[Paper Review] Verifiable Reinforcement Learning via Policy Extraction

Osbert Bastani, Yewen Pu+1 more|arXiv (Cornell University)|May 22, 2018

Reinforcement Learning in Robotics33 references115 citations

TL;DR

The paper introduces Viper, a method to extract compact, verifiable decision-tree policies from a high-performing DNN oracle and its Q-function, enabling efficient verification of safety, robustness, and stability for reinforcement learning tasks.

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.

Motivation & Objective

• Motivate the need for verifiable policies in safety-critical RL settings.
• Develop a policy extraction pipeline that yields verifiable, nonparametric decision trees from deep policies.
• Improve sample efficiency and policy size over prior imitation-learning baselines by leveraging Q-functions.
• Demonstrate verifiability via correctness, robustness, and stability analyses across multiple tasks.

Proposed method

• Define Q-Dagger, an imitation-learning algorithm that uses the oracle's Q-function to guide training.
• Introduce Viper, which extracts decision-tree policies by resampling data with weights based on a convex loss surrogate and training trees with CART.
• Formulate a theoretical comparison showing tighter performance bounds for Q-Dagger relative to prior work.
• Apply Viper to extract compact trees that achieve optimal or perfect rewards on selected tasks.
• Adapt verification techniques to check correctness (toy Pong), robustness (Atari Pong), and stability (cart-pole) for the extracted trees.

Experimental results

Research questions

• RQ1 Can a decision-tree policy learned from a DNN oracle achieve performance comparable to the original policy?
• RQ2 Does leveraging the Q-function in imitation learning yield smaller, more verifiable policies than Dagger?
• RQ3 Can the extracted decision-tree policies be efficiently verified for correctness, robustness, and stability across benchmark tasks?
• RQ4 What are the trade-offs between policy size, verifiability, and achieved rewards in these settings?

Key findings

• Viper learns relatively small decision trees (<1000 nodes) that achieve perfect or near-perfect rewards on Atari Pong (symbolic state space), a Pong-based toy game, and cart-pole.
• Compared to Dagger, Viper produces significantly smaller trees (e.g., 31-769 nodes vs thousands) while matching oracle performance.
• Viper enables verification of correctness, robustness, and stability more efficiently than approaches compatible with DNN policies.
• For Atari Pong, Viper-derived trees achieved perfect reward; robustness quantified at several sample states showed measurable margins.
• In cart-pole, a small tree achieved perfect reward, and SOS-based methods verified stability around the origin for a degree-5 Taylor model.