Certifiably Robust Reinforcement Learning through Model-Based Abstract Interpretation

TL;DR

The paper introduces CAROL, a reinforcement learning framework that produces policies with provable adversarial robustness certificates by integrating environment modeling and abstract interpretation, validated through theoretical bounds and experiments.

Contribution

CAROL is the first RL approach that combines environment modeling with abstract interpretation to provide certifiable robustness guarantees during learning.

Findings

CAROL achieves higher certified robustness bounds than existing methods.

CAROL maintains competitive performance under empirical adversarial attacks.

Theoretical bounds on worst-case reward are established for CAROL.

Abstract

We present a reinforcement learning (RL) framework in which the learned policy comes with a machine-checkable certificate of provable adversarial robustness. Our approach, called CAROL, learns a model of the environment. In each learning iteration, it uses the current version of this model and an external abstract interpreter to construct a differentiable signal for provable robustness. This signal is used to guide learning, and the abstract interpretation used to construct it directly leads to the robustness certificate returned at convergence. We give a theoretical analysis that bounds the worst-case accumulative reward of CAROL. We also experimentally evaluate CAROL on four MuJoCo environments with continuous state and action spaces. On these tasks, CAROL learns policies that, when contrasted with policies from the state-of-the-art robust RL algorithms, exhibit: (i) markedly enhanced certified performance lower bounds; and (ii) comparable performance under empirical adversarial attacks.