Abstract We present $$\varepsilon $$ , a general exploration strategy for reinforcement learning (RL) that encourages adherence to behavioral preferences while preserving the convergence guarantees of the underlying RL algorithm. $$\varepsilon $$ maintains a dynamic collection of retrain areas—regions of the state space where the agent previously violated a specified preference—and mixes the standard uniform restart distribution with states from these areas, according to a decaying parameter $$\varepsilon $$ . This mixed retraining thus focuses on enforcing the desired behaviors in the collected areas. We develop the theory for both policy and value-based methods, showing that: (i) in policy-based settings, our method retains monotonic improvement bounds; and (ii) in value-based settings, $$\varepsilon $$ preserves convergence properties without additional assumptions. The approach is simple to integrate into existing RL algorithms and improves sample efficiency and behavioral adherence in the locomotion, power systems, and navigation tasks tested. These results establish $$\varepsilon $$ as a lightweight, theoretically grounded mechanism for incorporating behavioral preferences into RL.

Ensuring safety in reinforcement learning (RL) is critical for deploying agents in real-world applications. During training, current safe RL approaches often rely on indicator cost functions that provide sparse feedback, resulting in two key limitations: (i) poor sample efficiency due to the lack of safety information in neighboring states, and (ii) dependence on cost-value functions, leading to brittle convergence and suboptimal performance. After training, safety is guaranteed via formal verification (FV) methods for deep neural networks, whose computational complexity hinders their application during training. We address the limitations of using cost functions via verification by proposing a safe RL method based on a violation value—the risk associated with policy decisions in a portion of the state space. Our approach verifies safety properties (i.e., state-action pairs) that may lead to unsafe behavior, and quantifies the size of the state space where properties are violated. This violation value is then used to penalize the agent during training to encourage safer policy behavior. Given the NP-hard nature of FV, we propose an efficient, sample-based approximation with probabilistic guarantees to compute the violation value. Extensive experiments on standard benchmarks and real-world robotic navigation tasks show that violation-augmented approaches significantly improve safety by reducing the number of unsafe states encountered while achieving superior performance compared to existing methods.

This paper introduces the Approximate Ethical Embedding Process, an algorithm for automating the design of ethical environments for learning agents. Our algorithm helps build environments wherein multiple agents learn policies that align with an ethical (moral) value while simultaneously pursuing their individual objectives. Therefore, we contribute to endowing environment designers with algorithmic tools for building ethical environments. We demonstrate the ethical design process for two different settings of an environment where agents have to adhere to beneficence to promote the collective survival of the population. Our experiments show that our approximate embedding process successfully generates environments that incentivise the learning of value-aligned policies.

Identifying safe areas is a key point to guarantee trust for systems that are based on Deep Neural Networks (DNNs). To this end, we introduce the AllDNN-Verification problem: given a safety property and a DNN, enumerate the set of all the regions of the property input domain which are safe, i.e., where the property does hold. Due to the #P-hardness of the problem, we propose an efficient approximation method called ε-ProVe. Our approach exploits a controllable underestimation of the output reachable sets obtained via statistical prediction of tolerance limits, and can provide a tight —with provable probabilistic guarantees— lower estimate of the safe areas. Our empirical evaluation on different standard benchmarks shows the scalability and effectiveness of our method, offering valuable insights for this new type of verification of DNNs.

Safety is essential for deploying Deep Reinforcement Learning (DRL) algorithms in real-world scenarios. Recently, verification approaches have been proposed to allow quantifying the number of violations of a DRL policy over input-output relationships, called properties. However, such properties are hard-coded and require task-level knowledge, making their application intractable in challenging safety-critical tasks. To this end, we introduce the Collection and Refinement of Online Properties (CROP) framework to design properties at training time. CROP employs a cost signal to identify unsafe interactions and use them to shape safety properties. Hence, we propose a refinement strategy to combine properties that model similar unsafe interactions. Our evaluation compares the benefits of computing the number of violations using standard hard-coded properties and the ones generated with CROP. We evaluate our approach in several robotic mapless navigation tasks and demonstrate that the violation metric computed with CROP allows higher returns and lower violations over previous Safe DRL approaches.

We consider Reinforcement Learning (RL) problems where an agent attempts to maximize a reward signal while minimizing a cost function that models unsafe behaviors. Such formalization is addressed in the literature using constrained optimization on the cost, limiting the exploration and leading to a significant trade-off between cost and reward. In contrast, we propose a Safety-Oriented Search that complements Deep RL algorithms to bias the policy toward safety within an evolutionary cost optimization. We leverage evolutionary exploration benefits to design a novel concept of safe mutations that use visited unsafe states to explore safer actions. We further characterize the behaviors of the policies over desired specifics with a sample-based bound estimation, which makes prior verification analysis tractable in the training loop. Hence, driving the learning process towards safer regions of the policy space. Empirical evidence on the Safety Gym benchmark shows that we successfully avoid drawbacks on the return while improving the safety of the policy.

