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As reinforcement learning (RL) has achieved great success and been evenadopted in safety-critical domains such as autonomous vehicles, a range ofempirical studies have been conducted to improve its robustness againstadversarial attacks. However, how to certify its robustness with theoreticalguarantees still remains challenging. In this paper, we present the firstunified framework CROP (Certifying Robust Policies for RL) to providerobustness certification on both action and reward levels. In particular, wepropose two robustness certification criteria: robustness of per-state actionsand lower bound of cumulative rewards. We then develop a local smoothingalgorithm for policies derived from Q-functions to guarantee the robustness ofactions taken along the trajectory; we also develop a global smoothingalgorithm for certifying the lower bound of a finite-horizon cumulative reward,as well as a novel local smoothing algorithm to perform adaptive search inorder to obtain tighter reward certification. Empirically, we apply CROP toevaluate several existing empirically robust RL algorithms, includingadversarial training and different robust regularization, in four environments(two representative Atari games, Highway, and CartPole). Furthermore, byevaluating these algorithms against adversarial attacks, we demonstrate thatour certification are often tight. All experiment results are available atwebsite https://crop-leaderboard.github.io.

CROP: Certifying Robust Policies for Reinforcement Learning through Functional Smoothing