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Function approximation has enabled remarkable advances in applyingreinforcement learning (RL) techniques in environments with high-dimensionalinputs, such as images, in an end-to-end fashion, mapping such inputs directlyto low-level control. Nevertheless, these have proved vulnerable to smalladversarial input perturbations. A number of approaches for improving orcertifying robustness of end-to-end RL to adversarial perturbations haveemerged as a result, focusing on cumulative reward. However, what is often atstake in adversarial scenarios is the violation of fundamental properties, suchas safety, rather than the overall reward that combines safety with efficiency.Moreover, properties such as safety can only be defined with respect to truestate, rather than the high-dimensional raw inputs to end-to-end policies. Todisentangle nominal efficiency and adversarial safety, we situate RL indeterministic partially-observable Markov decision processes (POMDPs) with thegoal of maximizing cumulative reward subject to safety constraints. We thenpropose a partially-supervised reinforcement learning (PSRL) framework thattakes advantage of an additional assumption that the true state of the POMDP isknown at training time. We present the first approach for certifying safety ofPSRL policies under adversarial input perturbations, and two adversarialtraining approaches that make direct use of PSRL. Our experiments demonstrateboth the efficacy of the proposed approach for certifying safety in adversarialenvironments, and the value of the PSRL framework coupled with adversarialtraining in improving certified safety while preserving high nominal reward andhigh-quality predictions of true state.

Certifying Safety in Reinforcement Learning under Adversarial Perturbation Attacks