A Unified and Constrained View of Regularization-Based Robust Reinforcement Learning

Significant progress has been made in safeguarding deep reinforcement learning (DRL) policies against input perturbations. Developing robust DRL involves three main stages: algorithm design, implementation, and evaluation. In this work, we identify and address a key limitation at each stage. First, we introduce Adversarial Importance Sampling (Advis), a method that uses importance sampling over trajectories from standard training to estimate and optimize verifiable worst-case returns. Advis satisfies three desirable criteria not jointly achieved by prior work: it requires no additional environment interactions, no auxiliary networks, and captures long-term robustness. Second, we introduce advrl, a modular PyTorch library that provides clean, single-file implementations of existing robustness methods and adversarial attacks, facilitating rapid prototyping and enabling reproducible and traceable evaluations. Third, we revisit evaluation under learned adversaries and show that optimal adversarial hyperparameters do not transfer across agents, which can lead to an overestimation of robustness when using a limited set of attacker configurations. Accordingly, we evaluate policies against a large and diverse set of attackers, using 6-14x more configurations than prior work. Finally, we evaluate our approach on continuous control environments, demonstrating its effectiveness relative to existing baselines. The code is available at: https://github.com/AmineAndam04/advrl

Entropy regularization is widely used in continuous-time reinforcement learning (RL) to reduce sensitivity to environmental perturbations, yet its robustness benefits lack a rigorous theoretical foundation. This paper establishes the first robustness guarantees for entropy-regularized continuous-time Markov decision processes. We show that maximizing an entropy-regularized objective yields a lower bound on a worst-case robust RL problem with joint reward and transition perturbations. We analytically characterize the induced robust sets and prove that they expand monotonically with the regularization strength, justifying the empirical observation that stronger entropy improves robustness. In contrast to prior discrete-time analyses, our results remove the intractable state-distribution entropy term and provide guarantees invariant to action frequency. Experiments on queueing network control and market making confirm our theory, showing that entropy-regularized policies outperform greedy and $ε$-greedy baselines under dynamics perturbations.

Reinforcement learning policies parametrized by deep neural networks have achieved strong performance for continuous control, yet even small input perturbations may lead to unpredictable behavior. This sensitivity limits their use in safety-critical domains, where robustness guarantees are required. Our work addresses this gap between state-of-the-art adversarial training methods and formal verification to train verifiably robust agents. Previous works train networks with individual adversarial perturbations, making them only robust against the specific adversarial attacks used. In contrast, our approach propagates entire perturbed input sets, enclosing all possible adversarial attacks within a single network pass. We leverage this to explicitly penalize the size of the output set (minimizing closed-loop uncertainty) and thereby make the actor robust against all possible attacks. This is realized by the use of set-based policy gradients, where each output within the set has a different gradient, thereby balancing the accuracy and robustness of the network. Doing so, we achieve formal verifiability across different verification frameworks for up to 9 times larger input perturbations compared to standard reinforcement learning and improve certified worst-case performance.