In this section we describe the mathematical framework underlying Distral.

Recent advances in reinforcement learning (RL) enable its use on increasingly complex tasks, but the lack of formal safety guarantees still limits its application in safety-critical settings. A common practical approach is to augment the RL policy with a safety filter that overrides unsafe actions to prevent failures during both training and deployment. However, safety filtering is often perceived as sacrificing performance and hindering the learning process. We show that this perceived safety-performance tradeoff is not inherent and prove, for the first time, that enforcing safety with a sufficiently permissive safety filter does not degrade asymptotic performance. We formalize RL safety with a safety-critical Markov decision process (SC-MDP), which requires categorical, rather than high-probability, avoidance of catastrophic failure states. Additionally, we define an associated filtered MDP in which all actions result in safe effects, thanks to a safety filter that is considered to be a part of the environment. Our main theorem establishes that (i) learning in the filtered MDP is safe categorically, (ii) standard RL convergence carries over to the filtered MDP, and (iii) any policy that is optimal in the filtered MDP-when executed through the same filter-achieves the same asymptotic return as the best safe policy in the SC-MDP, yielding a complete separation between safety enforcement and performance optimization. We validate the theory on Safety Gymnasium with representative tasks and constraints, observing zero violations during training and final performance matching or exceeding unfiltered baselines. Together, these results shed light on a long-standing question in safety-filtered learning and provide a simple, principled recipe for safe RL: train and deploy RL policies with the most permissive safety filter that is available.

Ensuring safety via safety filters in real-world robotics presents significant challenges, particularly when the system dynamics is complex or unavailable. To handle this issue, learning-based safety filters recently gained popularity, which can be classified as model-based and model-free methods. Existing model-based approaches requires various assumptions on system model (e.g., control-affine), which limits their application in complex systems, and existing model-free approaches need substantial modifications to standard RL algorithms and lack versatility. This paper proposes a simple, plugin-and-play, and effective model-free safety filter learning framework. We introduce a novel reward formulation and use Q-learning to learn Q-value functions to safeguard arbitrary task specific nominal policies via filtering out their potentially unsafe actions. The threshold used in the filtering process is supported by our theoretical analysis. Due to its model-free nature and simplicity, our framework can be seamlessly integrated with various RL algorithms. We validate the proposed approach through simulations on double integrator and Dubin's car systems and demonstrate its effectiveness in real-world experiments with a soft robotic limb.

In this paper, we present an approach for learning collision-free robot trajectories in the presence of moving obstacles. As a first step, we train a backup policy to generate evasive movements from arbitrary initial robot states using model-free reinforcement learning. When learning policies for other tasks, the backup policy can be used to estimate the potential risk of a collision and to offer an alternative action if the estimated risk is considered too high. No matter which action is selected, our action space ensures that the kinematic limits of the robot joints are not violated. We analyze and evaluate two different methods for estimating the risk of a collision. A physics simulation performed in the background is computationally expensive but provides the best results in deterministic environments. If a data-based risk estimator is used instead, the computational effort is significantly reduced, but an additional source of error is introduced. For evaluation, we successfully learn a reaching task and a basketball task while keeping the risk of collisions low. The results demonstrate the effectiveness of our approach for deterministic and stochastic environments, including a human-robot scenario and a ball environment, where no state can be considered permanently safe. By conducting experiments with a real robot, we show that our approach can generate safe trajectories in real time.

Most deep reinforcement learning algorithms are data inefficient in complex and rich environments, limiting their applicability to many scenarios. One direction for improving data efficiency is multitask learning with shared neural network parameters, where efficiency may be improved through transfer across related tasks. In practice, however, this is not usually observed, because gradients from different tasks can interfere negatively, making learning unstable and sometimes even less data efficient. Another issue is the different reward schemes between tasks, which can easily lead to one task dominating the learning of a shared model. We propose a new approach for joint training of multiple tasks, which we refer to as Distral (distill & transfer learning).

Deep reinforcement learning (RL) policies, although optimal in terms of task rewards, may not align with the personal preferences of human users. To ensure this alignment, a naive solution would be to retrain the agent using a reward function that encodes the user's specific preferences. However, such a reward function is typically not readily available, and as such, retraining the agent from scratch can be prohibitively expensive. We propose a more practical approach - to adapt the already trained policy to user-specific needs with the help of human feedback. To this end, we infer the user's intent through trajectory-level feedback and combine it with the trained task policy via a theoretically grounded dynamic policy fusion approach. As our approach collects human feedback on the very same trajectories used to learn the task policy, it does not require any additional interactions with the environment, making it a zero-shot approach. We empirically demonstrate in a number of environments that our proposed dynamic policy fusion approach consistently achieves the intended task while simultaneously adhering to user-specific needs.

This work develops a zero-shot mechanism for an agent to satisfy a Linear Temporal Logic (LTL) specification given existing task primitives. Oftentimes, autonomous robots need to satisfy spatial and temporal goals that are unknown until run time. Prior research addresses the problem by learning policies that are capable of executing a high-level task specified using LTL, but they incorporate the specification into the learning process; therefore, any change to the specification requires retraining the policy. Other related research addresses the problem by creating skill-machines which, given a specification change, do not require full policy retraining but require fine-tuning on the skill-machine to guarantee satisfaction. We present a more a flexible approach -- to learn a set of minimum-violation (MV) task primitive policies that can be used to satisfy arbitrary LTL specifications without retraining or fine-tuning. Task primitives can be learned offline using reinforcement learning (RL) methods and combined using Boolean composition at deployment. This work focuses on creating and pruning a transition system (TS) representation of the environment in order to solve for deterministic, non-ambiguous, and feasible solutions to LTL specifications given an environment and a set of MV task primitive policies. We show that our pruned TS is deterministic, contains no unrealizable transitions, and is sound. Through simulation, we show that our approach is executable and we verify our MV policies produce the expected symbols.

Reinforcement learning (RL) has emerged as a promising paradigm in complex and continuous robotic tasks, however, safe exploration has been one of the main challenges, especially in contact-rich manipulation tasks in unstructured environments. Focusing on this issue, we propose SRL-VIC: a model-free safe RL framework combined with a variable impedance controller (VIC). Specifically, safety critic and recovery policy networks are pre-trained where safety critic evaluates the safety of the next action using a risk value before it is executed and the recovery policy suggests a corrective action if the risk value is high. Furthermore, the policies are updated online where the task policy not only achieves the task but also modulates the stiffness parameters to keep a safe and compliant profile. A set of experiments in contact-rich maze tasks demonstrate that our framework outperforms the baselines (without the recovery mechanism and without the VIC), yielding a good trade-off between efficient task accomplishment and safety guarantee. We show our policy trained on simulation can be deployed on a physical robot without fine-tuning, achieving successful task completion with robustness and generalization. The video is available at https://youtu.be/ksWXR3vByoQ.