways for future work. These include extending the applicability of decision tree policies to more complex domains and exploring automatic repair mechanisms for identified policy errors. Additionally, the work hints at the potential integration of these verification-aiding policies within safe RL paradigms, allowing for more broadly applicable and robust solutions in AI systems dealing with safety-critical tasks.

In conclusion, by addressing the intersection of reinforcement learning effectiveness and policy verifiability, this paper contributes an important methodology that advances both the practical deployment and theoretical reliability of RL systems. While challenges remain in scaling these methods to high-dimensional tasks, the groundwork laid here provides a robust framework for continued exploration and application within AI fields necessitating rigorous safety assurances.