Recent Multi-Agent Deep Reinforcement Learning approaches factorize a global action-value to address non-stationarity and favor cooperation. These methods, however, hinder exploration by introducing constraints (e.g., additive value-decomposition) to guarantee the factorization. Our goal is to enhance exploration and improve sample efficiency of multi-robot mapless navigation by incorporating a periodical Evolutionary Policy Search (EPS). In detail, the multi-agent training “specializes” the robots' policies to learn the collision avoidance skills that are mandatory for the task. Concurrently, in this work we propose the use of Evolutionary Algorithms to explore different regions of the policy space in an environment with only a single robot. The idea is that core navigation skills, originated by the multi-robot policies using mutation operators, improve faster in the single-robot EPS. Hence, policy parameters can be injected into the multi-robot setting using crossovers, leading to improved performance and sample efficiency. Experiments in tasks with up to 12 robots confirm the beneficial transfer of navigation skills from the EPS to the multi-robot setting, improving the performance of prior methods.

We propose a novel benchmark environment for Safe Reinforcement Learning focusing on aquatic navigation. Aquatic navigation is an extremely challenging task due to the non-stationary environment and the uncertainties of the robotic platform, hence it is crucial to consider the safety aspect of the problem, by analyzing the behavior of the trained network to avoid dangerous situations (e.g., collisions). To this end, we consider a value-based and policy-gradient Deep Reinforcement Learning (DRL) and we propose a crossover-based strategy that combines gradient-based and gradient-free DRL to improve sample-efficiency. Moreover, we propose a verification strategy based on interval analysis that checks the behavior of the trained models over a set of desired properties. Our results show that the crossover-based training outperforms prior DRL approaches, while our verification allows us to quantify the number of configurations that violate the behaviors that are described by the properties. Crucially, this will serve as a benchmark for future research in this domain of applications.

We study the problem of multi-robot mapless navigation in the popular Centralized Training and Decentralized Execution (CTDE) paradigm. This problem is challenging when each robot considers its path without explicitly sharing observations with other robots and can lead to non-stationary issues in Deep Reinforcement Learning (DRL). The typical CTDE algorithm factorizes the joint action-value function into individual ones, to favor cooperation and achieve decentralized execution. Such factorization involves constraints (e.g., monotonicity) that limit the emergence of novel behaviors in an individual as each agent is trained starting from a joint action-value. In contrast, we propose a novel architecture for CTDE that uses a centralized state-value network to compute a joint state-value, which is used to inject global state information in the value-based updates of the agents. Consequently, each model computes its gradient update for the weights, considering the overall state of the environment. Our idea follows the insights of Dueling Networks as a separate estimation of the joint state-value has both the advantage of improving sample efficiency, while providing each robot information whether the global state is (or is not) valuable. Experiments in a robotic navigation task with 2 4, and 8 robots, confirm the superior performance of our approach over prior CTDE methods (e.g., VDN, QMIX).

Deep Reinforcement Learning (DRL) is a viable solution for automating repetitive surgical subtasks due to its ability to learn complex behaviours in a dynamic environment. This task automation could lead to reduced surgeon’s cognitive workload, increased precision in critical aspects of the surgery, and fewer patient-related complications. However, current DRL methods do not guarantee any safety criteria as they maximise cumulative rewards without considering the risks associated with the actions performed. Due to this limitation, the application of DRL in the safety-critical paradigm of robot-assisted Minimally Invasive Surgery (MIS) has been constrained. In this work, we introduce a Safe-DRL framework that incorporates safety constraints for the automation of surgical subtasks via DRL training. We validate our approach in a virtual scene that replicates a tissue retraction task commonly occurring in multiple phases of an MIS. Furthermore, to evaluate the safe behaviour of the robotic arms, we formulate a formal verification tool for DRL methods that provides the probability of unsafe configurations. Our results indicate that a formal analysis guarantees safety with high confidence such that the robotic instruments operate within the safe workspace and avoid hazardous interaction with other anatomical structures.

In the last years, neural networks achieved groundbreaking successes in a wide variety of applications. However, for safety critical tasks, such as robotics and healthcare, it is necessary to provide some specific guarantees before the deployment in a real world context. Even in these scenarios, where high cost equipment and human safety are involved, the evaluation of the models is usually performed with the standard metrics (i.e., cumulative reward or success rate). In this paper, we introduce a novel metric for the evaluation of models in safety critical tasks, the violation rate. We build our work upon the concept of formal verification for neural networks, providing a new formulation for the safety properties that aims to ensure that the agent always makes rational decisions. To perform this evaluation, we present ProVe (Property Verifier), a novel approach based on the interval algebra, designed for the analysis of our novel behavioral properties. We apply our method to different domains (i.e., mapless navigation for mobile robots, trajectory generation for manipulators, and the standard ACAS benchmark). Results show that the violation rate computed by ProVe provides a good evaluation for the safety of trained models.

Our goal is to investigate whether discrete state space algorithms are a viable solution to continuous alternatives for mapless navigation. To this end we present an approach based on Double Deep Q-Network and employ parallel asynchronous training and a multi-batch Priority Experience Replay to reduce the training time. Experiments show that our method trains faster and outperforms both the continuous Deep Deterministic Policy Gradient and Proximal Policy Optimization algorithms. Moreover, we train the models in a custom environment built on the recent Unity learning toolkit and show that they can be exported on the TurtleBot3 simulator and to the real robot without further training. Overall our optimized method is 40% faster compared to the original discrete algorithm. This setting significantly reduces the training times with respect to the continuous algorithms, maintaining a similar level of success rate hence being a viable alternative for mapless navigation.